Domain-Specific Families

505 families grouping the 11,505 domain-specific abstractions by their neighborhood in structural-signature space — k-means clusters over structural-signature embeddings. Each abstraction belongs to one family. Families are recomputed when the catalog changes, so membership can shift. Click any column header to sort.

Family	Abstractions	Description
Abstract Algebra & Category Theory	25	Abstractions about algebraic and categorical structures, including groups, categories, filtrations and coherence conditions, spanning number-theoretic curiosities like amicable triples, set-theoretic notions like stationary sets, and foundational categories like FinSet.
Accessible Communication & Inclusive Design	8	Abstractions about ensuring communication and interfaces work for people with varied abilities — accessibility design principles (perceivable design, operable design, motion-triggered harm), augmentative and functional-communication assessment (AAC, functional communication), and communication-theory or neural models of goal-directed messaging (goals-plans-action theory, salience network).
Adversarial AI & Security Attacks	14	Abstractions about how adversaries exploit machine-learning systems and security boundaries, including attacks on training data and models (data poisoning attack, model theft, transfer-learning attack), attacks that manipulate deployed model inputs or outputs (evasion attack, prompt injection, model inversion attack), and foundational security design principles (Kerckhoffs's principle, blue-on-blue risk).
Algebraic Number Systems & Symmetry	8	Abstractions about extended number systems and their symmetry structure, spanning hypercomplex number systems (octonion, Hurwitz quaternion, Pauli matrices), functional-algebraic structures (Banach algebra), and elementary arithmetic or group-action concepts (casting out nines, integral part, orbit in group theory).
Algebraic Operations & Quasigroup Structures	13	Abstractions about algebraic operations and the laws they satisfy, covering non-associative and partial-inverse structures (quasigroups, loops, orthodox semigroups), identity and inverse elements and permutation groups, operation-closure and order-compatible structures (clones, cyclically ordered groups, Heyting algebras), and combinatorial constructs like Hadamard matrices and zero-sum problems.
Algebraic Structures & Homological Invariants	15	Abstractions about algebraic objects and their invariants, including cohomology and cyclic homology, group and ring constructions like semidirect products and torsion-free groups, and operator or differential-calculus generalizations over algebras.
Algebraic Structures & Operator Algebras	24	Abstractions about algebraic structures generalizing rings, algebras, and their representations, including operator algebras (Calkin algebra, nuclear C*-algebra, Jordan operator algebra), coalgebra and Hopf-type structures (bialgebra, Lie coalgebra, quasi-Hopf algebra), and classification invariants or constructions (Gelfand-Kirillov dimension, Schur functor, term algebra).
Algebraic Structures & Order Relations	18	Abstractions that define algebraic and order-theoretic structures — group and ring constructions (direct product of groups, nilpotent algebra, metanilpotent group, primal ideal), order-theoretic notions (atom, linear order, product order), and structural classification devices borrowed into other fields such as binade and set theory in music.
Algebraic Structures, Groups & Operators	44	Abstractions that are specific named objects in abstract algebra and topology, including operators and correspondences such as affiliated operators and the Calkin correspondence, group and Lie-theoretic structures like maximal tori and complex Lie groups, and cohomological constructions such as Hochschild homology and dual modules.
Algebraic Substructures & Closures	12	Abstractions about algebraic structures and the distinguished substructures they generate or contain, covering rings, ideals and principal ideals, fields and adjunction, module and group substructures such as essential extensions and the Frattini subgroup, K-theoretic resolution, and combinatorial number results like barycentric sums and centered polygonal numbers.
Algebraic Topology & K-Theory	26	Abstractions about topological invariants and duality built from homotopy and cohomology, spanning generalized K-theory (KR-theory, twisted K-theory, Milnor K-theory), duality theorems (Poincaré, Lefschetz, Verdier, Pontryagin duality), and homotopy-theoretic constructions (Eilenberg-MacLane spaces, rational homotopy theory, virtual fundamental classes).
Algebraic Varieties & Arithmetic Cohomology	7	Abstractions about algebraic geometry and its arithmetic variants — varieties and hypersurfaces (cubic fourfold, quasi-projective variety), field-theoretic classification (quasi-finite field, Ree group), and cohomological or intersection-theoretic invariants such as Monsky-Washnitzer cohomology and the Segre class.
Algebraic Varieties & Topological Invariants	27	Abstractions about specific invariants and spaces in algebraic geometry and topology, including varieties and their invariants such as secant variety, degree of a variety and J-multiplicity, cohomology theories and spectral sequences like equivariant cohomology and the Adams spectral sequence, and classifying spaces such as fiber bundles and Stone spaces.
Algorithmic Coordination & Fair Allocation	15	Abstractions that use algorithms to coordinate distributed processes or allocate resources fairly, covering distributed consensus and leader-election methods (Berkeley and bully algorithms, multi-trials technique), fair-division and preference-aggregation criteria (envy-free division, Pareto efficiency, rank aggregation), and optimization heuristics like stochastic programming.
Allocation Rules & Succession Arrangements	17	Abstractions that govern how scarce roles, assets, or turns are allocated among competing claimants — succession and vacancy rules like tanistry, countback, and locum tenens, property and tenancy arrangements such as rent control and reprivatization, and scheduling or contractual mechanisms like round-robin scheduling and requirements contracts.
Allocation, Ranking & Bargaining Models	11	Abstractions about how agents are ranked, matched, or allocated shares, covering matching and fair-division problems (stable roommates problem, individual-pieces set), bargaining and coalition models (Rubinstein bargaining model, strong Nash equilibrium), ranking and vote-counting rules (standings, dot-voting, ballot exhaustion), and unequal positions (bid rent, class stratification).
Analytical Measurement & Thermal Properties	27	Abstractions that quantify chemical, thermal, or physiological states through calibrated measurement — calorimetry, differential scanning calorimetry, enzyme assays, internal standards, and molar or volume concentration — alongside related thermal thresholds and safety processes such as fire point, vapor pressure deficit, and blast chilling.
Animal Sensory Ecology	5	Abstractions about how animals sense and interact with prey, mates and each other — active and passive sensing (animal echolocation, sound localisation, prey detection), and population-level timing and interference effects such as predator satiation and reproductive interference.
Applied Assessment Frameworks & Practices	26	Abstractions that structure evaluation and intervention across varied applied fields, including clinical rating scales, statistical tests, recruitment and design methods, and organizational practices like appreciative inquiry, unified mainly as practical measurement frameworks.
Argumentation & Rhetorical Devices	23	Abstractions that name figures, fallacies, and moves within argument and rhetoric — rhetorical figures (antithesis, litotes, rhetorical question), informal fallacies that misdirect a dispute (false equivalence, tu quoque, special pleading, motte-and-bailey), and strategic argumentative postures such as concession, if-by-whiskey and rhetorical listening.
Argumentation Fallacies & Inference	15	Abstractions about the validity and failure modes of reasoning patterns, spanning circular and question-begging arguments, inference fallacies and paradoxes (Hempel's paradox, naturalistic and moralistic fallacies, belief bias), logical validity results (Peirce's law, Lewis's triviality result), and legal and moral argument schemas (legal syllogism, Golden Rule).
Arithmetic Geometry & Local Fields	14	Abstractions about arithmetic geometry and number theory — local-field theory (local field, higher local field, local class field theory, norm group), p-adic and crystalline cohomology (F-crystal, p-adic Hodge theory, Hodge-Arakelov theory), and arithmetic objects tied to curves and representations (arithmetic surface, Brandt matrix, Néron-Tate height).
Artistic & Craft Techniques	13	Abstractions about hands-on techniques for making and manipulating visual and material art, covering surface and printmaking methods (Burnishing, Carborundum Printmaking, Stipple Engraving, Damascening), drawing and photographic techniques (Contour Drawing, Panoramic Photography, Ken Burns Effect), and construction or lighting practices like Modular Art and Stage Lighting.
Astrophysical & Gravitational Structures	16	Abstractions about the physics of stars, gravity and cosmic structure, including stellar equilibrium equations, relativistic and entropic gravity models, dark-matter and cosmological scenarios, and thermal or magnetic phenomena in astrophysical plasmas.
Atmospheric & Meteorological Phenomena	16	Abstractions about atmospheric moisture, energy, and wind phenomena — thermodynamic diagrams and indices like the emagram, aridity index, and moist static energy, convective storm features such as dry thunderstorms, gustnadoes, and sting jets — and diagnostic tools like the wind rose.
Audio Recording & Acoustic Phenomena	10	Abstractions about capturing, processing and hearing sound — recording workflows (binaural recording, double-system recording, mix automation), room and microphone acoustics (reverberation, room modes, proximity effect), signal-shaping and correction (chorus effect, digital room correction, adaptive feedback cancellation), and auditory filter bandwidth.
Auditory Perception & Speech Processing	9	Abstractions about how sound and speech are perceived, remembered, and reproduced — perceptual effects like phonemic restoration and repetition blindness, memory and acquisition processes such as rehearsal, speech repetition, and language acquisition, and technical or notational systems like colored music notation and sound recording.
Automata & Formal Grammar Models	9	Abstractions about formal models of computation and language generation, including automaton models such as the deterministic finite automaton and Turing machine, grammar and production systems like regular grammars and post canonical systems, and related structured proof or retrieval formalisms such as ludics and postings lists.
Autonomous Control & Learning Systems	12	Abstractions about systems that plan, learn or self-organize their own behavior, covering control-theoretic tools (Control-Lyapunov Function, LQR-RRT, Pullback Attractor), autonomous and self-organizing computing (Organic Computing, Vehicular Automation, Action Model Learning), and equilibrium or verification concepts like Wardrop Equilibrium and Symbolic Trajectory Evaluation.
Banach & Topological Vector Spaces	30	Abstractions about vector spaces equipped with norms, metrics, or order structures — Banach, Fréchet, Riesz, and sequence spaces — and the convergence, compactness, and integration notions, such as the Bochner integral, weak compactness, and absolute or normal convergence, that characterize functions and functionals on them.
Behavioral Biases in Choice & Information	10	Abstractions that explain systematic gaps between rational prediction and observed behavior, covering risk and time-preference anomalies (ambiguity aversion, certainty effect, present bias), information-seeking or avoidance puzzles (information avoidance, privacy paradox, Mooers's law), and collective-action problems like the paradox of voting.
Behavioral Economics & Startup Dynamics	20	Abstractions about decision-making biases and entrepreneurial practice, including cognitive effects like the IKEA effect and ostrich effect, startup methods such as effectuation and innovation accounting, and economic concepts like excludability and human capital.
Biological & Ecological Classification	12	Abstractions about placing organisms and landscapes into meaningful categories and patterns — taxonomic naming and phylogenetic relations (phylogenetic nomenclature, type species, sister groups), molecular and numerical identification (DNA barcoding, metabarcoding, numerical taxonomy), ecosystem and vegetation classification, and biodiversity patterns such as latitudinal gradients and umbrella species.
Biomedical Signal Sensing & Recording	21	Abstractions about measuring physiological and electrical signals, covering bioelectric and biomagnetic recording techniques (electrocardiography, magnetoencephalography, electrocochleography, magnetogastrography), signal-processing methods for extracting weak signals (correlated double sampling, pulse compression), and reflex mechanisms like the acoustic reflex.
Boolean & Formal Logic Structures	29	Abstractions about the algebraic and syntactic structure of formal logic, including Boolean algebra and its operators (logic gate, XOR gate, disjunctive and negation normal forms), formal fragments and expressiveness results (monadic second-order logic, functional completeness, MAX-3SAT), and foundational logical principles (deductive closure, vicious circle principle, principle of distributivity).
Categorical & Representation-Theoretic Structures	8	Abstractions about algebraic structures built from categorical and representation-theoretic constructions, covering tensor and module structures (Bimodule, Exterior Algebra, Associativity Isomorphism), representation theory (Character Theory, Fusion Category), and combinatorial or group-theoretic constructs like the Baxter Permutation and Sastry Automorphism.
Categorical Constructions & Dualities	33	Abstractions about categories and their higher-dimensional generalizations — limits, colimits, functors, and dualities such as Stone and Isbell duality — spanning universal constructions like pushouts and the Karoubi envelope, and monoidal, enriched, or n-categorical structures like double categories and triangulated categories.
Categories, Sheaves & Homotopy	21	Abstractions that use category theory to organize algebraic, geometric and homotopical structure — higher and monoidal constructions (2-categories, Day convolution, categorical trace), toposes and sheaf-theoretic geometry (ringed spaces, closed immersions, Gabriel–Rosenberg reconstruction), homological functors (delta, effaceable functors), and model-category formalisms (Joyal model structure, Quillen adjunction).
Category Theory & Higher Structures	18	Abstractions about categories, functors, and their higher-dimensional generalizations, covering foundational categorical constructions (mathematical categories, subterminal objects, joins of categories, Yoneda extensions), higher-categorical and homotopical structures (3-categories, higher stacks, pseudomonads, simplicial localization), and invariants like K-theory.
Category Theory & Homotopical Algebra	18	Abstractions about categorical structure and its homotopical refinements, spanning core categorical notions (functors, sections, adequate subcategories, isomorphism theorems), monoidal and operadic structures (Cartesian monoidal category, A∞-operad, strong monad), and homotopy-theoretic constructions (homotopy fiber, simplicial space, directed algebraic topology).
Category Theory Foundations	48	Abstractions that define the basic objects and constructions of category theory itself — categories, functors and natural transformations, limits and colimits (coequalizer, coproduct, pullback), monoidal and enriched categories, and higher-categorical structures like quasi-categories and 2-groups.
Causal Inference & Identification Design	7	Abstractions about identifying causal effects from observational data, covering quasi-experimental designs (difference-in-differences, regression discontinuity, natural experiments), identification assumptions (instrumental variables, selection on observables), and evaluation tools like the ROC curve and type M error.
Causal Inference & Regression Modeling	15	Abstractions about estimating causal effects and relationships from data, covering identification strategies and validity concepts (Causal Inference, External Validity, Lord's Paradox), regression frameworks (Nonlinear Least Squares, Regression, Variance Function), and specific tests or scores like the Chow Test and Continuous Individualized Risk Index.
Cellular & Evolutionary Biological Processes	16	Abstractions about biological processes at the cellular and population level, covering cell-division and cell-biology mechanisms (Embryonic Cleavage, DNA Laddering, Cell Cycle Analysis), genetic and evolutionary processes (Law of Segregation, Evolutionary Process, Ring Species), and specialized techniques like Microcell-Mediated Chromosome Transfer and Endosymbiosis.
Chemical Structure & Reactivity Concepts	22	Abstractions about molecular structure and reactivity, including bonding and hybridization, catalytic cycles, protein secondary-structure rules, and empirical relationships like Clar's rule, spanning organic, inorganic and biochemical phenomena.
Circuit Logic & Physical Irreversibility	5	Abstractions that share only a loose connection through circuits and physical efficiency, gathering logic-circuit implementations (diode logic, random flip-flop, reversible computing), thermodynamic irreversibility accounting (Gouy-Stodola theorem), and a materials-recovery practice, refrigerant reclamation, as an honest miscellany rather than one structure.
Classical & Trade Economic Theory	20	Abstractions that formalize classical economic theory and international development, covering production and demand fundamentals (law of demand, household production function, marginal demand), growth and trade models (industrialization, Jones model, trade globalization), and monetary or welfare concepts like metallism.
Classical Mechanics & Orbital Kinematics	14	Abstractions about motion and force in classical mechanics and astrodynamics, including formulations of dynamics such as action and generalized forces, free-fall and projectile reasoning like the equations for a falling body and Newton's cannonball, and orbital or rotational descriptors such as radial trajectory and true longitude.
Climate & Earth-System Feedback Processes	15	Abstractions about Earth's climate and ecological systems, including atmospheric and oceanic circulation such as general circulation models and the Australian northwest cloudband, reinforcing feedback and cycling processes like ice-albedo feedback, cloud feedback and the carbon cycle, and modeling frameworks for ecosystems and hazards such as the NPZ model and wildfire modeling.
Clinical Assessment & Behavioral Bias	8	Abstractions about assessing and interpreting clinical and behavioral phenomena, including severity and diagnostic scoring (SCORTEN scale, subgroup analysis), cognitive and social biases affecting judgment (selective abstraction, physical attractiveness stereotype, dysfunctional impulsivity), and structured clinical assessment and intervention methods (therapeutic assessment, positive behavior support, sexological testing).
Clinical Trial & Research Methodology	20	Abstractions about designing and evaluating empirical and clinical research — trial designs (community-based clinical trials, single-arm studies, stepped-wedge trials), statistical estimators and diagnostics (fixed-effects estimator, relative risk reduction, Youden's J statistic), and considerations shaping study validity (clinical data management, self-licensing, scientific consensus).
Clinical Trial Design & Drug Safety	23	Abstractions about how clinical research and drug therapy are structured and evaluated, including trial design and validity concepts (clinical study design, assay sensitivity, carryover effect, clinical-trial stratification), and categories of medication-related harm and safety (adverse drug reaction, medication error, polypharmacy, therapeutic duplication).
Clustering Methods & Validity Measures	14	Abstractions about grouping data and validating the resulting groupings, covering clustering algorithms (k-means, complete-linkage clustering, medoids), cluster-quality and similarity measures (silhouette, Davies-Bouldin index, Rand index, adjusted mutual information), and related structures like locality-sensitive hashing and exponential trees.
Coastal & Ocean Carbon Cycling	7	Abstractions about the movement and storage of carbon and sediment in coastal and ocean environments, covering carbon-cycle processes (Biological Pump, Blue Carbon, Oceanic Carbon Cycle), coastal sediment transport (Longshore Drift, Sediment Budget), and stratigraphic or ice-related coastal features like Sequence Stratigraphy and Ice Dune.
Codes, Matrices & Combinatorial Problems	33	Abstractions that share only loose connective tissue as formal tools for encoding and searching structured objects, spanning error-correcting codes (parity-check matrix, repetition code, noisy channel model), matrix methods (Gram matrix, QR decomposition), combinatorial and decision problems (GI-completeness, emptiness problem, matroid rank), and meaning representations.
Cognition, Memory & Learning	33	Abstractions about how minds attend, learn, and remember, covering perceptual and attentional phenomena (categorical perception, coincidence detection, attenuation theory), memory processes (echoic memory, state-dependent memory, multiple trace theory), and learning mechanisms (classical conditioning, statistical learning, perceptual learning).
Cognitive & Behavioral Theories	16	Abstractions about how mind, behavior, and cognition are theorized and modeled, including behaviorism and behavioral repertoires (ethograms), situated, ecological, and embodied cognition (image schemas), neural models of consciousness and language processing, and design-oriented or computational accounts like function-behavior-structure ontology and simulation.
Cognitive Control & Skill Automation	9	Abstractions about how cognitive processes govern skilled and automatic behavior, including architectures and dual-process models of cognition (ACT-R, dual-process theory), costs and failures of switching or over-monitoring skilled performance (task-switching cost, Humphrey's law, initiative loss), and learning approaches that transfer skill from experience (apprenticeship learning, model-free reinforcement learning, automation).
Cognitive Fixation & Memory Interference	10	Abstractions about how prior knowledge and structure interfere with memory and problem-solving, covering fixation effects (Einstellung Effect, Problem-Solving Fixation, Mental Rotation), memory-interference and encoding findings (Fan Effect, Levels-of-Processing Effect, Picture Superiority Effect), and related pattern-matching concepts like Callback Hell and YARA.
Combinatorial Covering & Dispatch Structures	6	Abstractions that select or organize discrete elements to satisfy a covering or lookup requirement — blocking sets and covering designs in incidence structures, Pascal's rule for subset counting, and lookup structures such as branch tables and CIDR address-prefix allocation — loosely joined by the geometric polyhedron.
Combinatorial Enumeration & Sequences	38	Abstractions about counting and enumerating discrete structures, including integer sequences, permutation statistics, partitions, lattice paths and symmetric functions, together with the algebraic transforms and inequalities that relate them.
Combinatorial Optimization & Discrete Structures	31	Abstractions about discrete mathematical structures and combinatorial optimization problems, including graph and hypergraph properties (giant component, width of a hypergraph, D-interval hypergraph), geometric covering and packing problems (disk-covering problem, strip packing problem, smallest-circle problem), and algorithms or metrics for search and design (A-star algorithm, Fréchet distance, Plackett-Burman design).
Combinatorial Optimization & Game Problems	12	Abstractions about optimizing or analyzing discrete combinatorial and game-theoretic problems — partitioning and covering problems (partition problem, quadratic knapsack, matroid-constrained partitioning, Steiner system), location and scheduling problems (1-center problem, maximum subarray), and game-theoretic models such as graphical game theory and Silverman's game.
Combinatorial Optimization on Graphs	16	Abstractions about optimization problems defined over graphs and networks — matchings, flows, and cuts such as circulation, closure, and multi-commodity flow problems — and routing problems including the traveling-salesman, Steiner tree, and shortest-path variants solved by structured algorithms like Held–Karp.
Combinatorial Set Systems & Counting	9	Abstractions about structured families of sets and counting arguments, covering set-system axioms (Antimatroid, Independence System, Helly Family), counting and correction techniques (Inclusion-Exclusion Principle, Bonferroni Correction), and algorithmic methods like Divide-and-Conquer Algorithm and the Isolation Lemma.
Communication, Learning & Information Practices	15	Abstractions that describe how people teach, communicate, and exchange information, spanning educational methods (Direct Method, Audiovisual Education, Appreciative Inquiry), communicative and reference practices (Digital Reference Services, Collaborative Model of Reference, Elicitation Technique), and related phenomena like Informational Listening and Social Invisibility.
Commutative Algebra & Ring Structures	28	Abstractions about the structure of rings and commutative algebra, covering ideals, localization, and completion constructions (prime ideals, nilradical, localization), module and algebra structures (semisimple modules, Grothendieck groups, Gerstenhaber algebras), and specialized ring classes like seminormal rings.
Commutative Rings & Arithmetic Structures	7	Abstractions about rings with special arithmetic or valuation properties, spanning ring-theoretic closure conditions (Arf ring, Euclidean domain, Cohen ring), arithmetic analogues of calculus (P-derivation), and number-theoretic or K-theoretic constructions (Dedekind zeta function, Steinberg group).
Competitive Strategy & Market Entry	11	Abstractions about how actors compete, cooperate and leverage position, spanning market-entry strategies (go-to-market wedge, copy to China), incumbent and cross-market responses (incumbent backlash, multimarket contact, Baxter's law), mixed rivalry and asymmetric exchange (coopetition, patron–client relationships), and winner-take-all dynamics.
Compiler & Language Runtime Constructs	29	Abstractions that make up programming-language and compiler machinery — intermediate representations, bytecode, register allocation, static single-assignment form, and type systems — alongside runtime constructs like exception handling, weak and phantom references, virtual functions, and structural typing.
Complex & Holomorphic Function Theory	10	Abstractions about the analytic structure of holomorphic and harmonic functions, including domains and extension results for holomorphic functions (domain of holomorphy, Ohsawa-Takegoshi L2 extension theorem, Remmert-Stein theorem), pairing of real and complex structure (harmonic conjugate, zeros and poles), and singularity invariants (Milnor number).
Composite Probability Distributions	5	Abstractions about probability distributions built by combining or decomposing simpler ones — sums of uniforms in the Bates distribution, convolutions of components in the Delaporte and mixture distributions, copula-based joint construction via Sklar's theorem, and distributions that resist such decomposition entirely.
Computability & Recursion Theory	16	Abstractions that describe what functions or sets can be effectively computed or enumerated within computability theory, including growth and hierarchy results such as the Ackermann function and Grzegorczyk hierarchy, reducibility and degree structures like Turing degree and enumeration reducibility, and machine or numbering models such as nondeterministic Turing machines.
Computation Models & Complexity Classes	37	Abstractions that formalize computation and its cost, spanning abstract machine models (Mealy machines, counter machines, Boolean circuits), complexity-class hierarchies (NC, NE, FPT, co-RE-complete), and programming-language mechanisms (coroutines, subtyping, opaque data types, parameterized macros).
Computational Complexity & Hardness	18	Abstractions about classifying computational difficulty and its limits — complexity classes and time bounds (complexity class, NTIME, QMA, strongly-polynomial time), foundational impossibility results (P versus NP, Rice's theorem, FLP impossibility), and reduction or hardness techniques such as pseudo-polynomial transformation and computational hardness assumptions.
Computational Complexity Classes & Hierarchies	30	Abstractions about the theory of computational complexity, defining resource-bounded classes such as AC0, PSPACE and EXPSPACE, hierarchies built from bounded computation like the polynomial hierarchy and counting hierarchy, and proof techniques used to separate or reduce them, including padding arguments and the switching lemma.
Computer Systems & Network Architecture	20	Abstractions about how computer systems and networks are organized and interoperate, including execution and isolation environments such as application domains and protection rings, networking and addressing schemes like IP addressing, NAT traversal and routing, and software or service architecture styles such as service-oriented and web-oriented programming.
Concurrency & Parallel Computation	35	Abstractions about coordinating simultaneous or interacting computations — synchronization primitives (semaphores, locks, thread pools), classic concurrency problems (dining philosophers, sleeping barber, fork bombs), distributed protocols (two-phase commit, terminating reliable broadcast), and models for analyzing parallel algorithms and scheduling.
Condensed Matter & Many-Body Physics	16	Abstractions about collective quantum behavior in materials, spanning superconductivity and pairing phenomena (BCS theory, Josephson effect, topological superconductor), periodic-lattice and band-structure models (particle in a one-dimensional lattice, Zak phase, plane wave expansion method), and correlated many-body methods (dynamical mean-field theory, Hartree-Fock method, Frenkel-Kontorova model).
Condensed Matter & Physical Chemistry Models	26	Abstractions about models and measurement techniques in condensed-matter physics and physical chemistry, including lattice and electronic models (Hubbard model, Su-Schrieffer-Heeger model, heavy-fermion material), simulation and estimation methods (Joback method, Projector Augmented-Wave method, water model), and transport or optical phenomena (Nernst effect, stochastic resonance, STED microscopy).
Consent, Pleading & Clinical Documentation	5	Abstractions about formalized acknowledgment and response in legal and clinical contexts — pleading strategies like confession and avoidance, rights forfeited through delay via acquiescence, consent-adjacent decisions such as informed assent and informed refusal, and structured clinical documentation via the SOAP note.
Constitutional Doctrine & Governmental Authority	9	Abstractions about the legal limits and procedures of governmental power, covering doctrines of deference and restraint (judicial deference, political question, Purcell principle), formal mechanisms for authorizing or limiting action (ratification, sunset provisions, executive privilege), and process rules like jury selection and legal competence.
Continuum Mechanics & Field Models	42	Abstractions about named mathematical models and formulas drawn from continuum mechanics, fluid dynamics, and geometry, including elasticity and rheology laws (Glen–Nye, Gent, Yeoh), fluid phenomena (Rankine vortex, Moffatt eddies, hydrostatic equilibrium), and coordinate or surface constructions.
Contract, Property & Legal Doctrine	44	Abstractions about legal doctrines that structure contracts, property interests, and adjudication, covering contract formation and discharge (accord and satisfaction, mistake, invitation to treat), property and family-law rules, evidentiary methods, and principles of legality and legal reasoning.
Controlled Vocabularies & Term Mapping	22	Abstractions about naming concepts and declaring the relations among them, covering label management (preferred, alternative, and hidden labels), cross-vocabulary mappings and cross-reference relations, relation-bearing models like concept maps and associative entities, and governing structures such as knowledge organization systems, standards, and UML profiles.
Convergence Modes in Function Spaces	6	Abstractions about specialized notions of convergence and stability in analysis — flat convergence of currents, vague topology on measures, and Γ-convergence of functionals, and stability of approximate functional equations via Hyers–Ulam–Rassias stability — alongside the fractal Weierstrass–Mandelbrot function and the sequence space C.
Convex Analysis & Optimization Structures	8	Abstractions that formalize convexity for use in optimization, including convex sets and their generating operations such as the convex hull, absorbing sets and supporting hyperplanes, dual and conjugate constructions like the convex conjugate, subderivative and proximal operator, and hard-constraint representations such as indicator functions and linear matrix inequalities.
Convex Geometry & Measure Constructions	12	Abstractions about convexity, covering, and measure in geometric analysis, including convex function and fixed-point results (proper convex function, Schauder fixed-point theorem), covering and directional geometric problems (Kakeya set, Tarski's plank problem, edge tessellation), and space-comparison or construction tools (Gromov-Hausdorff convergence, box spline, spherical design).
Convex Optimization & Iterative Methods	8	Abstractions about solving structured optimization and linear-system problems, including iterative linear-system solvers (Gauss-Seidel method, Jacobi method), convexity properties enabling efficient optimization (conic optimization, self-concordant function), and combinatorial structures related to polyhedra and graphs (Balinski's theorem, integer points in convex polyhedra, maximum matching).
Cooperative Game Theory & Power Indices	12	Abstractions about allocating value and power in games, covering cooperative-game solution concepts (Shapley value, imputations, Mertens-stable equilibrium), voting-power measures (Banzhaf and Shapley-Shubik indices), and strategic paradoxes or mechanisms like the chainstore and lottery paradoxes and truthful cake-cutting.
Coordinate Systems & Spatial Measures	29	Abstractions about coordinate systems, manifolds, and spatial measurement, covering specialized coordinate frames (elliptic cylindrical coordinates, upper half-plane, Riemann sphere), interpolation and projection methods (cubic Hermite splines, spherical linear interpolation), and geometric measures like isoperimetric inequality.
Craft & Decorative Art Techniques	12	Abstractions about traditional and artistic production techniques, including textile and dyeing methods such as thrumming, tsutsugaki and decoupage, printmaking and reproduction processes like chromolithography, electrotyping and surface tone, and image-making practices driven by chance or material behavior such as drip painting and klecksography.
Craft & Fabrication Techniques	10	Abstractions about hands-on techniques for shaping and decorating physical materials — casting methods such as lost-wax casting, cast paper, and type casting, mosaic and inlay work like opus vermiculatum and pietra dura, and print-related conventions including ink trap and typometry.
Creative Design & Ideation Methods	7	Abstractions about generating and testing ideas through structured creative process — human-centered design frameworks (design thinking, exhibit design, signage), speculative and facilitated ideation techniques (science fiction prototyping, Disney method, cultural probe), and integrative learning approaches such as STEAM education.
Critical & Continental Social Theory	18	Abstractions that theorize culture, meaning, and social structure from continental philosophy and critical theory, covering concepts of space and power (heterotopia, line of flight), epistemic and metaphysical frameworks (Kant's antinomies, naive realism, impossible worlds), and pedagogical theories like problem-posing education.
Cryptographic & Combinatorial Hardness Problems	5	Abstractions about computationally hard problems and structured combinatorial objects, covering cryptographic hardness assumptions (Diffie-Hellman Problem, Short Integer Solution Problem), number-theoretic representability questions (Sums of Three Cubes), and interpolation or matrix structures like Newton Polynomial and Supnick Matrix.
Cryptographic Protocols & Ciphers	15	Abstractions about securing information through cryptographic and authentication schemes — classical ciphers like the Caesar and transposition ciphers and frequency analysis, quantum key-distribution protocols such as BB84, B92, and the six-state protocol, and hardness assumptions and authentication models like multi-factor and passwordless authentication.
Crystallography & Nuclear/Material Physics	13	Abstractions about the physical structure of matter at atomic and nuclear scales, including crystal lattices and space groups, nuclear decay modes, diffraction techniques, and material phenomena like glass formation and pyroelectricity.
Data Grouping & Rate Measures	5	Abstractions that loosely connect grouping data and measuring rates or change — visualization and preprocessing techniques (alluvial diagram, data binning), and rate- or change-sensitive quantitative indicators such as effective data transfer rate, negative volume index and the p-chart.
Data Structures & Graph Variants	17	Abstractions about data structures and specialized graph forms, including tree and heap structures such as the 2-3 heap, radix tree and random binary tree, specialized graph families like the complement graph, lollipop graph and Moore graph, and structural measures built on them such as dendrograms and cophenetic correlation.
Data Visualization Chart Forms	10	Abstractions about visual encodings for exploring and presenting data, covering chart types (Area Chart, Horizon Chart, Mosaic Plot, Parallel Coordinates, Scatter Plot), joint and specialized displays (Biplot, Domain Coloring), and broader visualization disciplines like Data and Information Visualization and Scientific Visualization.
Debt, Credit & Contractual Obligation	20	Abstractions about financial obligations, contracts and market power, spanning debt and credit ratios (cash-flow-to-debt ratio, debt-to-income ratio, debt service ratio), contract and property-law doctrines (caveat emptor, perfection, lease purchase contract), and pricing or market-power mechanisms like transfer pricing and cornering the market.
Decision & System Modeling Frameworks	30	Abstractions that formalize systems, decisions or processes as explicit models for analysis, prediction or optimization under uncertainty, including decision and risk models (Decision Tree Model, Chance-Constrained Programming, Two-Moment Decision Model), quality and reliability frameworks (Design for Six Sigma, Fault Tree Analysis, Taguchi Loss Function), and computational modeling paradigms (Core Model, Ecosystem Model, SATPlan).
Decision Rules Under Uncertainty	6	Abstractions about making optimal decisions from uncertain or imprecise probabilistic information, covering classification and loss-based decision rules (Bayes classifier, loss function, decision-theoretic rough sets), robust and belief-based inference (gamma-minimax inference, pignistic probability), and a self-organizing map for unsupervised pattern discovery.
Decisions Under Constraint & Commitment	9	Abstractions that loosely share a concern with choosing and committing under constraint — decision-theoretic biases and rules (Buridan's ass, illusion of control, rational inattention, robust optimization), and binding agreements or fixed cycles that structure future action (breach of contract, contingent contract, orbital period, solar calendar).
Demand Elasticity & Consumer Response	11	Abstractions about how consumer demand responds to prices and income, covering elasticity measures (Cross Elasticity of Demand, Income Elasticity of Demand), good classifications by demand behavior (Giffen Good, Inferior Good), and the decomposition of price effects into income and substitution components via Engel Curve and Hicksian Demand Function.
Descriptive Statistics & Correlation Measures	40	Abstractions about quantifying spread, association and distributional shape in data, spanning dispersion measures (variance, coefficient of variation, geometric standard deviation), correlation coefficients (Pearson, Kendall, polychoric), hypothesis tests (F-test, Z-test, sign test), and summary statistics like quartiles.
Design, Process & Business Methods	18	Abstractions that share only loose connective tissue around designing and organizing work, spanning engineering and design practices (cardboard modeling, design for the environment, virtuality in software design), process and project methods (business-process modeling, project management, mobile DevOps), and business-organizational concepts (industrial market segmentation, virtual business model, production budget).
Detection Limits & Fault Diagnosis	5	Abstractions about distinguishing genuine signals or failures from noise and background, covering detection thresholds and discriminability measures (detection limit, sensitivity index), background-rejection techniques like electronic anticoincidence, and system-level fault or failure detection frameworks in distributed and control systems.
Developmental & Clinical Mechanism Hypotheses	13	Abstractions that loosely connect developmental, cognitive, and clinical mechanism hypotheses, including brain and body development such as interactive specialization and the functional matrix hypothesis, attachment and communication theories like the internal working model of attachment, and clinical diagnostic frameworks such as Manning criteria and N-of-1 trials.
Differential Geometry & Curvature	10	Abstractions about smooth manifolds and curvature, including geodesics, distributions, the second fundamental form and volume elements, plus accessibility results like the Chow-Rashevsky theorem and fractal constructions like the Apollonian gasket.
Digital Circuit & Memory Architecture	12	Abstractions about hardware design and low-level machine behavior, including CMOS and dynamic-logic techniques, datapath organizations like bit-serial architecture, tagged and transactional memory architectures, performance hazards such as false sharing and memory disambiguation, and circuit-level conventions like timing diagrams and position-independent code.
Digital Logic & Finite-State Machines	10	Abstractions about circuits and abstract machines that compute with discrete states, spanning logic-gate technologies (NOR logic, inverter logic gate, integrated injection logic, high-threshold logic), finite-state computation models (Moore machine, Wang B-machine, switching circuit theory), and circuit-related complexity classes (TC, NEXPTIME) alongside learned networks (artificial neural network).
Digital Resource Formats & Metadata	7	Abstractions about how digital resources are packaged, described and located, covering file and delivery formats (File Format, Distribution Form), metadata fields binding resources to encodings (Format Relation), and distributed-storage or linking infrastructure like Distributed Data Store and OpenURL Knowledge Base.
Disaster Risk & Hazard Management	12	Abstractions about how societies anticipate, respond to, and recover from hazards — foreseeable-but-ignored risks like the black elephant and mitigation neglect, compounding and displaced hazards such as compound-hazard stacking and risk transfer without reduction, and response failures like evacuation shadow and recovery inequity.
Discourse, Genre & Aesthetic Coherence	17	Abstractions that judge how a discourse or artwork fits its context and internal constraints, covering rhetorical canons and genres such as invention, delivery, and epideictic and forensic rhetoric, sociolinguistic and dialogic frameworks like heteroglossia and the markedness model, and aesthetic coherence judgments such as decorum and Chekhov's gun.
Dispersion Measures & Multilevel Regression	11	Abstractions about modeling heterogeneity and dispersion in grouped or clustered data, covering regression extensions for clustered outcomes (Hierarchical Generalized Linear Model, Binomial Regression, Multilevel Regression with Poststratification), dispersion statistics (Lexis Ratio, Variation Ratio, Interaction), and selection-correction methods like Heckman Correction.
Distributed Systems Theorems & Fallacies	19	Abstractions about fundamental trade-offs, false assumptions and resource models in distributed and parallel computing — consistency-availability theorems (CAP, PACELC, strong consistency), the classic fallacies of distributed computing (reliable network, zero latency), shared-memory consistency and architecture (release consistency, cache-only memory), and failure modes such as split-brain.
Domain-Specific Indicators & Measurement Methods	26	Abstractions that define specialized, context-bound indicators or methods for inferring a hidden quantity from indirect measurement, spanning bibliometric indices (Bibliographic Coupling, open-access citation advantage), biomedical and pharmacokinetic measures (Biomarker, Drug Accumulation Ratio), and physical or chemical dating and detection techniques (K-Ar dating, Nuclear Reaction Analysis, Chemical trap).
Domain-Specific Measurement Parameters	37	Abstractions that are specialized measurement quantities or inference techniques tailored to one physical or biomedical domain — optical imaging (optical coherence tomography, electron tomography), geophysical inversion (reflection seismology, aquifer tests), continuum-mechanics quantities (objective stress rate, second moment of area), and coastal, clinical or astronomical indices.
Drug Action & Receptor Pharmacology	16	Abstractions about how drugs act on and interact with biological targets, covering dose-response concepts (efficacy, potency, partial agonism), receptor and enzyme mechanisms (receptor antagonism, enzyme induction and inhibition, reuptake inhibition), and interaction or tolerance phenomena like pharmacokinetic interactions and tachyphylaxis.
Dynamical Systems & Chaos	17	Abstractions about how deterministic systems evolve and lose predictability — classical-mechanics constructs (generalized coordinates, adiabatic invariant, N-body problem), chaotic and iterative dynamics (chaotic scattering, Kaplan-Yorke map, strange nonchaotic attractor), and recurrence or classification results for maps and flows (rotation number, recurrent point, Fatou component classification).
Dynamical Systems & Differential Structures	38	Abstractions that describe how systems evolve or transform under differential, variational and geometric structure — stability and bifurcation analysis (Bogdanov–Takens, exponential stability, Floquet theory), variational and constrained mechanics (Lagrangian mechanics, Noether's second theorem), differential-geometric maps (exterior derivative, diffeomorphism, squeeze mapping), and spectral and topological tools.
Ecological Communities & Interactions	15	Abstractions about ecological communities and their dynamics, including sampling and measurement methods such as belt transects and species discovery curves, interaction and feedback processes like plant-soil feedback, prey switching and competition-colonization trade-offs, and community-organizing frameworks such as functional groups and pollination networks.
Economic & Financial Indicators	42	Abstractions about measuring economic and financial conditions through valuation ratios, macroeconomic indicators, cost and productivity measures, market-structure concepts, and monetary or development theories used to gauge performance and behavior.
Economic Cycles & Urban Form	9	Abstractions about recurring economic cycles and urban development patterns, including long-run cycle hypotheses such as the Kondratiev wave, Kuznets swing and business cycle, urban form and land-use patterns like urban sprawl, missing middle housing and mixed-use development, and related structural failures such as the Downs-Thomson paradox and scale-before-fit.
Economic Growth & Development Models	22	Abstractions about economic growth, structural development, and organizational planning, covering growth and trade models (North-South model, import replacement), financial and welfare indicators (return on invested capital, consumer leverage ratio, sustainable national income), and business planning frameworks like strategic planning.
Economic Indices & Price Measurement	5	Abstractions about constructing indices that track economic value over time, including inflation and Divisia indices, housing affordability and collectible-market indices, unified by weighted comparison against a base period.
Educational Practice & Policy	28	Abstractions about how learning is organized, taught, and governed — instructional approaches (active learning, blended learning, POGIL, spiral approach), school leadership and policy (instructional leadership, school choice, qualifications frameworks), and assessment-driven effects on institutions and learners (high-stakes testing, credentialism, value-added modeling).
Electromagnetic Fields & Responses	11	Abstractions about electric and magnetic fields and how matter and circuits respond to them, covering field sources and energy flow (dipoles, electromotive force, Poynting vector), magnetic response and flux paths (diamagnetism, anisotropy energy, magnetic circuits), and electrokinetic and magnetohydrodynamic effects, loosely joined by the curvelet transform.
Electronic Circuit Elements & Oscillators	5	Abstractions about electronic circuit elements and their dynamic behavior, including idealized and switching elements such as the nullator and astable multivibrator, transformer and induction modeling like the inductive circuit model of transformer and the Shockley-Ramo theorem, and nonlinear oscillation such as the Van der Pol oscillator.
Embodied & Mediated Communication	5	Abstractions about how bodies, media and avatars carry social meaning — nonverbal and touch-based communication (haptic communication), virtual-embodiment effects (Proteus effect, presence), and cultural transmission or memory practices such as the transmission chain method and memory work.
Empirical Measurement & Statistical Inference Methods	52	Abstractions that define procedures for measuring, testing, or estimating quantities from data, including statistical significance tests such as the Shapiro-Wilk and D'Agostino's K-squared tests, robust estimators like M-estimators and MAP estimators, and domain-specific diagnostic scales such as Killip class and famine scales.
Energy Systems & Sustainable Design	5	Abstractions that are loosely connected by energy production, use, and sustainability, including energy-output measurement (capacity factor), market mechanisms for grid management (local flexibility markets), a plasma-physics phenomenon (runaway electrons), and sustainable building and cooling technologies (solar air conditioning, sustainable architecture).
Energy Systems & Thermal Management	21	Abstractions about how energy is generated, moved, and managed in engineered systems — thermal exchange technologies (chilled beams, dynamic insulation, computer cooling), energy accounting and planning practices (monitoring and targeting, strategic energy management), and fundamental energy-transfer concepts such as energy carrier and energy quality.
Engineered Systems & Energy Transfer	7	Abstractions that generically define engineered systems and energy processes, including building-energy and structural systems, manufacturing processes, radiation efficiency and spectral density, framed as broad definitional categories across physical engineering.
Engineering Design & Systems Modeling	39	Abstractions about methods and representations for designing and analyzing engineered systems — diagrammatic models (block diagrams, bond graphs, free body diagrams), design processes (generative design, model-based design, product-family engineering), and system-level modeling or optimization techniques (function models, logic optimization, systems modeling).
Ensemble & Recurring Comic Devices	7	Abstractions about how multiple voices or repeated elements structure comedy and narrative, including multi-performer or multi-strand forms such as the double act, ensemble cast and hyperlink cinema, rhetorical and poetic recurrence structures like apo koinou construction and the pantoum, and jokes built on repetition such as the running gag.
Epistemic Norms & Informal Fallacies	16	Abstractions about reasoning, belief, and argumentative failure, including epistemic norms and commitments such as Clifford's principle and epistemic commitment, informal fallacies and biases like appeal to the stone and the rhyme-as-reason effect, and classic epistemological puzzles such as Hume's fork and Moore's paradox.
Equity, Property & English Trust Doctrines	7	Abstractions about equitable and property-law principles primarily from English law, including doctrines limiting enforcement or liability such as unconscionability, undue influence and liability of trustees inter se, and normative theories of just acquisition and unjust enrichment such as the homestead principle and English unjust enrichment law.
Euclidean & Geometric Structures	25	Abstractions about geometric objects and their defining properties — triangle and polygon classifications, symmetry groups, conics, and singularities like the tacnode — together with related integral transforms and combinatorial-geometric problems such as kissing numbers, foliations, and quadrisecants.
Evolutionary & Ecological Hypotheses	21	Abstractions about evolutionary and ecological processes such as speciation, reproduction and population structure, along with specific hypotheses explaining traits like floral color change, pollination syndromes and drift in genetic diversity across populations.
Evolutionary Adaptation Mechanisms	6	Abstractions about how populations adapt or fail to adapt over generations — mechanisms coupling learned behavior to heritable change (Baldwin effect, genetic assimilation), constraints on reversing evolution (Dollo's law), and evolved decision rules that can become miscalibrated (ecological trap, r/K selection theory).
Extremal Graph Theory & Bounds	7	Abstractions about optimizing graph and combinatorial parameters under structural constraints, covering extremal size problems (cages, the degree diameter problem, the Erdős–Ko–Rado theorem), structural measures such as cliques and pathwidth, uniform independent-set sizes in well-covered graphs, and minimum-weight triangulation.
Faceted Classification & Metadata	15	Abstractions about organizing information for retrieval through independent descriptive axes, covering faceted classification schemes (topic, form, and geographic facets versus precoordinated headings), metadata coverage declarations (spatial and temporal coverage), and discovery methods like literature-based discovery and patent maps.
Family Bonding & Attachment Dynamics	7	Abstractions about emotional bonds and stress within families, covering attachment and caregiving relationships (attachment, father figure, social bonding), family-level resilience and stress processes (family resilience, family stress model), and developmental phenomena like infant sleep training and the Westermarck effect.
Fiber Bundles & Manifold Constructions	15	Abstractions about manifolds, bundles and geometric constructions built on top of them, covering bundle types (Associated Bundle, Banach Bundle, Holomorphic Tangent Bundle), manifold and complex-geometry results (Almost Complex Manifold, Ddbar Lemma, Submersion), and topological surgery or quotient constructions like Dehn Surgery and Lens Space.
Field Extensions & Galois-Theoretic Structures	19	Abstractions about fields, their extensions and associated algebraic structures, covering field-extension types (Quadratic Field, Quadratic Extension, Étale Algebra), Galois-theoretic and arithmetic tools (Galois Theory, Norm Form, Cyclic Algebra), and related constructs like Real Closed Field and Standard Part Function.
Field Theory & Polynomial Structures	26	Abstractions about fields and polynomials in algebra and number theory, covering field-extension properties (algebraically closed, formally real, splitting and rupture fields), polynomial classes and operations (cyclotomic, symmetric, and Schubert polynomials, factorization), and arithmetic invariants like fundamental units.
Financial & Economic Ratios	23	Abstractions that express an economic or financial quantity as a ratio or normalized measure — earnings per share, price-to-book ratio, and working capital turnover — alongside dimensionless and per-unit constructs such as elasticity of complementarity, factor cost, and specific quantity.
Financial Fragility & Crisis Dynamics	17	Abstractions about how leverage, funding and expectations amplify financial and strategic instability, covering credit and collateral feedback loops (Financial Accelerator, Collateral Squeeze, Debt Overhang), crisis and run dynamics (Minsky Moment, Wholesale-Funding Run, Balance-Sheet Recession), and failure patterns like Unit-Economics Mirage and Regulatory Surprise.
Financial Indices & Trading Indicators	15	Abstractions about measuring and modeling financial markets, covering technical trading indicators (Donchian channel, RSI, put/call ratio, triple exponential moving average), index construction methods (capitalization-weighted, Törnqvist, Kauffman, and volume indices), and portfolio-theoretic models like the Kelly criterion.
Financial Markets & Pricing Anomalies	13	Abstractions about financial markets, pricing, and investor behavior, including asset-pricing models such as the Black-Scholes model, Hotelling's rule and Tobin's q, behavioral and information failures like the disposition effect, greater fool theory and phantom inventory, and market-structure puzzles such as the peso problem and volatility smile.
Financial Ratios & Instruments	22	Abstractions about measuring financial position and structuring transactions, covering valuation and risk ratios (cyclically adjusted P/E, debt service coverage ratio, Value at Risk, Sterling Ratio), balance-sheet and market concepts (deleveraging, inverted yield curve, financial network), and contractual instruments like cost-plus contract and secured transaction.
Fluid Flow & Aeroacoustic Phenomena	8	Abstractions about compressible and viscous flow behavior and its effects — vortex and shock phenomena (Kármán vortex street, sonic boom, supersonic speed), duct and pipe-flow modeling (mass injection flow, minor losses in pipe flow), and coupled control or reflex responses (electro-pneumatic control, medullary ischemic reflex).
Fluid Flow & Transport Phenomena	31	Abstractions about how fluids move and transport momentum, heat, and material, covering flow-measurement and simulation techniques (particle tracking velocimetry, immersed boundary method, pressure-correction method), wave and turbulence phenomena (inertial waves, chaotic mixing, wind-wave dissipation), and specialized fluid effects (Kaye effect, Marangoni number, acoustic streaming).
Forecast Accuracy & Climate Measures	5	Abstractions about evaluating predictions and climate data, including forecast-skill and error measures like directional symmetry and mean absolute scaled error, and climate-record adjustment through homogenization.
Formal Arithmetic & Incompleteness	6	Abstractions about the limits and comparative strength of formal arithmetic theories — incompleteness and undefinability results such as the Gödel sentence, Tarski's undefinability theorem, and the Paris–Harrington theorem, and theories calibrated to feasible or self-verifying reasoning like bounded arithmetic and self-verifying theories.
Formal Grammar & Syntactic Structure	18	Abstractions about specifying and analyzing linguistic and formal-language structure, covering grammar formalisms and normal forms (conjunctive, harmonic, and model-theoretic grammar, Chomsky normal form), syntactic representation devices (phrase structure rules, nodes), dependency and locality patterns (cross-serial dependencies, subjacency), and morphosyntactic phenomena such as agreement attraction and connegatives.
Formal Grammars & Parsing Complexity	7	Abstractions about formal grammars, parsing, and graph complexity measures, covering grammar classes constrained by production rules (leftist, noncontracting, and straight-line grammars), parsing algorithms and complexity classes (deterministic parsing, LOGCFL), and structural graph parameters like aperiodicity and twin-width.
Formal Grammars & String Rewriting	21	Abstractions about generating and constraining formal languages, covering grammar hierarchies and classes (Chomsky hierarchy, context-sensitive grammar, matrix grammar), string-rewriting and automaton systems (L-systems, Markov algorithms, nested stack automata), and structural word or pattern properties (shortlex order, star height problem, ABACABA pattern).
Formal Logic & Axiomatic Foundations	21	Abstractions about the syntax and axiomatic structure of formal systems, covering proof calculi and metatheory (Hilbert system, Gödel numbering, metalogic, reverse mathematics), set-theoretic foundations (Zermelo set theory, Von Neumann-Bernays-Gödel set theory, extensionality), and algebraic encodings of logic like the Lindenbaum-Tarski algebra.
Formal Logic & Computation Systems	24	Abstractions about formal reasoning and computational systems, including logical inference rules, type theory, automata, rewriting systems, and nonmonotonic or temporal logics, spanning proof systems, decision problems and specification frameworks.
Formal Logic & Language Constructs	20	Abstractions that formalize reasoning and symbolic expression — inference rules like existential instantiation, universal generalization, and forward chaining, and logic systems such as modal, three-valued, and equational logic — alongside related linguistic or programming constructs including categorial grammar, predicate abstraction, and typed strings.
Formal Logic & Propositional Structure	14	Abstractions about the structure and interpretation of logical statements, including categorical propositions, quantification, logical form and interpretation, plus related inference fallacies and encoding devices like pairing functions.
Formal Logic & Semantic Systems	18	Abstractions about formal systems for reasoning and meaning — logical frameworks and their laws (De Morgan's laws, infinitary logic, computability logic), semantic theories of language and formal systems (dynamic semantics, operator grammar), and formal methods for specification and computation (B-Method, conjunctive query, false position method).
Formal Models & Logical Foundations	33	Abstractions about building and verifying formal representations — modal and many-sorted logics (normal modal logic, S4, branching quantifiers), proof and model theory (cut elimination, quantifier elimination, non-standard models), set-theoretic hierarchies and large cardinals (cumulative hierarchy, huge cardinals), and correctness frameworks such as proof of correctness.
Formal Notation & Symbol Conventions	5	Abstractions about notational and symbolic conventions in formal systems, including comparison and grouping symbols such as the much-greater-than relation and symbols of grouping, programming-language operators like the null coalescing operator and weak symbol, and formal axiomatic encodings of arithmetic such as typographical number theory.
Formal Sequences & Language Structure	18	Abstractions about strings and sequences analyzed formally, covering repetition-avoiding and recurrent word patterns (square-free words, unavoidable patterns, locally catenative sequences), automata and the pumping lemma, string data structures (tries, suffix trees, ropes, abstract syntax trees), and morphological or phonotactic decomposition.
Formal Systems & Discrete Structures	18	Abstractions that formalize discrete structures and computational or security systems through explicit axioms and state, spanning security and access-control models (Bell-LaPadula Model, Harrison-Ruzzo-Ullman Security Model), automata and decision problems (Generalized Büchi Automaton, Intersection Non-Emptiness Problem), and algebraic or topological constructs like Matroid and Distributivity.
Formally Specified Procedures & Problems	10	Abstractions that share a generic defining template — 'a formally specified procedure or entity that ...' — applied across domains: computational methods (numerical method, optimizing compiler), problem specifications (optimization problem, logic puzzle), and other bounded scholarly constructs (academic approach, space trajectory, software architecture recovery).
Foundations of Probability & Inference	29	Abstractions about the basic apparatus of probability theory and statistical inference — foundational objects (random variables, probability distributions, empirical measures), limit theorems and inequalities (Lévy's continuity theorem, Kolmogorov's three-series theorem, Jensen's inequality), information measures and distances (entropy, maximum entropy, Hellinger distance), and pitfalls like the gambler's fallacy.
Function Analysis & Numerical Methods	51	Abstractions about characterizing functions by continuity, differentiability, and integrability, and about the analytic and numerical machinery used to evaluate them — complex-analytic tools like contour integration and meromorphic functions, integral transforms, quadrature rules, and domain-decomposition preconditioners.
Functional Analysis & Operator Theory	16	Abstractions about the structure of Hilbert and Banach spaces and the operators on them, including kernel and duality constructions (positive-definite kernel, predual, Fredholm kernel), operator classification (strictly singular operator, weak trace-class operator), and specialized space constructions (Tsirelson space, Liouville space, multiresolution analysis).
Game-Theoretic Models & Paradoxes	38	Abstractions about strategic interaction formalized as games, covering decision paradoxes and thought experiments (Allais, Ellsberg, St. Petersburg, Monty Hall), canonical named games (Chicken, Centipede, Ultimatum, Prisoner's Dilemma variants), and equilibrium refinements (Nash, subgame perfect, trembling-hand, Bayesian).
Game-Theoretic Strategy & Equilibria	20	Abstractions about strategic interaction in games, including equilibrium concepts, solution refinements and player strategies, spanning cooperative and non-cooperative games, dynamic and mean-field settings, and mechanism design across networked or repeated play.
Gauge & Field-Theoretic Structures	8	Abstractions about geometric structures underlying gauge and field theories — connections and curvature such as the Bismut connection and the Yang–Mills equations, dualities between coupling regimes like Montonen–Olive duality, and models unifying or classifying fields such as the non-linear sigma model and unified field theory.
Gauge Theory & Characteristic Classes	5	Abstractions about curvature and characteristic classes in gauge theory, including Chern-Weil and Chern-Simons constructions, Yang-Mills flow, and their higher-categorical generalizations to infinity-bundles.
Gaze, Framing & Attention	5	Abstractions about how looking, framing, and unmet knowledge shape perception and meaning, including gaze as a social and interpretive act (gaze, female gaze, eye contact effect), and frameworks for how language or need directs attention (terministic screen, information need).
Generative & Efficient Neural Architectures	7	Abstractions about training and compressing neural network models, covering generative-modeling frameworks (Generative Adversarial Network, Deep Belief Network, Discrete Diffusion Model), their failure modes like Mode Collapse, and efficiency-oriented architectures and techniques such as MobileNet, Model Compression and Data Augmentation.
Generic Domain Practice Definitions	22	Abstractions that share one defining template — 'a standardized, repeatable procedure or pattern that ...' — applied across unrelated domains: assessment instruments (clinical assessment instrument, performance measure, trading indicator), professional practices (journalism, management, marketing practice), and modeling constructs (psychological model, decision method).
Generic System & Interface Definitions	27	Abstractions that define a domain by describing it as a governed arrangement of components, interfaces, and rules, spanning technical systems such as software architectures, logic circuits and data formats, institutional systems like legal systems, currencies and naming systems, and other organized structures such as musical structure and molecular geometry.
Genetic Variant & Phenotype Expression Patterns	7	Abstractions about how genetic variation produces phenotypic outcomes, including patterns of causal variant diversity such as allelic heterogeneity and locus heterogeneity, parent-of-origin and dosage effects like genomic imprinting and hemizygosity exposure, and environmentally responsive expression such as phenotypic plasticity.
Geographic Mapping & Positioning	14	Abstractions about representing and navigating geographic space, including map projections, coordinate conversion, GNSS positioning and enhancement, and spatial models like central place theory and rural-urban gradients.
Geologic Processes & Earth Dynamics	15	Abstractions about the physical processes that shape and are recorded in the Earth — tectonic and seismic phenomena (convergent boundary, intraplate deformation, Gutenberg-Richter law, earthquake forecasting), erosional and sedimentary processes (hydraulic action, coastal sediment transport, pediment), and dating or provenance methods (absolute dating, provenance, paleoliquefaction).
Geological & Geographic Interpretation	10	Abstractions that loosely share a concern with reading and protecting physical ground: relative sequencing of strata and finds (succession, seriation), surface interpretation and naming (aerial photographs, planetary nomenclature), protective supports and barriers (shoring, sacrificial layers, positive pressurization), with outliers like comminution and Internet autonomous systems.
Geometric Figures & Constructions	32	Abstractions about geometric objects, figures, and foundational constructions, covering polygons and polyhedra (hexagons, kites, cyclic quadrilaterals, dual and ideal polyhedra), coordinate and metric constructions (orthants, quasi-isometries, Vincenty's formulae), and number-theoretic foundations like surreal numbers.
Geometric Objects & Transformations	24	Abstractions about spatial objects and the transformations acting on them — curves and constructed loci (helix, cissoid, hodograph), coordinate systems and reference frames (log-polar coordinates, number line, unit sphere), and symmetry-preserving maps such as shear mapping, Procrustes transformation and translational symmetry.
Geophysical & Atmospheric Measurement Methods	21	Abstractions about measuring or modeling Earth's atmosphere, oceans, and subsurface, including atmospheric diagnostics such as convective available potential energy and thermal wind, geodetic and positioning techniques like free stationing and local tangent plane coordinates, and geophysical survey methods such as interferometric synthetic-aperture radar and vertical electrical sounding.
Geophysical Wave & Flow Parameters	12	Abstractions that quantify wave and flow behavior across fluid and geophysical systems, covering flow and transport parameters (Bickley jet, helicity, volume viscosity, Nusselt number), wave propagation and inversion methods (Stokes wave, wave vector, surface-wave inversion, receiver function), and instability or coastal-change processes (tearing mode, Bruun rule).
Grammar Derivation & Word Complexity	9	Abstractions about how strings and sentences are generated, parsed or measured — context-free, recursive, LL and operator-precedence grammars, left recursion in top-down parsing, factor complexity counting distinct subwords, and breaks or substitutions in written form (anacoluthon, typographic approximation).
Grammatical Case & Reference	10	Abstractions about how languages mark grammatical relations and reference, covering case systems (nominative, equative, and construct-state marking), noun-classification systems like grammatical gender, and how words form and refer, including conversion word-formation and referring expressions.
Grammatical Case & Syntactic Structure	18	Abstractions about how languages encode grammatical relations and structure, covering case- and alignment-marking systems (absolutive case, ergative-absolutive alignment, polypersonal agreement), morphosyntactic categories (grammatical person, morpheme, demonstrative), and syntactic dependency phenomena (crossover effects, preposition stranding, operator).
Graph Classes & Invariants	40	Abstractions that classify graphs by structural constraints — regularity, degree sequences, cliques, symmetry, connectivity — and define numeric invariants such as degeneracy, domatic number, rank-width, and Zagreb indices, or construction operations like Cartesian products, clique-sums, and local complementation.
Graph Coloring & Invariants	18	Abstractions about assigning labels or values to graph structures, spanning vertex- and edge-coloring schemes (equitable, exact, greedy, and rainbow coloring), coloring-related graph polynomials and invariants (chromatic polynomial, chromatic symmetric function, Wiener index), and special coloring problems (conflict-free coloring, monochromatic triangle, snark).
Graph Regularity & Width Parameters	6	Abstractions that constrain graphs by forbidden substructures or width — even-hole-free graphs, girth, partial k-trees, and homogeneous graphs whose local isomorphisms extend globally — alongside the Frobenius formula for symmetric-group characters derived from related combinatorial data.
Graph Structures & Algorithms	24	Abstractions about graphs and their structural or algorithmic properties, including special graph families such as complete bipartite, chordal bipartite and prism graphs, graph-theoretic invariants and operations like edge covering number and graph power, and algorithms or models built on graphs such as Prim's algorithm and graph dynamical systems.
Graph Structures & Combinatorial Objects	46	Abstractions that formalize discrete, graph-based and cellular structures — graph invariants and colorings (arboricity, edge and fractional coloring), decompositions and embeddings (biconnected components, planarity, duality), algebraically defined graphs (Cayley, hypercube, zero-divisor graphs), polytopes and polyhedral complexes, and applied abstractions like topological sorting.
Graph Theory Structures & Invariants	48	Abstractions that define graph classes, operations and structural invariants, including planarity, treewidth, clique-width and crossing number, spanning graph products, colorings, matchings and connectivity measures used to classify and compare graphs.
Graphical & Network Models of Dependence	16	Abstractions that represent probabilistic, physical, or computational dependence as a graph or network — Bayesian networks, factor graphs, ancestral graphs, and signal-flow graphs — including self-organizing network models like the Bak–Sneppen and shortcut models, and graph-based algorithms for flow, connectivity, and pointer analysis.
Group Dynamics & Collective Behavior	19	Abstractions about how groups perform, cooperate, and compete — performance and leadership effects (assembly bonus effect, cognitive resource theory, design leadership), pathologies of collective judgment (bikeshedding, crab mentality, social comparison bias), and structures for coordinated or distributed group work (epistemic community, distributed collaboration).
Group Structure & Subgroup Properties	10	Abstractions about the internal structure of groups and related algebraic sets, covering subgroup relations (central subgroups, complements, subgroup order), set-theoretic and combinatorial group properties (IP sets, the number of groups of a given order, the axiom of regularity), and applied constructs like group codes and confinement attacks.
Group-Theoretic Structures & Subgroups	41	Abstractions about groups and semigroups classified by internal structure — subgroup and conjugacy relations, characteristic subgroups, automorphism groups, group actions — and about representation-theoretic and combinatorial results, such as Clifford theory, Maschke's theorem, and the word and conjugacy problems, built on them.
Group-Theoretic Subgroup & Cohomology Structures	7	Abstractions about subgroup structure, representations and cohomology in group theory, including canonical and level-defined subgroups (cosocle, congruence subgroups, SQ-universal groups), group-action algebras like the crossed product, representation-theoretic tools such as covariants and Schur orthogonality, and the inflation-restriction exact sequence.
Growth Dynamics & Productivity Puzzles	13	Abstractions about long-run economic growth and productivity — convergence and trap dynamics such as the catch-up effect, the Malthusian and middle-income traps, and the Kuznets curve — and puzzles linking technology investment to measured output like the productivity paradox and Verdoorn's law.
Harmonic Analysis & Time-Frequency Functions	12	Abstractions about functions and operators in harmonic analysis, including time-frequency atoms and transforms such as the Gabor atom, Mathieu wavelet and Zak transform, boundary and potential-theoretic operators like harmonic measure and the Neumann-Poincare operator, and maximal-function tools such as the Hardy-Littlewood maximal function.
Homological Algebra Constructions	19	Abstractions that describe exactness and resolution in homological algebra, including chain-complex and exact-sequence machinery such as cokernels, exact sequences and the zig-zag lemma, derived and spectral-sequence tools like derived functors and the Lyndon-Hochschild-Serre spectral sequence, and categorical resolution frameworks such as Koszul algebras and Waldhausen categories.
Inferential Fallacies & Research Biases	18	Abstractions that name flawed patterns of inference or measurement in research and public reasoning — hasty generalization, argument from anecdote, the Table 2 fallacy, and randomized response — alongside related judgment biases such as normalcy bias, outcome bias, and zero-risk bias.
Informal Fallacies of Perspective	6	Abstractions that identify reasoning errors arising from mistaken assumptions about perspective or knowledge, including fallacies projecting present knowledge or feeling onto past or hidden events (historian's fallacy, furtive fallacy, psychologist's fallacy), and related principles about introspection and interpretation (KK thesis, virtuality fallacy, fallacy of accent).
Information Control & Disclosure Failures	5	Abstractions that loosely share only a concern with controlling, tracking or misrepresenting information — timed-release and confidentiality arrangements (embargo, off the record), signals whose apparent meaning outruns the underlying reality (milestone theater, secret sprawl), and bibliographic identity at the level of a single copy (item).
Information Theory & Error-Correcting Codes	20	Abstractions about quantifying and transmitting information reliably, covering entropy and typicality (binary entropy function, asymptotic equipartition property, min-entropy), channel models (binary erasure channel, directed information), and error-correcting code constructions and decoding methods (polar codes, Parvaresh-Vardy codes, sequential decoding).
Inheritance & Succession Law	8	Abstractions about legal rules governing inheritance, succession, and formal identity, including doctrines shaping heirs' shares and liability such as advancement, beneficium inventarii and right of survivorship, the immediate transfer of a deceased person's assets as in saisine, and related formal designations such as company formation and regnal number.
Institutional & Relational Categories	12	Abstractions that define broad social, legal and mathematical relations, including markets, jurisdictions, kinship and employment arrangements, legal frameworks and quasi-contracts, unified as generically framed relational or institutional categories.
Integer & Divisor Number Theory	45	Abstractions about the structure of positive integers under divisibility and factorization, covering special integer classes (perfect, amicable, highly composite numbers), primality and sieve methods (Miller-Rabin test, Brun sieve), and number-theoretic functions (Mertens function, Dirichlet series, prime-counting function).
Integer Classifications & Arithmetic Functions	45	Abstractions about classifying integers by divisor-sum and multiplicative properties (perfect, deficient, hyperperfect, sublime numbers), named integer sequences (Fermat, Cullen, Thabit numbers), arithmetic functions (totient, Möbius, Dedekind psi), and related notions like modular inverses and factorization.
Integer Properties & Number-Theoretic Sets	15	Abstractions about special classes and properties of integers, covering divisor and factorization conditions (smooth numbers, square-free elements, refactorable and untouchable numbers), additive and density-based sets (sum-free and primefree sequences, Schnirelmann density), and named integer classifications like Giuga and Descartes numbers.
Interface & Interaction Design Methods	20	Abstractions about designing and modeling human-computer interaction, including design approaches centered on user activity or context (activity-centered design, ecological interface design, task-focused interface), models of the interaction cycle (GOMS, human action cycle, user modeling), and design methods and artifacts (design system, paper prototyping, usage-centered design).
International Law Theory & Sovereignty	5	Abstractions about the theoretical foundations of international law and its relationship to states, covering the monism-dualism debate over domestic and international law, doctrines of territorial and colonial legal authority (Discovery Doctrine, Standard of Civilisation), and procedural concepts like Entry into Force and Law Without the State.
International Trade & Macroeconomic Dynamics	13	Abstractions about cross-border economic forces and policy responses — trade-theoretic results (Lerner symmetry theorem, immiserizing growth, new trade theory, home bias puzzle), currency and exchange-rate mechanics (currency crisis, gold points), and monetary or econometric tools such as the Taylor rule and hedonic regression.
Interpersonal Communication & Pragmatics	14	Abstractions about how speakers position themselves and manage meaning in interaction — pragmatic speech patterns (guiltive, persuasive definition, epithet), interpretive and evaluative stances (principle of charity, thick concept, truthiness), and communicative styles or competencies such as assertiveness, rhetorical stance and universal pragmatics.
Knot & Link Invariants	9	Abstractions about knots and links classified up to equivalence — polynomial invariants such as the bracket and HOMFLY polynomials, numerical invariants like the linking number, and structural classes such as torus knots, virtual knots, and link concordance, plus the related perfect spline construction.
Knowledge Representation & Information Systems	31	Abstractions about organizing, retrieving and reasoning over information, including knowledge acquisition, indexing, metadata standards and state-space models, spanning AI knowledge representation, information retrieval and structured data modeling.
Language Change & Cohort Analysis	5	Abstractions about how language and behavior shift across generations, including the apparent-time hypothesis, cohort effects, second-language acquisition, and semantic narrowing or widening of word meaning.
Language Production & Comprehension Models	8	Abstractions about how language is produced, comprehended and changes over time, covering production and perception theories (Speech Production, Motor Theory of Speech Perception, Functional Discourse Grammar), embodied and neural grounding hypotheses (Embodied Bilingual Language, Neuronal Recycling Hypothesis), and historical-linguistic diffusion via the Wave Model.
Language Structure & Communication Channels	15	Abstractions about how language is structured and conveyed, including morphology, phonemes and prosody, acquisition and comprehension processes, plus communication-channel frameworks like media richness theory and nonverbal communication.
Language Structure & Grammar Formalisms	23	Abstractions about the formal and social structure of language, including grammatical formalisms and syntactic theory (formal syntax, constraint grammar, lexicalist hypothesis), units and patterns within a language (bound variable, multiword expression, bare nouns), and connotative or stylistic devices (connotation, scare quotes, catachresis).
Language Variation & Social Identity	17	Abstractions about how language variety, policy, and use intersect with social identity and power, including institutional language management (language planning, language policy, codification), variation tied to social groups (register, gender paradox, linguistic profiling), and language's role in identity and bias (reappropriation, linguistic intergroup bias, gender pronoun transposition).
Language, Mind & Meaning-Making	69	Abstractions about how language, mind and culture make meaning — grammatical and sound-system structure (alignment, chain shifts, topic markers), rhetorical and lexical devices (asyndeton, euphemism, calque), mental and memory phenomena (epiphany, semantic memory), and community interpretive practices (cultural mapping, vernacular memory).
Legal & Moral Philosophy Principles	17	Abstractions about legal doctrines and philosophical arguments concerning rights, responsibility and justice, including doctrinal legal principles such as at-will employment, privity of contract and presumption of innocence, philosophical thought experiments like Frankfurt cases and Kavka's toxin puzzle, and jurisprudential theories such as law in action and Rechtsstaat.
Legal Doctrines & Evidentiary Standards	15	Abstractions about legal reasoning and procedure, covering evidentiary and procedural rules (evidence law, offer of proof, procedure in conflict of laws), doctrines qualifying liability or rights (imperfect self-defense, quasi-delict, undisclosed principal), and threshold or standing concepts (probable cause, standing, materiality).
Legal Doctrines & Jurisprudence	12	Abstractions that are named legal doctrines and jurisprudential theories — constitutional-review doctrines (basic structure doctrine, doctrine of colourability), jurisdictional and procedural rules (forum non conveniens, Rooker-Feldman doctrine, rescue doctrine), and theories of how law and courts operate (legal formalism, political jurisprudence, polycentric law).
Legal Doctrines & Organizational Authority	36	Abstractions about rules that allocate legal accountability and institutional authority: procedural and natural-justice doctrines (audi alteram partem, interlocutory injunctions, res judicata), criminal responsibility and its limits (perpetration through another, decriminalization), constitutional validity and amendment rules, liability doctrines, and organizational control patterns like bureaucracy.
Legal Doctrines & Procedural Bars	7	Abstractions about legal doctrines that bar or shape claims, including preclusion rules like collateral estoppel and law of the case, illegality and fraud defenses, and licensing or statutory-interpretation doctrines.
Legal Procedure & Liability Standards	13	Abstractions about courtroom procedure and standards of legal liability, covering trial and evidentiary mechanisms (cross-examination, motion to strike, perjury, exigent circumstance), procedural doctrines governing jurisdiction and timing (service ex juris, reasonable time, Lord Advocate's Reference), and liability rules like ultrahazardous activity.
Legal Rights & Land-Use Regulation	12	Abstractions about legally recognized rights and the regulation of land and activity, covering rights frameworks (Legal Right, Right to Mobility, Right to Rest and Leisure), land-use and planning controls (Zoning, Newbury Principles), and access or participation arrangements like Pay-to-Play and GPS-Based Game.
Lexical & Compositional Semantics	24	Abstractions about how word meaning is structured, composed, and represented, including lexical relations and processes such as hypernymy, back-formation and lexicalization, formal and distributional semantic models like componential analysis, latent semantic analysis and word embeddings, and applied semantic tasks such as word-sense disambiguation and semantic parsing.
Lie Groups & Representation Theory	17	Abstractions about the structure theory of Lie groups and algebras — group and algebra families (Heisenberg group, SO(8), En Lie algebras, current algebra), decomposition and classification tools (Iwasawa decomposition, restricted root system, real form), and representation-theoretic objects such as Verma modules and discrete series representations.
Linear Control & Circuit Systems	12	Abstractions about analyzing and controlling linear dynamical and electrical systems, covering state-space control concepts (Full State Feedback, Separation Principle, State-Transition Matrix, Hautus Lemma), stability criteria (Stable Polynomial, Proper Transfer Function), and circuit or fuzzy-control constructs like LC Circuit and Y-Δ Transform.
Literary Form & Critical Method	12	Abstractions about literary construction and interpretation — formal constraints and techniques (constrained writing, cut-up technique, regulated verse, stanza), genre and mode categories (hybrid genre, mock-heroic), and critical-analytical frameworks such as new historicism, thing theory and mimesis criticism.
Literary Theory & Cultural Reception	20	Abstractions about how texts and cultural artifacts are produced, classified and received, including genre, canon, intertextuality, implied readers and reader-response, plus related fallacies and phenomena like chronological snobbery and the Tiffany problem.
Logical & Analytical Diagnostics	6	Abstractions that share only loose connective tissue around diagnosing structure or failure, spanning analytic classification (classification of discontinuities, transitive set), inference and reasoning tools (condensed detachment, variable elimination, Newton's flaming laser sword), and perceptual or memory displacement (representational momentum).
Logical Connectives & Formal Systems	13	Abstractions about logical connectives and formal proof systems, including propositional inference rules, satisfiability variants like planar SAT, grammar and sequent formalisms, and semantic conventions governing names and meaning.
Logical Inference, Modality & Conditional Structures	28	Abstractions that define validity, status, or dependency through formal or conditional rules — modal and metaphysical status (logical possibility, grounding), inference and quantification (modus ponens, material conditional, existential quantification), self-reference and contrast failures (liar paradox, distinction without a difference), and rule-governed branching such as guards.
Logical Semantics & Many-Valued Systems	12	Abstractions about how formal logics build formulas and assign them truth, covering syntactic units (atomic sentences, propositional formulas), semantic relations (logical consequence, tautology, equisatisfiability), quantifier-alternation definability hierarchies, and many-valued and fuzzy systems such as four-valued and Gödel–Dummett logic.
Machine Learning Models & Representations	25	Abstractions about how machine-learning systems learn, represent, and generalize from data, spanning neural-network architecture components (hidden layer, attention, Neural Turing machine), learning paradigms (transfer learning, zero-shot learning, ensemble learning), and theoretical or evaluative constructs (concept class, neural scaling law, out-of-bag error).
Macroeconomic Growth & Equilibrium Models	22	Abstractions about formal macroeconomic models of growth, output, and equilibrium, including growth models tracking capital and savings (Solow-Swan model, Harrod-Domar model, golden rule savings rate), equilibrium frameworks relating markets and aggregates (IS-LM model, AD-AS model, circular flow), and named relations or paradoxes linking policy to outcomes (Phillips curve, Laffer curve, paradox of thrift).
Macroeconomic Policy & Fiscal Dynamics	11	Abstractions about government fiscal and monetary policy effects on the macroeconomy, covering fiscal-stance concepts (Austerity, Public Debt, Operating Surplus, Tax Buoyancy), monetary-policy anomalies (Monetarist Paradox, Price Puzzle, Wallace Neutrality), and shock or downturn phenomena like Growth Recession and Sudden Stop.
Manifold Topology & Classification	12	Abstractions about the topological classification and construction of manifolds — duality and realization theorems such as Alexander duality and the Steenrod problem, exceptional and exotic structures like exotic R4 and the Eells–Kuiper manifold, and modification techniques such as surgery theory and the double of a manifold.
Manifold Topology & Homology Theories	28	Abstractions about the structure of manifolds and topological spaces, including CW complexes, homology and cohomology theories, spectral sequences, decompositions of 3-manifolds and fibration-related constructions used to classify spaces up to homotopy.
Manifolds, Stacks & Classifying Spaces	18	Abstractions about geometric-topology spaces built from local models — manifold variants (Fréchet manifold, solvmanifold, quaternion-Kähler manifold), stack and groupoid presentations (gerbe, differentiable stack, Haefliger structure), and classification constructions such as classifying space, the Kirwan map and topological quantum field theory.
Manifolds, Tensors & Curvature	48	Abstractions about the differential-geometric machinery for describing manifolds and objects on them, including tensor and index notation, tangent bundles, connections and covariant derivatives, curvature and space curves, and coordinate systems such as curvilinear and orthogonal frames.
Market & Economic Indices	5	Abstractions about how price, output, and market activity are measured or interpreted through indices and stochastic patterns, including compiled statistical indices (producer price index, cost-weighted activity index), market-breadth and technical-analysis constructs (TRIN, Elliott Wave Principle), and stochastic-process characterizations of price paths (quasimartingale).
Market Structure & Competition Models	7	Abstractions that formalize markets and competitive interaction — general-equilibrium models such as the abstract economy and the Arrow–Debreu exchange market — and models of imperfect competition like monopolistic competition, differentiated Bertrand competition, Chamberlinian monopolistic competition, and consumer networks.
Market Structure & Competitive Dynamics	31	Abstractions about how market structure and competitive strategy shape prices and welfare, covering oligopoly and monopoly power (Bertrand and Edgeworth paradoxes, Lerner index, monopsony), surplus measures (consumer, producer, social surplus), and product-strategy pathologies like feature creep and bundling.
Markov Chains & Probabilistic Computation	7	Abstractions about stochastic state-transition models and their computational uses — structured Markov chain variants (nearly completely decomposable Markov chain, telescoping Markov chain, trellis), sampling algorithms such as the Metropolis algorithm, and probabilistic verification or reversible-computing models (probabilistic CTL, billiard-ball computer).
Markov Processes & Random Generation	8	Abstractions about stochastic transitions between states — Markov kernels, chains, operators, and their categorical formalization as the category of Markov kernels — together with decision-making under partial observability via POMDPs, and the generation of randomness through pseudorandom seeds and physical entropy.
Matrices, Measures & Numeric Structures	30	Abstractions that formalize numeric and structural representations, including specialized matrices, distance and similarity measures, number and naming systems, plus algorithmic techniques like low-rank approximation and symbolic factorization, a loosely connected miscellany of quantitative tools.
Matrix Structures & Matroids	11	Abstractions about structured matrices and their combinatorial abstractions, covering sparse and patterned matrix classes (anti-diagonal, Hessenberg, pentadiagonal, and skyline matrices), specialized determinant and matrix conditions (Moore determinant, G-matrix), and matroid structures that generalize linear and algebraic independence.
Meaning-Making, Self & Social Interpretation	27	Abstractions about how people construct meaning, identity, and belief through social and psychological processes, including self-narrative and identity (narrative identity, subpersonality, sinthome), belief and behavior distortion (self-deception, insufficient justification, communal reinforcement), and interpersonal communication and interpretation (interpersonal gap, hyperpersonal model, sign).
Measure & Probability Foundations	42	Abstractions about the foundational objects of measure theory and probability — measurable spaces and sigma-algebras, types of measures (Borel, invariant, product, vector), measure-theoretic pathologies (non-measurable sets, Vitali sets), and core probability results such as the probability axioms and the Radon-Nikodym theorem.
Measure Theory & Probability Measures	8	Abstractions about measures and their properties, including null and perfect sets, isotropic and Radon measures, and functionals like the Laplace functional that characterize random or invariant measures.
Measure-Theoretic Constructions	10	Abstractions about generalized measures and integration on abstract spaces, covering measure types (Borel Regular Measure, Counting Measure, Locally Finite Measure, Fuzzy Measure Theory), integration theories (Pettis Integral, Projection-Valued Measure), and geometric-measure-theory notions like Spherical Measure and Uniformly Distributed Measure.
Measurement Standards & Material Properties	11	Abstractions about how physical and chemical quantities are standardized and measured — normalization conventions (base conditions), concentration measures and ratios (mass concentration, body-fluid-to-serum ratios), solution and interface laws (colligative properties, Raoult's law, Szyszkowski equation), chromatographic resolution, and measurement procedures and distributions.
Measurement, Approximation & Numerical Error	17	Abstractions about quantifying and approximating physical or computational quantities, spanning error and precision concepts (truncation error, arithmetic underflow, significant figures), numerical approximation methods (iterative methods, residuals, log-log plots), and measurement conventions (physical quantity, metrication, coefficient).
Media Distortion & Correction Dynamics	5	Abstractions about how media coverage distorts belief and how corrections fail to keep pace, covering attention and framing distortions (agenda distortion, headline-body mismatch, false precision), asymmetric correction dynamics that let errors outlast their fixes, and a memory-encoding phenomenon, the generation effect.
Media Economics & Persuasion Techniques	10	Abstractions about media markets and persuasive communication, including advertising and distribution metrics like cost per mille and four-wall distribution, propaganda techniques, and cultural phenomena such as hyperreality and 15 minutes of fame.
Media Influence & Attention Dynamics	5	Abstractions about how attention and information exposure shape belief and behavior at scale, covering media-effects theories (Agenda-Setting, Filter Bubble, Spotlight Fallacy), congestion and coordination models (El Farol Bar Problem), and adversarial or adaptive social dynamics like Jailbreak Adaptation.
Media, Propaganda & Public Discourse	13	Abstractions about how media and institutions shape public attention and belief, including agenda-building, propaganda and disinformation models, media convergence and networked publics, and frameworks describing journalistic and hybrid-warfare dynamics.
Media-Induced Emotional Response	6	Abstractions about how media content shapes audience emotion and behavior, covering contagion effects on suicide risk (Werther and Papageno effects), engineered emotional provocation (rage-baiting), and one-sided audience relationships and evoked-emotion techniques like parasocial interaction and the objective correlative.
Medical & Veterinary Interventions	7	Abstractions about direct physical interventions on the body, covering diagnostic and access procedures (emergency ultrasound, fetoscopy), therapeutic or occlusive techniques (neurolytic block, vascular occlusion, injection), and a euthanasia method, cervical dislocation, sharing the theme of controlled physical intervention on tissue.
Memory Architecture & Address Spaces	25	Abstractions about how computer systems organize, access and move data through memory, covering address spaces and translation (virtual memory, virtual address space, memory address), cache structures and coherence protocols (CPU cache, cache hierarchy, Firefly and MERSI protocols), and memory-management techniques like demand paging and buffering.
Memory Encoding & Retrieval Effects	21	Abstractions about how information is encoded, stored and retrieved from memory, covering context- and state-matching effects (Context-Dependent Memory, State-Dependent Learning, Transfer-Appropriate Processing), positional and salience effects (Primacy, Recency, Serial-Position, Von Restorff), and reconstructive distortions like the Misinformation Effect and Google Effect.
Memory Storage, Retrieval & Encoding	9	Abstractions that model how information is stored, encoded, and retrieved, spanning human-memory systems (Atkinson-Shiffrin memory model, storage, recall, cue-dependent forgetting), external and encoded memory aids (exosomatic memory, error-correcting code, online codes), and related computational constructs for ordering and messaging (heapsort, higher-order message).
Metaphysics of Mind & Knowledge	23	Abstractions about philosophical positions on mind, reality and knowledge — theories of the mind-body relation (epiphenomenalism, emergent materialism, psychophysical parallelism, neutral monism), metaphysical stances on existence (physicalism, substance theory, philosophical realism), and epistemological frameworks such as phenomenal conservatism and radical constructivism.
Metric Geometry & Curvature	14	Abstractions about distance structures and curved-space geometry, spanning metric-space foundations (complete field, formal ball, injective metric space), curvature and convexity notions (geodesic convexity, Hadamard space, nonpositive-curvature CAT(0) spaces), and geometric measure objects (varifold, collapsing manifold, relative convex hull).
Metric Geometry & Packing	11	Abstractions about scale, covering, and packing in metric and geometric spaces, including scale-uniform space properties (doubling space, dyadic cubes, fat object), dimension and density measures (packing dimension, Hausdorff density), and geometric packing and covering problems (tetrahedron packing, Danzer set, perfect rectangle).
Metric Space Foundations	9	Abstractions about the basic axioms and combinatorics of metric spaces, covering distance axioms and their variants (triangle inequality, ultrametric space, equivalence of metrics), covering and separation properties (covering number, positively separated sets, uniformly disconnected space), and metric-indexed data structures (BK-tree, isometry group, CAT(k) space).
Metric Space Structures & Distance Maps	11	Abstractions about distance and its structural consequences in metric and inner-product spaces — distance-preserving or distance-controlling maps such as metric maps and quasisymmetric maps, generalized means and products like the Fréchet mean and dot product, and space-level invariants such as equilateral dimension and reach.
Microeconomic Theory & Welfare Criteria	13	Abstractions about consumer choice and welfare in microeconomic theory, including classifications of goods by how they are valued or evaluated (composite good, experience good, positional good), formal results linking demand and welfare (Roy's identity, feasibility condition, theory of the second best), and normative criteria for aggregating welfare (Nash welfare rule, wealth maximization, Greenwald-Stiglitz theorem).
Military Strategy & Operational Decision-Making	5	Abstractions about how campaigns and frontline decisions are structured and can fail, spanning operational-level design (operational art, line of operation), decision-rule and blowback failures (rules-of-engagement ambiguity, collateral-damage blowback), and perceptual bias in rapid decisions (shooting bias).
Models of Health & Disease	8	Abstractions about how health and disease are conceptualized and studied, spanning explanatory health models (biomedical model, one health model, social uterus), epidemiological study designs (natural history study, pool chlorine hypothesis), and health-measurement or rights concepts (Pignet index, right to health).
Molecular & Atomic Electronic Structure	12	Abstractions about the electronic and energetic structure of atoms and molecules — quantum-chemical models and approximations such as the molecular Hamiltonian, Slater–Condon rules, and zero differential overlap — and related effects like the inert-pair effect, vibrational energy redistribution, and the spin Hall effect.
Molecular & Cellular Biology Mechanisms	16	Abstractions about molecular and cellular mechanisms, including protein structure and folding, genetic coding and translation, chromosome segregation, and post-transcriptional or transport processes that shape macromolecule function.
Molecular & Developmental Biology Mechanisms	21	Abstractions about biochemical and developmental regulation, covering metabolic and molecular pathways (citric acid cycle, cometabolism, control coefficients), gene-expression and developmental mechanisms (epigenetics, pattern formation, germ-band extension, left-right asymmetry), and cellular processes like quorum sensing and cold hardening.
Molecular Biology & Genetic Engineering Methods	16	Abstractions about manipulating and designing biological molecules, including synthesis and editing techniques such as artificial gene synthesis and CRISPR gene editing, discovery and modeling methods like expression cloning, fragment-based lead discovery and homology modeling, and regulatory or delivery mechanisms such as position effect and targeted drug delivery.
Molecular Structure & Chemical Bonding	35	Abstractions about the electronic and structural principles governing molecules and materials — bonding and orbital effects (agostic interaction, mesomeric effect, octet rule), formal descriptors of composition and charge (chemical formula, oxidation state, charge number), and characterization methods such as Tanabe-Sugano diagrams and crystal structure prediction.
Molecular Structure & Interaction Models	20	Abstractions about how molecular structure, bonding, and energy are modeled in chemistry, including geometric and bonding classifications (capped trigonal prismatic molecular geometry, metal-ligand multiple bond, tertiary carbon), energetic and thermodynamic models (Flory-Huggins solution theory, Kapustinskii equation, helix-coil transition model), and computational or spectroscopic methods (COSMO solvation model, machine-learned interatomic potential, Förster resonance energy transfer).
Moment Problems & Measure Recovery	6	Abstractions about recovering measures from their moment sequences, including the Hausdorff, Hamburger and Stieltjes moment problems, related transforms, and probabilistic inequalities governing measure and event probabilities.
Monetary Theory & Policy Constraints	13	Abstractions about the relationship between money, prices, and interest rates — the quantity theory of money, liquidity preference, the money multiplier, and velocity of money — and structural constraints on monetary policy such as the impossible trinity, the liquidity trap, and the zero lower bound.
Moral & Political Concepts	9	Abstractions about ethical dilemmas and political-social arrangements, spanning moral thought experiments (drowning child analogy, lesser of two evils principle, Mandeville's paradox), political governance concepts (patrimonialism, political freedom, religious cleansing), and welfare-incentive dilemmas (Samaritan's dilemma, luxury belief, relational goods).
Multisensory Perception & Binding	15	Abstractions about how the brain combines, attends to, and stabilizes sensory information, covering cross-modal integration (McGurk effect, ventriloquism effect, visual capture), perceptual stability and binding (perceptual constancy, temporal binding), auditory and attentional phenomena (precedence effect, dichotic listening), and sensorimotor coupling like gain fields and Braitenberg vehicles.
Multivariate & Heavy-Tailed Distributions	16	Abstractions about specialized probability distributions and their moments, covering multivariate and matrix-valued families (complex normal, matrix t, matrix variate Dirichlet), heavy-tailed and generalized continuous distributions (Weibull variants, variance-gamma, multivariate Pareto), and distributional statistics like cokurtosis and quantization error.
Multivariate & Spectral Signal Analysis	10	Abstractions about decomposing signals and multivariate data into structured components, including Fourier-type and elliptic filters, canonical correlation and Karhunen-Loeve analysis, and statistical dependence concepts underlying spectral and dimensionality-reduction methods.
Music Theory & Performance Techniques	23	Abstractions about musical structure and performance practice, including harmonic and rhythmic devices like chord progressions and tresillo, notational and pedagogical systems, and specialized instrumental or vocal techniques such as portato and blind octaves.
Music Theory Concepts & Notation	20	Abstractions about how music is organized, notated, and perceived, spanning pitch and interval relationships such as ambitus, tetrachord and enharmonic equivalence, structural and performative concepts like musical improvisation and transformational theory, and cross-domain or novelty musical practices such as protein music and eye music.
Musical & Poetic Form	11	Abstractions about the structural patterns of music and verse, covering musical practices and measures (basso continuo, transposition, pitch interval, boogie rhythm), recording and alignment techniques (dummy-head recording, music alignment), and fixed poetic forms like the Petrarchan sonnet, rictameter, and common measure.
Musical Form & Rhythmic Devices	15	Abstractions about musical structure, rhythm and expressive notation, covering large-scale forms (Rondo Form, Period Structure, Virelai), rhythmic and metrical devices (Syncopation, Catalexis), and performance articulations like Cymbal Choke and the Fortepiano dynamic marking.
Musical Form & Texture	10	Abstractions about how musical works are organized and perceived, spanning large-scale formal templates (sonata form, strophic form, through-composed form), textural and timbral qualities (monophony, timbre, fugue's imitative texture), and listening-experience phenomena (playing by ear, the sharawadji effect, musical formalism).
Musical Intervals & Voice Texture	9	Abstractions about pitch relationships and multi-voice texture in music, including interval structures such as the musical interval, all-interval tetrachord and major limma, textural organization of simultaneous voices like counterpoint and musical texture, and tonal reference points such as the tonic and atonality.
Named Analytic Theorems & Operators	39	Abstractions that are named theorems, operators, or invariants from mathematical analysis and geometry, including convergence and continuity results such as Egorov's theorem and the Weierstrass M-test, functional-analytic operators like densely defined operators and functional determinants, and dynamical or geometric quantities such as heteroclinic orbits and filling radius.
Named Cognitive & Behavioral Effects	32	Abstractions that name a specific, mechanism-explained psychological effect — attentional, perceptual, or motivational — such as the Stroop, Simon, placebo, and near-miss effects, procedural memory, and stimulus-response compatibility, each describing how an internal process is biased or reshaped by context.
Named Physical Phenomena & Theoretical Constructs	16	Abstractions that name a specific physical phenomenon or theoretical construct, mostly in relativity, optics, and quantum physics — black holes and cosmic censorship, gravitational memory effects, zero-point energy, and conical refraction — each tied to a particular named model, equation, or hypothesis.
Narrative Devices & Literary Forms	15	Abstractions about storytelling technique and literary form, including narrative devices like analepsis and frame tales, character types such as dynamic characters and Mary Sues, and fixed poetic forms like the villanelle.
Narrative Structure & Storytelling Devices	26	Abstractions about how stories are built and analyzed — structural roles and units like the actant, diegesis, plot, and obligatory scene, narrative techniques such as nonlinear narrative, the nut graf, and characterization — and archetypal or genre elements like the dark lord and superhero.
Narrative Voice & Rhetorical Devices	23	Abstractions about how narratives and rhetoric shape meaning and audience relation, covering narrative-structuring devices such as focalisation, plot and posthumous narrative, classical rhetorical figures and genres like apostrophe, hypotyposis and invitational rhetoric, and cultural forms carrying humor or moral content such as jokes, parables and the wise fool.
National Accounts & Monetary Systems	22	Abstractions about how money, saving, and international balances are measured and governed at the national level, including national accounting identities (flow of funds, saving identity, gross national product), international monetary relationships (exchange rate, purchasing power parity, net foreign assets), and banking or policy mechanisms (fractional-reserve banking, tight money policy, Triffin dilemma).
Network Architecture & Transport Protocols	26	Abstractions about how computer networks move and manage data, covering switching and routing architectures (packet switching, virtual circuits, wormhole switching, overlay networks), transport-layer control mechanisms (TCP congestion control, ECN, bandwidth-delay product), and network management concepts like segmentation and QoS.
Network Models & Graph Generation	6	Abstractions about generating and computing over network structures, including random and recursively generated graphs, graph neural networks, Petri nets for concurrency, and graph invariants like Shannon capacity.
Network Security Vulnerabilities & Trust	32	Abstractions about how networked systems establish trust and where it fails — web and API vulnerabilities (cross-site scripting, mass assignment, server-side request forgery), identity and verification mechanisms (federated identity, message authentication codes, proof-carrying code, zero trust), and network communication and architecture (protocols, link-state routing, peer-to-peer systems).
Network Structure & Centrality	12	Abstractions about the structure and connectivity of networks, including measures of node importance (betweenness centrality, Katz centrality), models of network growth and community formation (fitness model, Louvain method, triadic closure), and global structural properties (small-world network, modularity, weighted network).
Neural & Cognitive Representation Models	11	Abstractions about how brains and models organize sensory and spatial representation, including biologically inspired computational models (neocognitron, hierarchical temporal memory, BCM theory), neural maps and category-specific processing (sensory map, neural processing for individual categories of objects), and psychophysical measurement methods (two-alternative forced choice, cocktail party effect).
Neuronal Signaling & Plasticity	14	Abstractions about how neurons transmit signals and adapt over time, including synaptic transmission and its modulation (neurotransmission, inhibitory postsynaptic potential, spike-timing-dependent plasticity), structural and cellular support for signaling (myelination, axonal transport, dendritic integration), and models of learning and spatial representation in neural circuits (synaptic plasticity, place field, central pattern generator).
Nonlinear & Optimal Control Design	14	Abstractions about designing controllers for dynamical systems, covering nonlinear stabilization techniques (backstepping, feedback linearization, sliding mode control, Lyapunov redesign), optimal and robust control formulations (optimal control, H-infinity loop-shaping, trajectory optimization), and analytical tools like the Kalman-Yakubovich-Popov lemma.
Normative Ethics & Moral Standing	8	Abstractions about the grounds and application of moral norms, spanning normative-ethical doctrines (principle of double effect, moral particularism, norm in philosophy), moral-standing concepts (speciesism, moral authority), and applied or professional ethics (professional ethics, justice tourism, value in ethics).
Nuclear Physics & Isotope Phenomena	21	Abstractions about atomic nuclei, their transformations, and detection, including nuclear stability and decay boundaries (nuclear drip line, decay energy, neutrinoless double beta decay), isotope classification and tracking (isodiapher, isotopic labeling, seed nucleus), and measurement techniques and astrophysical processes (muon spin spectroscopy, nuclear resonance fluorescence, r-process, standard solar model).
Number & Formal Language Properties	7	Abstractions that define special classes of numbers, operations, and formal languages, including numeric classifications (Achilles number, sexy primes, dyadic rational), degenerate or foundational operations (empty sum, ternary operation), and formal-language constructions (Dyck language, quotient of a formal language).
Number Theory & Packing Conjectures	5	Abstractions that span open problems and local methods in number theory and geometry, including packing and lattice-point conjectures (Ulam's packing conjecture, Kemnitz's conjecture), asymptotic enumeration techniques (analytic combinatorics), and structural or prime-by-prime analysis (local analysis, Iwasawa group).
Number-Theoretic Properties & Tests	22	Abstractions about divisibility, primality, and related arithmetic properties of numbers and polynomials, covering primality testing (AKS test, trial division, Fermat's little theorem, probable primes), factorization-related properties (square-free integers, greatest common divisor, least common multiple), growth and density measures (average order, large sets), and related combinatorial constructs.
Numeral Systems & Digit Algorithms	11	Abstractions about representing numbers and manipulating their digits — positional and fixed-point encodings (Q number format, Z-order curve, division algorithm), digit-based number properties (cyclic number, normal number, multiplicative digital root, sum-product number), and arithmetic procedures exploiting digit structure such as the Bailey-Borwein-Plouffe formula.
Numeral Systems & Integer Sequences	22	Abstractions about how numbers are represented and generated, spanning positional and non-standard numeral systems (bijective numeration, non-integer base of numeration, decimal representation), recursively defined integer sequences (Perrin, Leonardo, Golomb numbers), and special constants or puzzles (Champernowne constant, Josephus problem, complete sequence).
Numeric Representation & Encoding Schemes	7	Abstractions about encoding numbers for computation, covering signed and biased integer encodings (offset binary, signed number representations), alternative arithmetic systems (logarithmic number system, residue number system, symmetric level-index arithmetic), and approximation techniques like the alpha max plus beta min algorithm.
Numerical Root-Finding & Quadrature Methods	8	Abstractions about numerical methods for solving equations and evaluating integrals, including interval enclosure (bisection method, interval arithmetic), integral-equation recovery like Carleman's equation, weighted quadrature and special functions (Gauss–Jacobi quadrature, multivariate gamma function), and density-based sampling such as slice sampling and uniform distributions.
Observation, Attention & Perceptual Bias	8	Abstractions about how observation, attention, and framing distort or organize perceived reality, including recording and validity practices in field research (fieldnotes, fieldnote backfill, invisible auditor), attentional and probability biases (frequency illusion, subadditivity effect), and narrative or recognition effects tied to context (foreshadowing cue, word superiority effect, ELIZA effect).
Ocean Circulation & Coastal Dynamics	32	Abstractions about large-scale ocean and geophysical fluid movement — wind-driven transport (Ekman transport, coastal upwelling), basin-scale circulation (ocean gyres, Walker circulation, Indian Ocean Dipole), stratification and buoyancy-driven mixing (Brunt–Väisälä frequency, salt fingering, internal wave breaking), and estuarine density processes (salt wedge, tidal mixing).
Operator Algebras & Commutant Structures	9	Abstractions about algebras of operators and their commutation structure, covering von Neumann and C*-algebra constructions (Von Neumann Algebra, Positive Element, Gelfand Representation), commutant relations (Bicommutant, Killing Form), and related categorical or measurability notions like Yetter-Drinfeld Category and Weakly Measurable Function.
Operator Theory & Functional Analysis	28	Abstractions about linear operators on normed and Hilbert spaces and the function spaces they act on, covering operator classes (normal, unitary, hyponormal, Toeplitz), spectral notions (spectrum, pseudospectrum, spectral abscissa), norms and inequalities (Schatten norm, Cauchy-Schwarz), and structures like seminorms and operator topologies.
Operators, Functions & Data Abstractions	11	Abstractions that generically define operations and transformations, including algebraic and logical operations, mathematical operators and functionals, invariants, and computational data types, framed as broad definitional categories across mathematics and computing.
Optical & Astrophysical Phenomena	25	Abstractions that describe how light, waves, or radiation propagate and are measured — diffraction, reflection, beam optics, and photometry — applied to astronomical objects through stellar classification and spectroscopic parallax, and to atmospheric phenomena like downbursts and zodiacal light.
Optical Imaging & Light Transport	27	Abstractions about how light, images, and radiation are captured, projected, and rendered, covering imaging and projection geometry (3D projection, image rectification, visual hull, shape from focus), radiative and light-transport models (physical optics, path tracing), and measurement techniques like spectrophotometry.
Optical Wave & Imaging Systems	10	Abstractions about how light propagates and forms images in optical systems, including wave-propagation and diffraction principles (Huygens-Fresnel principle, moiré pattern, pupil function), formalisms for polarized light and scattering (Jones calculus, discrete dipole approximation), and imaging or diagnostic techniques (scanning laser ophthalmoscopy, simulated fluorescence process algorithm, swinging light test).
Optimization Algorithms & Methods	19	Abstractions about solving optimization problems, including metaheuristics like ant colony and particle swarm methods, line-search and interval-reduction techniques, and problem classes such as bilinear, nonlinear and semi-infinite programming.
Optimization Theory & Feasibility	8	Abstractions about optimization problems and their solvability, including feasible-set and constraint structure such as the feasible region and generalized semi-infinite programming, equilibrium and extremum theorems like the minimax theorem and Bauer maximum principle, and information-theoretic projection methods such as information projection.
Orbital Mechanics & Celestial Dynamics	13	Abstractions about the motion and configuration of astronomical bodies, covering orbital elements and maneuvers (Longitude of the Ascending Node, Orbital Inclination Change, Universal Variable Formulation), binary and multi-body systems (Binary System, Binary Mass Function, Lissajous Orbit), and observational phenomena like Astronomical Transit and Gravitational Keyhole.
Order, Type & Classification Foundations	49	Abstractions that classify mathematical objects up to a declared equivalence or structural rule, spanning binary-relation and order properties such as reflexive relations and interval orders, type-theoretic foundations like identity, unit and intersection types, and representation-theoretic classifications such as partition algebras and indecomposable modules.
Ordinal Functions & Series Convergence	9	Abstractions about limits, continuity, and series in real and ordinal analysis, including ordinal-indexed continuity such as continuous and normal functions, series and sum approximation like Riemann sums and Helly's selection theorem, and generalized calculus operators such as the differintegral, transseries and Z-transform.
Organic Reaction Mechanisms & Kinetics	11	Abstractions about mechanisms and kinetics of chemical reactions, including cyclization and ene reactions, elementary radical steps such as free-radical addition and hydrogen-atom abstraction, cooperative and hydrogen-bond-donor catalysis, stereoelectronic control of bond cleavage, and enzyme kinetics such as the Michaelis-Menten model.
Organizational & Operational Failure Modes	38	Abstractions that diagnose how complex human-technical systems break down, covering command and coordination failures (unity-of-command breakdown, handoff loss, plan-execute gap), safety and human-factors pathologies (automation bias, latent conditions, target fixation), and crisis-response mismatches.
Organizational Governance & Process Methods	46	Abstractions about frameworks and methods for organizing, planning, and governing work within institutions, including scheduling and prioritization techniques (critical path method, Gantt chart, MoSCoW method), knowledge and memory systems (organizational memory, SECI model), and structures for authority, control, and change (change control, linking pin model, strategic control).
Organizational Patterns & Management Concepts	29	Abstractions that name recurring patterns in organizations and system design, including governance and compensation structures (broadbanding, viable system model, academic administration), organizational antipatterns (mushroom management, doorman fallacy, magic pushbutton), and software or domain-modeling methods (feature-driven development, role class model, enterprise data modeling).
Orthogonal Polynomials & Special Functions	14	Abstractions about named special functions and orthogonal polynomial families — Gegenbauer, Faber, Lommel, Zolotarev, and Pidduck polynomials — along with their generating identities, generalized hypergeometric forms, and classification theorems such as Bochner's theorem and the Christoffel–Darboux formula.
Pedagogy, Testing & Learning Methods	18	Abstractions about teaching methods and educational assessment, spanning instructional approaches (dialogic pedagogy, synthetic phonics, slow education), assessment and testing design (anchor test, automatic item generation, standard-setting study), and learning-context effects (acculturation gap, the Scarr-Rowe effect, family literacy).
Perception, Narrative & Moral Cognition	13	Abstractions that examine how minds perceive, narrate and morally judge experience, covering perceptual and cognitive constructs (Active Perception, Imagination Inflation, Word-Learning Biases), literary and narrative forms (Dream Vision, High Concept, Rotation Method), and moral or critical frameworks like Poisonous Pedagogy and Imperial Boomerang.
Persuasion & Interpersonal Communication	17	Abstractions about how messages persuade and communication unfolds between people, including elaboration and processing routes, credibility and bias effects, deceptive or strategic signaling, and models of interpersonal and mediated exchange.
Philosophical Concepts & Thought Experiments	27	Abstractions about philosophical positions, thought experiments and historical scientific ideas, including metaphysical theories like nominalism and pantheism, epistemic puzzles like Russell's teapot, and superseded hypotheses such as vitalism and recapitulation.
Philosophy of Religion & Fate	12	Abstractions about theological and existential questions of meaning, fate, and belief, including wagers and arguments for belief such as Pascal's wager and the atheist's wager, conceptions of divine nature like dipolar theism and divine hiddenness, and deterministic or purpose-denying worldviews such as the clockwork universe and fatalism.
Phonological & Typological Language Variation	6	Abstractions about how languages vary and change at the sound and word-structure level, including phonological features and processes such as advanced and retracted tongue root and palatalization, morphological classification like morphological typology and the unidirectionality hypothesis, and word-recognition or variation models such as the cohort model and free variation.
Phonological Classification & Sound Change	8	Abstractions that classify speech sounds and their patterned variation — secondary articulation as in labialized velar consonants, shared-vowel groupings called lexical sets, weight-sensitive stress and poetic metre, stress-driven vowel reduction and cross-word contraction like crasis — loosely joined by the unrelated WYSIWYG interface concept.
Phonological Structure & Sound Patterning	8	Abstractions about the organization of speech sounds within words, spanning syllable and cluster structure (consonant cluster, sonority sequencing principle, anaptyxis), featural and rule-based representations (distinctive feature, phonological rule, phonological opacity), and numeral notations built from sound units (alphasyllabic numeral system).
Phonological Units & Speech Processing	11	Abstractions about sound structure in language, including allophones, diaphonemes and morphomes as units of phonological variation, habitual articulatory settings, rhyme as patterned sound recurrence, variety continua between dialects, and the perceptual and developmental processes of speech acquisition and perception.
Phylogenetics & Evolutionary Descent	24	Abstractions about ancestry, descent, and evolutionary classification, covering genealogical and phylogenetic-tree concepts (most recent common ancestor, pedigree collapse, quartet distance, lineage), speciation and evolutionary-tempo mechanisms (allopatric speciation, punctuated gradualism, deep homology), and classification methods.
Physical & Geometric Dynamical Quantities	29	Abstractions that describe motion, invariance, or coordinate structure across dynamical, geometric and physical systems, spanning celestial and continuum dynamics such as barycenters, tides and rotating black holes, analytic operators and coordinate frames like the P-Laplacian and parabolic cylindrical coordinates, and structural invariants such as invariant subspaces and matrix equivalence.
Physical Quantities, Operators & Formulas	33	Abstractions about named physical quantities, operators, and empirical formulas spanning quantum mechanics, solid-state physics, and physical chemistry, including field and momentum operators (magnetic vector potential, crystal momentum, angular momentum operator), model systems (Einstein solid, Rutherford model, eight-vertex model), and derived formulas (semi-empirical mass formula, Bethe-Feynman formula, steric factor).
Physical Systems & Operational Planning	18	Abstractions that share only loose connective tissue, spanning relativistic and astrophysical phenomena (relativity of simultaneity, mass-energy equivalence, carbon-burning process), spaceflight trajectories and vehicles (parking orbit, gravity loss, sphere of influence, atmospheric entry), control by gain scheduling, and scheduling or capability-restoration plans (linear scheduling method, military reset).
Physical Units & Measurement Quantities	8	Abstractions that define physical quantities and how they are measured or expressed — electrical and radiometric quantities (characteristic admittance, radiant intensity, inductor), ratio-based measures expressed logarithmically or geometrically (logarithmic frequency ratio, roof pitch, radiation angle), and systems for organizing units such as absolute pressure measurement.
Plate Tectonics & Geodynamic Processes	19	Abstractions about the mechanics of Earth's lithosphere and its deformation, spanning plate-boundary processes (subduction, rift zones, back-arc basins), volcanic and magmatic behavior (effusive and explosive eruptions, flux melting, volcanism), and crustal response mechanisms (isostasy, uplift, lithospheric drip).
Poetic Forms & Language Ideology	8	Abstractions about poetic form and language attitudes, including fixed metrical and rhyme structures like bahr and Asefru, and linguistic-philosophical positions such as phonocentrism, nation language and Bakhtinian dialogue.
Point-Set Topology & Measure Structures	14	Abstractions about the fine structure of topological and metric spaces, spanning separation and covering properties (collectionwise normal space, compactness, Gδ sets), discrete point-set configurations (Delone sets, Sierpiński sets, sphere packing), and measure-theoretic constructions (cylinder set measure, inner measure, ideal on a set).
Point-Set Topology Foundations	17	Abstractions that define the basic vocabulary of topological spaces — open and closed sets, interior, and the topology axioms themselves — together with covering and separation properties such as paracompactness, caliber, and the Phragmén–Brouwer theorem, and structures built atop them like sheaves and strictly positive measures.
Point-Set Topology Structures	51	Abstractions about point-set topology, covering how open sets, covers, compactness, and separation axioms define topological spaces, including special examples like the Cantor set and Sorgenfrey plane, and topological vector-space structures like Fréchet and nuclear spaces.
Political & Cultural Theory Frameworks	25	Abstractions that theorize large-scale social, political and cultural transformation, including class and power dynamics (Class Struggle, Power-Knowledge, Proletarian Internationalism), globalization and world-systems concepts (Globalization, World-System, Geopolitical Economy), and frameworks for cultural change and identity (Cultural Assimilation, Transculturalism, Third Space Theory).
Political & Strategic Game Models	11	Abstractions about strategic conflict and political organization, including game-theoretic solution concepts and generalized games, asymmetric warfare and political engineering, plus institutional theories like cartel parties and Hoshin Kanri planning.
Political Discourse & Power Structures	9	Abstractions about how political power, speech, and authority are structured and contested, including institutional distributions of power (asymmetric federalism, decolonization), and public communication and disagreement (discourse, public sphere, dissent, hostile media effect).
Political Power, Governance & Legitimacy	17	Abstractions about how political power is organized, exercised, or abused, including institutional and electoral structures such as estates of the realm, decoy lists and demoicracy, forms of illegitimate influence like corruption, cronyism and heresthetic, and macro-level political-economic conditions such as state capitalism and the Kindleberger trap.
Polynomial Functions & Field Structures	21	Abstractions about polynomial functions and the algebraic structures that support them — degree-classified polynomials like quadratic, cubic, and quintic functions, formal power series, and ordered fields — plus specialized constructs such as auxiliary functions, resultants, and dual numbers used in transcendence theory.
Polynomial Rings & Rational Approximants	15	Abstractions about polynomials viewed through ring-theoretic and approximation structure — monomial ideals, Newton polytopes, monic polynomials, and generalized polynomial families like the Humbert and Peters polynomials — alongside rational and continued-fraction approximation devices such as the Padé table and Birkhoff factorization.
Polynomials & Algebraic Invariants	20	Abstractions about polynomial-like algebraic objects and their invariants, covering generalized polynomial forms (Laurent polynomials, quasi-polynomials, exponential polynomials), invariant-theoretic constructions (invariant polynomial, characteristic polynomial of a graph, Contou-Carrère symbol), and algebraic-geometric polynomial structures (determinantal variety, generic fiber, Rees decomposition).
Population Ecology & Species Dispersal	17	Abstractions about how density, dispersal, and species interactions shape ecological and evolutionary outcomes, covering density-dependent effects (Allee effect, enemy release, Janzen-Connell hypothesis), consumer and facilitation relations (functional response, facilitation cascades), abundance and trophic patterns (occupancy-abundance relationship, ecological pyramids), body-size rules, and dispersal mechanisms like larval dispersal.
Population Genetics & Evolutionary Dynamics	30	Abstractions about how populations evolve under selection and inheritance, spanning quantitative-genetic models (infinitesimal model, additive genetic effects, selection coefficient), population-level processes (evolutionary rescue, secondary contact, minimum viable population), and sexual-selection hypotheses (sensory trap, koinophilia, sexual antagonistic coevolution).
Population Genetics & Selection	11	Abstractions about how selection and inheritance shape populations, including equilibrium and fixation dynamics (Hardy-Weinberg principle, fixation, Fisher's fundamental theorem of natural selection), kin-based and social selection (Hamilton's rule, kin selection, inclusive fitness), and mating and sex-ratio dynamics (disassortative mating, Fisher's principle, Haldane's sieve).
Price Theory & Market Equilibrium	13	Abstractions about how prices and markets are modeled in economics, covering demand and equilibrium theory (demand curve, general equilibrium theory, Heckscher-Ohlin model), price-setting and market-power concepts (competitor indexing, duopsony, marginal profit), and measurement or welfare tools (market basket, isovalue lines, welfare cost of business cycles).
Probability Distributions & Second-Moment Structures	32	Abstractions about probability distributions and dependence structure, covering distribution families such as location-scale, noncentral and reciprocal distributions, second-moment and covariance tools like covariance operators, whitening transformations and uncorrelatedness, and estimation methods such as U-statistics, functional principal component analysis, and control variates.
Probability Distributions & Transforms	22	Abstractions about characterizing and transforming probability distributions — specific distribution families (hyperbolic, zeta, truncated normal, Johnson's SU), transform and summary functions (characteristic function, cumulative distribution function, quantile function), and results relating random variables to their derived distributions (ratio distribution, probability integral transform).
Probability Transforms & Tail Behavior	7	Abstractions about transforming and bounding probability distributions — generating-function-based encodings like the cumulant and Esscher transform, tail and concentration measures such as Bernstein inequalities, the Q-function, and tail dependence, and specific distributions like the Linnik distribution and probability weighting function.
Process, Data & Business Modeling	9	Abstractions about modeling business processes and data, including artifact-centric process models, dimensional data warehousing, cumulative flow diagrams, and pricing or replenishment strategies like razor-and-blades and log shipping.
Processor Architecture & Instruction Sets	9	Abstractions about how processors are specified and built — instruction-set contracts (instruction set architecture, register-memory architecture), design and compilation frameworks (processor design, polyhedral model, random-access machine), and a characteristic runtime failure, the segmentation fault.
Product-Market Fit & Adoption Dynamics	9	Abstractions about how products gain market traction, including product-market and problem-solution fit, adoption-curve gaps like crossing the chasm, competitive location models like Hotelling's law, and loyalty effects like the service recovery paradox.
Program Execution & Runtime Concepts	34	Abstractions about how programs and their data are translated, run, stored, and recovered: compilation and transformation (compilers, basic blocks, profile-guided optimization), runtime memory behavior (working sets, thrashing, register windows), memory-corruption and injection defects, stream processing, and state preservation through backups and checkpoints.
Program Scope & Nesting Disciplines	10	Abstractions about how programs tie work and context to nested scopes and parent-child relations, covering captured environments and point-free definitions (closures, tacit programming), task lifetimes (structured concurrency, fork–join, zombie processes), nested-syntax attachment (dangling else, L-attributed grammars), and misplaced state like the temporary field.
Programming Language Concepts & Notation	24	Abstractions about how programs and formal languages are structured and evaluated, including variable binding and scope, paradigms like declarative and applicative programming, notations such as Polish notation, and mechanisms like pattern matching and marshalling.
Projective Geometry & Line Bundles	16	Abstractions about projective space and the algebraic-geometric structures built on it, covering projective constructions (projectivization, projective bundles, collineations, translation planes), positivity and growth invariants of line bundles (ample line bundles, Iitaka dimension), and classical projective curves like quaternary cubics.
Property Ontology & Code Smells	18	Abstractions that loosely connect how properties attach to bearers across philosophy, data design and inference — ontological accounts (quality inherence, immaterial spatial entities), data and schema models (attribute–value systems, relational model), code smells (data class, primitive obsession, refused bequest), and scope fallacies (accident, quantifier shift).
Property Ownership & Title Doctrines	15	Abstractions about how ownership and possession of property are acquired, divided, and transferred — original-acquisition modes like occupatio and alluvion, title and recording rules such as marketable title and race to the courthouse, and divided or equitable interests like usufruct, trusts, and proprietary estoppel.
Protein Structure Prediction & Folding	7	Abstractions about predicting and modeling protein structure, covering folding and threading methods (Protein Threading, Loop Modeling, Levinthal's Paradox), sequence-alignment scoring (Gap Penalty), and conformational-search techniques like Searching the Conformational Space for Docking and THEMATICS.
Psychometric Measurement & Judgment Biases	29	Abstractions about how psychological traits and attitudes are measured — item response theory, content validity, differential item functioning, and scaling methods like Thurstone scales — alongside cognitive and judgment biases such as overconfidence, narrative bias, and outcome primacy, and stage-based behavior-change theories.
Public Choice & Political Economy	11	Abstractions that apply economic reasoning to politics and institutions — public-choice theories of state behavior (public choice, government failure, rent-seeking trap, Tullock paradox), property-rights and bargaining results (Coase theorem, crowding in), and institutional pathologies of spending and redistribution (maverick spend, Wagner's law, resource curse).
Pursuit Games on Graphs	5	Abstractions about pursuit-evasion games played on graphs, including cop number and cop-win graphs, entanglement and eternal domination, and topological games generalizing capture dynamics to abstract spaces.
Qualitative Research & Fieldwork Methods	31	Abstractions about the practices and validity concerns of qualitative and field-based inquiry — data-gathering methods (participant observation, focus groups, key informants, ethnoarchaeology), rigor and reflexivity practices (analytic memos, reflexive journals, peer debriefing, confirmability), and institutional or spatial concepts researchers study (defensible space, placemaking, feminist institutionalism).
Quantum & Statistical Simulation Methods	7	Abstractions about simulating quantum and statistical-mechanical systems — quantum computational and dynamical methods (quantum annealing, quantum master equation, stochastic quantization), and polymer or many-body Monte Carlo techniques such as reptation Monte Carlo and Scheutjens-Fleer theory.
Quantum Electronic States & Transport	14	Abstractions about how electrons and their quantum excitations behave and move in solids and nanostructures, covering tunneling and quantized conduction (quantum point contact, field emission, diffusons), interface and trap barriers (Schottky–Mott rule, Poole–Frenkel effect), excitons and fractionalized excitations, and spin, crystal-field and qubit-coupling effects.
Quantum Entanglement Criteria & Measures	5	Abstractions about detecting and quantifying quantum entanglement, covering separability tests (Peres-Horodecki Criterion, Reduction Criterion), entangled-state constructions (Greenberger-Horne-Zeilinger State), and distinguishability or correlation measures like the Diamond Norm and Reflected Entropy.
Quantum Field Theory & Lattice Models	42	Abstractions about mathematical structures and methods in quantum field theory and statistical mechanics, spanning symmetry classification (accidental symmetry, Eightfold Way, Grand Unified Theory), lattice spin models (Ising model, Potts model, classical XY model), and computational or formal techniques (Ewald summation, Hubbard-Stratonovich transformation, Pauli-Villars regularization).
Quantum Many-Body & Particle Physics	24	Abstractions about collective and particle-scale physical phenomena, covering many-body quantum states (Fermi liquids and gases, Bogoliubov quasiparticles, jellium, ferrimagnetism), particle-physics processes and models (muon capture, nuclear fission, Two-Higgs-Doublet Model, Primakoff effect), and associated formalisms like pole mass.
Quantum Operators & State Labels	15	Abstractions about the mathematical machinery underlying quantum mechanics, including operators and transformations such as antiunitary operators, exchange operators and the Wigner-Weyl transform, discrete labels for quantum states like quantum number and Fock state, and related algebraic structures such as the canonical commutation relation and theta representation.
Quantum Protocols & Circuit Models	20	Abstractions about quantum computing and information protocols, spanning circuit and gate models (quantum circuits, Fredkin gate, KLM protocol), quantum-information tasks (superdense coding, state-merging, no-cloning theorem), and foundational quantum phenomena (einselection, quantum jump, incompatibility of measurements).
Quantum States & Computational Models	12	Abstractions about quantum states, dynamics and computational models, covering quantum-state descriptions and entanglement processing (Density Matrix, Entanglement Distillation), computational classes and formulations (Exact Quantum Polynomial Time, Path Integral Formulation, Quantum-Computation Model), and information-theoretic quantities like Quantum Relative Entropy and Information Causality.
Quantum States & Information Measures	26	Abstractions about quantum states, measurement and information — specific state types (Bell diagonal, cat and Fock states), correlation and distinguishability measures (purity, quantum Fisher information), quantum control and protection (dynamical decoupling, Zeno effect, gnu codes), and entanglement-based computation (entanglement swapping, quantum walks, one-way quantum computing).
Queueing, Networks & Concurrent Systems	9	Abstractions about coordinating flows and access in networked or concurrent systems, spanning queueing and occupancy theorems (Jackson's theorem, Bartlett's theorem), network protocol and mapping concepts (network allocation vector, network mapping, reachability analysis), and scheduling or dependency patterns (time-sharing, sequential coupling, unambiguous Turing machine).
Recursive Construction Schemes	8	Abstractions that are built through recursive or successive construction — natural numbers and paramorphisms generated by induction, folds reducing structured data, recursively computed nimbers, method chaining and ind-schemes as direct limits — loosely joined by compositional consistency conditions like Beck–Chevalley and fourth normal form.
Regime Change & Political Authority	5	Abstractions about how political regimes and public authority shift over time, covering democratization processes (democratic transition and consolidation), governance-accountability structures (dual subordination), and shifts in the locus of political action or ownership like extra-parliamentary opposition and remunicipalization.
Regression Diagnostics & Linear Models	11	Abstractions about fitting and diagnosing linear statistical models, covering estimation methods (generalized least squares, best linear unbiased prediction, stepwise regression), diagnostic tools for model fit (DFFITS, partial residual plot, portmanteau test), and variance or sensitivity concepts (homoscedasticity, variance-based sensitivity analysis, smearing retransformation).
Relational Database Theory	13	Abstractions about structuring and querying relational data — schema and normalization concepts (database schema, third normal form, entity cardinality), transactional guarantees (database transaction, bitemporal modeling), and query or identifier mechanisms such as query rewriting, the Hi/Lo algorithm and Codd's theorem.
Reproductive Isolation & Sex-Linked Evolution	7	Abstractions about how reproduction and sex differences shape evolution, spanning hybrid-incompatibility and isolation mechanisms (Drosophila hybrid sterility, Haldane's rule, Wallace effect), sex-specific trait expression (sex-limited genes, Rensch's rule), and asexual reproduction (parthenogenesis).
Research Design & Measurement Bias	23	Abstractions about designing studies and diagnosing distortions in measurement or inference, covering bias types (verification bias, spurious relationship, weekend effect), agreement and dispersion statistics (concordance correlation coefficient, qualitative variation), and study designs like multiple baseline design and round-robin test.
Resource Flow & System Accounting	6	Abstractions about tracking flows of material, credit, or physical assets through systems, covering material and resource accounting (material flow analysis, non-renewable resource classification), feedback-based system modeling (system dynamics, credit channel), and lifecycle management practices like terotechnology and coprecipitation.
Response Functions & Signal Analysis	7	Abstractions about how systems respond to and transform signals, including causal response-function relations (Kramers-Kronig relations, dissipation factor, semilinear response), simulation and stability methods for wave and field equations (pseudospectral time-domain method, Von Neumann stability analysis), and frequency-domain filtering and feedback representation (log Gabor filter, causal loop diagram).
Rhetorical Fallacies & Persuasion Tactics	24	Abstractions about how arguments persuade or mislead, cataloging informal fallacies that substitute emotion, authority or repetition for evidence (Ad Hominem, Ad Populum, Genetic Fallacy, Straw Man), and rhetorical strategies for framing and defending a position (Prolepsis, Apologia, Two-Sided Message, Poisoning the Well).
Riemannian & Symplectic Geometry	18	Abstractions about curvature, symmetry, and structure in differential geometry, including manifolds defined by curvature conditions (Hadamard manifold, isoparametric manifold, complex hyperbolic space), minimal-surface constructions and conjectures (Björling problem, K-noid, Yau's conjecture), and symplectic or spinorial constructions (symplectization, symplectic spinor bundle, Kosmann lift).
Rigid-Body Kinematics & Rotation	8	Abstractions about the motion and mechanical behavior of rigid bodies, including rotational description such as angular displacement, Euler angles and centrode, specific mechanical points and elements like the center of percussion, inerter and rigid rotor, and schematic representation of mechanisms such as the kinematic diagram.
Ring & Module Structure Theory	15	Abstractions about the structural properties of rings and modules, covering finiteness and dimension conditions (finite algebras, Jaffard rings, length of a module), depth conditions (Cohen-Macaulay and Buchsbaum rings), gradings (graded rings, supermodules), special ideal types like test ideals, and decomposition results for PID and serial modules.
Ring & Module Theory	17	Abstractions about the internal structure of rings and modules, including classification by ideal and radical properties (radical of a ring, semiprimitive ring, primitive ring), homological invariants of modules (depth, grade, free presentation), and special ring types defined by structural conditions (perfect ring, polynomial identity ring, Gelfand ring).
Sampling, Monte Carlo & Estimation	23	Abstractions about drawing samples and estimating quantities under uncertainty, covering sampling-design methods (multistage sampling, systematic sampling, correct sampling), Monte Carlo and simulation techniques (Monte Carlo integration, umbrella sampling, variance reduction), and estimator properties (consistency, sampling error, buffered probability of exceedance).
Sampling, Selection & Accountability Procedures	9	Abstractions that describe how participants are selected or activities held to context-specific conditions, covering sampling and selection methods (snowball and convenience sampling, civic lottery), group-based gatekeeping like ascriptive inequality, and compliance frameworks such as context-based sustainability, equine drug testing, conditional technology moratoria and policy design.
Scaling Laws & Growth Patterns	13	Abstractions that describe regular scaling patterns and frequency statistics in data and language, spanning empirical scaling laws (Benford's, Heaps', and Gibrat's laws), growth notation (big O, L-notation), lexical frequency effects (type-token ratio, word frequency effect), and count-based sequence models (Kneser-Ney smoothing, prediction by partial matching).
Scheme Morphisms & Aperiodic Patterns	8	Abstractions that mostly classify morphisms of schemes by finiteness and smoothness conditions — finite, quasi-finite, and formally smooth maps, the Enriques–Kodaira surface classification, and the Rosati involution — loosely joined by two structural planar-pattern outliers, crease patterns and Penrose tilings.
Schemes, Varieties & Moduli Spaces	41	Abstractions about the objects and machinery of algebraic geometry, including scheme- and stack-theoretic foundations (morphisms, sheaves, formal schemes), varieties classified by geometric type (toric, ruled, spherical), and moduli constructions (Donaldson-Thomas theory, virtual fundamental classes, quotient stacks).
Selection, Speciation & Experimental Evolution	22	Abstractions about evolutionary change under selection and variation, covering fitness regimes (frequency-dependent selection, underdominance, genetic load, truncation selection), linkage and drift effects (genetic hitchhiking, Muller's ratchet), speciation and divergence (Bateson-Dobzhansky-Muller model, character displacement), and evolutionary algorithms (differential evolution, Holland's schema theorem).
Self, Identity & Social Cognition Biases	26	Abstractions about how people construct identity, act against their own judgment, and misjudge themselves or others — self-serving biases (choice-supportive bias, backfire effect), face and identity work (identity negotiation, impostor syndrome), practical irrationality (akrasia, instrumental versus value rationality), and motive models like the Burkean pentad.
Self-Perception Biases & Heuristics	22	Abstractions that explain systematic distortions in judging oneself and others, covering self-enhancement effects (illusory superiority, self-serving bias, worse-than-average effect), attribute-substitution heuristics (availability heuristic, halo effect, focusing effect), and egocentric-transfer phenomena (implicit egotism, name-letter effect, mere ownership effect).
Semantic Integration & Knowledge Modeling	13	Abstractions about reconciling and representing meaning across data systems — conceptual and graph-based models (entity-relationship model, conceptual graph, semantic triple), integration challenges and solutions (semantic heterogeneity, minimal mappings, canonical data model), and web-scale knowledge infrastructure such as URIs and the social semantic web.
Sequences, Mappings & Basepoint Structures	10	Abstractions that loosely connect mathematical constructions built from mappings and sequences, including function classification by iterative construction such as Baire functions, low-discrepancy and registration methods like the Halton sequence and point-set registration, and structure-preserving mappings such as inclusion maps, point reflection and tree rotation.
Service-Quality Rates & Queueing Metrics	13	Abstractions that quantify performance and quality in service and production systems, covering queueing and telecom metrics (Kingman's Formula, Grade of Service, Dropped-Call Rate, BCMP Network), statistical process-monitoring tools (Control Chart, Error Exponents), and miscellaneous domain-specific rates like Mean Systemic Pressure and Mean Log Deviation.
Set-Theoretic & Order Structures	54	Abstractions about the foundational architecture of infinite sets and ordered structures, spanning ordinal and cardinal arithmetic (aleph and beth numbers, admissible sets), order-theoretic completeness (lattices, ideals, posets), and set-theoretic forcing and combinatorics (diamond and square principles, Aronszajn trees, proper forcing axiom).
Sheaf Theory & Algebraic Geometry	12	Abstractions about how local algebraic or geometric data glue into global structures via sheaves, including sheaf types and their properties (coherent sheaf, torsion sheaf, twisted sheaf), functorial operations on sheaves (inverse image functor, direct image with compact support), and the categorical foundations of sheaf theory (Grothendieck topology, ringed topos, stalk).
Sheaves & Birational Geometry	23	Abstractions about sheaves, line bundles, and cohomological invariants in geometry, covering exact sheaf sequences (canonical, Euler, exponential), divisors and divisor-class groups (Picard group, Jacobian variety), cohomology and complexes (Dolbeault cohomology, elliptic complexes, Bockstein spectral sequence), and birational classification tools like the minimal model program.
Sign Systems, Irony & Narrative Meaning	7	Abstractions that loosely connect how meaning is produced or fails through signs and narrative structure, including semiotic and communicative models such as the organon model and social marker, narrative time-space and interpretive gaps like chronotope, irony and nonsense, and notational conventions for encoding meaning such as musical notation.
Signal Processing & Transform Methods	25	Abstractions about digital and analog signal processing, covering time-frequency transforms such as the chirplet transform, constant-Q transform and Gabor wavelet, coding and sampling techniques like ADPCM, line codes and oversampling, and estimation or denoising methods such as total variation denoising, signal averaging, and ESPRIT.
Simplicial Sets & Higher Categories	7	Abstractions about the combinatorial encoding of homotopy structure via simplicial sets, including foundational definitions and variants (simplicial set, delta set, opposite simplicial set), operations combining or transforming them (join of simplicial sets, extension of a simplicial set), and their correspondence to categorical and homotopical structures (Dold-Kan correspondence, simplicially enriched category).
Social Cognition & Attribution Theories	24	Abstractions about how people interpret and act within social contexts, covering attribution and persuasion models (correspondent inference theory, heuristic-systematic model), social-structural and normative concepts (norm of reciprocity, social trap, system justification theory), and identity-related phenomena (femmephobia, self-objectification, recognition).
Social Cognition & Perception	13	Abstractions about how people perceive, interpret, and respond to others and to information, including social-perceptual processes (empathy, eye contact, emotion perception), biases and interpretive tendencies (hostile attribution bias, cognitive specialization), and models of memory and attentional cognition (working memory training, memory inhibition, subitizing).
Social Identity & Structural Violence	9	Abstractions about how social structures shape identity, dignity and moral perception, covering citizenship and normativity concepts (Denationalized Citizenship, Heteronormativity), structural or symbolic violence (Dignity Taking, Redemptive Violence, Interpellation), and moral-philosophical frameworks like Ubuntu Philosophy and Moral Perception.
Social Influence & Persuasion Tactics	7	Abstractions about how requests, stances and commitments shape attitudes and action, covering sequential persuasion techniques (door-in-the-face, sequential compliance), the Ben Franklin effect, rhetorical and imaginative stances (accismus, suspension of disbelief), and aims meeting resistance or conviction, as in narrative conflict and the ethic of ultimate ends.
Social Networks & Communication Theory	12	Abstractions about how people and messages connect across networks, spanning network-structure phenomena (homophily, six degrees of separation, decentralised systems), communication-theoretic models (the source-message-channel-receiver model, meta-communication, warranting theory), and mediated social dynamics (algorithmic radicalization, e-leadership, social penetration theory).
Social Structure & Group Identity	12	Abstractions about how groups and hierarchies are organized and how individuals relate to them — power and status structures like the elite class, fusion of powers, and homoarchy, identity and belonging theories such as optimal distinctiveness and the social identity model, and normative influences on language and behavior.
Social Structure & Sociological Theory	17	Abstractions that theorize how social structures form and persist, covering macro-sociological theories (structuration's duality of structure, economic determinism, modernization theory), stratification and inequality concepts (social inequality, social mobility, structural inequality), and community or network patterns (age set, the 1% rule, embeddedness).
Sociological Theories & Concepts	22	Abstractions that are named theories or concepts within sociology and social theory — social structure and stratification (homogamy, sponsored mobility, gender polarization), macro-historical frameworks (ecological-evolutionary theory, theory of generations, grand theory), and constructs of culture and symbolic meaning (symbolic culture, social objects, metric power).
Software & Systems Architecture	32	Abstractions about structuring and governing engineered software and IT systems, covering modular design principles (single-responsibility principle, interface-based programming, functional design), infrastructure and enterprise-scale architectures (enterprise architecture, software-defined data centers, IaaS), and operational practices like patch management.
Software Architecture & Modeling Methods	23	Abstractions about methods and metrics for designing, modeling, and measuring software systems, including architectural description frameworks (4+1 architectural view model, metamodeling, structured analysis), complexity and size metrics (cyclomatic complexity, function point, Halstead complexity measures), and design patterns or principles (identity map pattern, service autonomy principle, unidirectional data flow).
Software Evolution Laws & Code Smells	17	Abstractions about how software systems degrade or must adapt over time, dominated by Lehman's laws of software evolution (continuing change, increasing complexity, declining quality, self-regulation), paired with code-quality anti-patterns (Code Smell, God Object, Lazy Class) and aphorisms about accumulating complexity like Greenspun's Tenth Rule.
Sound Change & Language Evolution	13	Abstractions about how languages change over time, spanning phonological sound-change mechanisms (lexical diffusion, open syllable lengthening, quantitative metathesis), lexical and morphological restructuring (reborrowing, rebracketing, analogical change), and comparative-linguistic methodology (historical glottometry, quantitative comparative linguistics, the combinatorial method).
Sound Transmission & Building Physics	11	Abstractions about how sound and moisture move through materials and structures, including sound propagation and blocking (acoustic transmission, soundproofing, acoustic shadow, absorption), building-envelope protection (damp proofing, passive ventilation), and specialized acoustic phenomena (thermoacoustics, sound from ultrasound).
Source Credibility & Argument Evaluation	10	Abstractions about evaluating claims, sources, and arguments, covering journalistic attribution and correction practices (anonymous sourcing, on background, corrections policy), argument-structure and fallacy analysis (Toulmin model, appeal to authority), and trust-calibration phenomena like the Gell-Mann amnesia effect and inter-annotator agreement.
Spacetime Geometry & Relativity	22	Abstractions about the geometric and algebraic structure of spacetime in relativity, including causal structure (Cauchy surface, closed timelike curve, globally hyperbolic spacetime), coordinate and frame formalisms (isotropic coordinates, tetrad formalism, proper reference frame), and symmetry or spinor structures (Poincaré group, Killing spinor, gamma matrices).
Spacetime Symmetry Groups & Toy Models	7	Abstractions about symmetry groups and simplified models in relativistic physics, covering spacetime symmetry groups (Einstein Group, Galilean Group, Wigner D-Matrix), toy models of gravity (CGHS Model, Causal Dynamical Triangulation), and geometric constructs like the Spherical 3-Manifold.
Spatial Data Structures & Meshing	17	Abstractions about representing and partitioning geometric space computationally, covering hierarchical spatial structures (quadtrees, binary space partitioning, unstructured and corner-point grids), mesh and surface construction (mesh generation, subdivision surfaces, polygon partition), and geometric-relation problems like visibility and motion planning.
Spatial Perception & Navigation	22	Abstractions about how people and systems represent and navigate spatial layout, including neural and perceptual spatial maps (retinotopy, somatotopy, depth perception), navigation and wayfinding in environments and interfaces (wayfinding system, orientation loss, imageability), and interface metaphors for spatial organization (desktop metaphor, virtual desktop, responsive-layout breakage).
Spatial Statistics & Geographic Analysis	20	Abstractions about measuring and modeling patterns across geographic space — spatial autocorrelation statistics like Moran's I and Geary's C, thematic mapping, and point-process distributions — and scale-dependent effects such as the uncertain geographic context problem and neighborhood effect averaging.
Special Functions & Series Convergence	7	Abstractions about analytic special functions and convergence tests, covering complex extensions of classical functions (the gamma function, Dirichlet eta function), computational approximation (Lanczos approximation), and series-convergence criteria (the ratio test, root test).
Spectral Operators & Special Functions	9	Abstractions about spectral operators and special functions in mathematical physics, including Jost functions, Riesz projectors, Meijer G-functions, Weyl's law and zeta-function regularization, characterizing spectra, asymptotics and analytic continuation.
Statistical Bias & Inference Pitfalls	7	Abstractions that diagnose bias and paradox in statistical estimation and decision-making, covering estimation pitfalls (endogeneity, Stein's paradox, ecological inference problem), fairness and imbalance issues in classification (class imbalance, equalized odds), and a descriptive risk model, cumulative prospect theory.
Statistical Estimation & System Inference	13	Abstractions about estimating unknown states or distributions under uncertainty, including Bayesian and likelihood-based inference such as Jeffreys prior, hidden Markov models and recursive Bayesian estimation, robust and consensus fitting methods like least absolute deviations and random sample consensus, and dynamical-system state representations such as state variables and moving horizon estimation.
Statistical Hypothesis Tests & Diagnostics	9	Abstractions about testing statistical models and hypotheses, spanning time-series diagnostic tests (augmented Dickey-Fuller test, Ljung-Box test, CUSUM), regression and similarity diagnostics (Breusch-Pagan test, Fisher kernel), and inferential-methodology critiques (misuse of p-values, one- and two-tailed tests, approximate Bayesian computation).
Statistical Inference & Hypothesis Testing	34	Abstractions about drawing conclusions from data through likelihood-based estimation, Bayesian posterior reasoning, hypothesis tests, error measures and generalization biases, spanning parametric, nonparametric and sequential inference methods.
Statistical Learning & Model Failure Modes	41	Abstractions that combine statistical, learning and signal-processing models with their failure modes — estimation methods (expectation–maximization, recursive least squares, kriging), matrix and signal decompositions (non-negative factorization, lifting scheme), estimation biases (attenuation, omitted variables), and distribution-shift and evaluation failures (covariate shift, imputation leakage).
Statistical Mechanics & Particle Phenomena	17	Abstractions about statistical ensembles and particle-level physical processes, spanning equilibrium ensembles and thermal motion (partition function, canonical ensemble, equipartition, Langevin dynamics, pair distribution), quantum state transitions (intersystem crossing, STIRAP), scattering and decay (scattering length, particle decay, Askaryan radiation), and graded state counting like the Witten index.
Statistical Process Control & Quality Management	15	Abstractions about monitoring and improving process quality through statistics and structured methods, including control charts for detecting process variation (X-bar chart, U-chart, regression control chart), capability and performance metrics (process capability index, process performance index, critical to quality), and quality-improvement frameworks (Capability Maturity Model, quality function deployment, quality storyboard).
Statistical Process Control Charts	7	Abstractions about monitoring process stability using control charts, including attribute-based charts such as the c-chart and np-chart, continuous and adaptive monitoring statistics like the EWMA chart and Shewhart individuals control chart, and the underlying variation concepts they rely on such as natural process variation and the Reynolds operator.
Statistical Tests & Choice Measurement	7	Abstractions that provide statistical or measurement methods for comparing groups and choices, including nonparametric hypothesis tests (Mann-Whitney U test, location test), latent-structure and ranking measurement methods (confirmatory factor analysis, PAPRIKA), and psychological phenomena around choice and recall (overchoice, free recall).
Stochastic Processes & Markov Dynamics	29	Abstractions about randomness evolving through time, spanning continuous-time Markov processes (transition-rate matrices, Kolmogorov's criterion, continuous-time Markov chains), diffusion and Brownian-motion constructions (geometric Brownian motion, reflected Brownian motion, Brownian snake), and applied stochastic models (ruin theory, stochastic Petri nets, tau-leaping).
Stochastic Processes & Martingale Theory	19	Abstractions about the formal machinery of stochastic processes, covering martingales and filtrations (Doob martingale, local martingale, natural filtration, stopping times), point-process and state-estimation models (Cox processes, filtering problems, projection filters), and structural properties like stationarity and ergodicity.
Storage & Lookup Data Structures	21	Abstractions about organizing data for storage and fast lookup, covering hash-based and probabilistic structures (hash tables, Bloom and quotient filters), ordered and keyed collections (sorted arrays, heaps, queues, multimaps, lookup tables), adaptive and multidimensional structures (self-organizing lists, k-d trees), and storage tiering.
Strategic Decision Biases & Mechanisms	29	Abstractions that model how agents and groups decide and misjudge under strategic or risky conditions — mechanism-design concepts (Revelation Principle, correlated equilibrium), judgment aggregation (Condorcet's jury theorem, belief aggregation), behavioral biases (endowment effect, status quo bias, pseudocertainty), and choice architecture and performance frameworks.
Strategic Games & Equilibrium Concepts	14	Abstractions about strategic interaction in classic games, covering canonical coordination and conflict games (stag hunt, battle of the sexes, hawk-dove game), solution concepts like dominant and dominated strategies, and design or auction mechanisms including game balance, kingmaker scenarios, and the Vickrey auction.
Structural & Geological Failure Mechanics	25	Abstractions about how structures, materials and geological formations deform or fail under stress — faults and slope failure (normal, thrust and transform faults, mass wasting), structural instability and load paths (self-buckling, funicular form), material deformation laws (strain, Maxwell model, dislocation creep), and near-boundary shear like the law of the wall.
Structural & Solid Mechanics	30	Abstractions about how structures and materials carry load and deform, spanning beam theory and structural-analysis methods (Euler-Bernoulli beam theory, conjugate beam method, stiffness matrix), stress and failure concepts (stress concentration, stress triaxiality, von Mises yield criterion, J-integral), and structural or bridge design forms.
Structural Mechanics & Materials	19	Abstractions about how structures and materials bear and transmit load, including truss and framing systems (truss, bowstring truss, timber framing), material and micromechanical models (Eshelby's inclusion, force chain, indentation size effect), and design and testing methods (permissible stress design, plane strain compression test, pure bending).
Structural Vibration & Seismic Analysis	13	Abstractions about characterizing vibration and ground motion in structures, covering modal and frequency-response analysis (Bode plots, FEM modal analysis, statistical energy analysis), seismic and dynamic-response measures (Arias intensity, long-period ground motion, seismic analysis), and forced-response methods like Duhamel's integral.
Structured Matrices & Linear Maps	43	Abstractions about matrices defined by special entry patterns or algebraic constraints — banded, circulant, Hadamard, Hankel, and Pascal forms, doubly stochastic matrices — alongside factorizations like LU and Schur complement, and related linear maps, bilinear forms, and scalar operations.
Supply Chain & Inventory Management	29	Abstractions about coordinating production, inventory and fulfillment, including order policies like just-in-time and economic order quantity, decoupling points such as make-to-order versus make-to-stock, and failure modes like stockouts and order-batching distortion.
Surface Geometry & Projective Transforms	6	Abstractions about the geometry of surfaces and curves and how they are projected or transformed, covering surface-metric structures (First Fundamental Form, Cocurvature), duality and projection constructions (Dual Curve, Isometric Projection), and integral-geometric transforms like the X-Ray Transform.
Survival Analysis & Demographic Rates	16	Abstractions about modeling event timing and population-level rates, covering survival and hazard models (Accelerated Failure Time Model, Discrete-Time Proportional Hazards, Logrank Test), demographic and health measures (Life Expectancy, Gross Reproduction Rate, Frailty Index), and longitudinal or causal methods like Propensity Score Matching.
Syntactic Alignment & Reference Marking	6	Abstractions about how languages mark grammatical relations and rhetorical structure, spanning alignment and case-marking typology (transitive alignment, double-marking language), reference-resolution ambiguity (nearest referent), and phonological or rhetorical patterning (prodelision, chiasmus).
Syntax, Semantics & Grammar Theory	24	Abstractions about how sentences and discourse are structured and interpreted — clauses, constituents, case roles, ellipsis, and anaphora — spanning formal grammatical frameworks like the minimalist program, categorial grammar, and discourse grammar, and compositional semantic theories such as discourse representation theory.
Targeted Marketing & Distribution Models	5	Abstractions about tailoring marketing and distribution to individuals or segments, including audience-targeting strategies (influencer marketing, micromarketing, personalized marketing), a dynamic model of advertising response (Sethi model), and a mechanism for controlled digital content distribution (superdistribution).
Teaching Techniques & Skill Acquisition	17	Abstractions about concrete methods for structuring instruction and skill development — cooperative and dialogic classroom techniques (jigsaw, four corners, reciprocal teaching), language-teaching methods (natural approach, dogme, silent way), and models of how learners progress toward competence (gradual release of responsibility, Dreyfus model, transformative learning).
Temporal & Expectation Biases	8	Abstractions about systematic misjudgments of time, change and expectation, spanning forecasting biases (declinism, end-of-history illusion, exaggerated expectation), belief-updating errors (conservatism bias, hindsight bias), and expectation-comparison effects (expectancy disconfirmation, pratfall effect, cultivation theory).
Textile & Manufacturing Processes	8	Abstractions about physical fabrication techniques, including textile finishing methods like beetling and compaction, and manufacturing concepts such as boutique production, nesting and form-fit-function equivalence.
Theology & Scriptural Interpretation	5	Abstractions about religious thought and textual interpretation, spanning theological syntheses and methods (Christian humanism, queer theology, theistic evolution), and scriptural interpretive practices (tropological reading, textual criticism).
Thermodynamic & Transport Processes	34	Abstractions about energy and matter transport across physical, chemical, and biological systems, covering thermodynamic cycles and laws (heat engines, critical points, endothermic processes), flow phenomena (plug flow, diffusion, drainage systems), and process-specific mechanisms like fermentation and dewetting.
Thermodynamic Cycles & Engineering Measures	8	Abstractions about thermodynamic processes and engineering measurement in fluid and combustion systems, spanning refrigeration and cylinder mechanics (cascade refrigeration, single- and double-acting cylinders), phase-change and combustion phenomena (retrograde condensation, octane rating), and acoustic or enthalpy measurement tools (end correction, enthalpy-entropy chart).
Thermodynamic States & Processes	32	Abstractions about thermodynamic systems and their transformations, including state and process functions (Gibbs free energy, enthalpy, entropy), classifications of processes as spontaneous, exothermic or exergonic, phase-equilibrium relations (freezing-point depression, Duhem-Margules), and heat- or mass-transfer diagrams and methods.
Thermodynamics & Dissipative Systems	22	Abstractions about energy, its limits, and how systems gain or dissipate it, covering thermodynamic bounds and quantities (Carnot's theorem, energy conversion efficiency, thermodynamic activity, Maxwell's demon), dissipative structures and driven instabilities (galloping, diffusive-thermal instability, Fermi acceleration), and circuit, biomechanical, and signal-energy models that quantify losses.
Time-Frequency Signal Analysis	10	Abstractions about representing signals jointly in time and frequency — transform families (discrete-time Fourier transform, S transform, Wigner distribution function), techniques for suppressing artifacts or localizing content (modified Wigner distribution function, Hilbert spectral analysis), and elementary analyzing functions such as the modified Morlet wavelet.
Time-Series & Process-Variation Analysis	17	Abstractions about analyzing signals and processes over time, including spectral and structural estimation methods such as Bartlett's method, fractal analysis and recurrence plots, process-monitoring displays like run charts and seasonal subseries plots, and rhythm or segmentation concepts such as ultradian rhythm and time-series segmentation.
Tonal Harmony & Key Structure	14	Abstractions about tonal music's harmonic organization, including key and scale identity such as A-flat major, musical key and tonality, chord types and progressions like the diminished triad, Coltrane changes and pedal point, and formal or textural devices built on them such as the development section and homophony.
Topological & Functional-Analytic Spaces	13	Abstractions about classes of topological and functional-analytic spaces, including separation axioms, convexity and metrizability conditions, cones and boundaries, used to distinguish spaces by their topological or normed-space properties.
Topological Vector Spaces	10	Abstractions that classify locally convex and topological vector spaces by boundedness and duality properties — barrelledness variants (infrabarrelled space, countably quasi-barrelled space, DF-space), compactness-related classes (Montel space, Grothendieck space, scattered space), and set-theoretic coding devices such as Wallman compactification.
Transport Access & Mobility Constraints	5	Abstractions about how movement across space is enabled, restricted, or unequally distributed, including administrative and route-level controls such as internal border control and rat running, and structural determinants of access like maritime transport, threshold population and the transport divide.
Truth, Meaning & Argumentation	37	Abstractions about how truth, meaning, and reasoning are analyzed in philosophy and logic, including formal fallacies and argument evaluation (appeal to consequences, argument to moderation), theories of truth and reference (deflationary theory of truth, T-schema, direct reference theory), and semantic or logical frameworks (doxastic logic, relevance logic, propositional attitude).
Type Systems & Functional Constructs	20	Abstractions about how programs and expressions are typed, composed, and dispatched, covering type systems and theories (type inference, simply typed lambda calculus, intuitionistic type theory, kinds, bottom types), functional constructs (anonymous functions, Mogensen-Scott encoding, monad transformers), and classes, predicate dispatch, and Liskov substitution.
Unclustered & Miscellaneous	2769	Domain-specific abstractions that did not settle into a coherent structural family—either because their cluster had fewer than five members or because the cluster was too diffuse to name. This catch-all keeps the clustering's limits visible while preserving every entry.
Urban Planning Models & Settlement Forms	5	Abstractions about historical models for organizing urban and suburban growth — planned neighborhood and infrastructure frameworks (neighbourhood unit, green infrastructure), and settlement-morphology patterns such as ribbon development, the sector model and the urban transect.
Usability & Interaction Design Failures	13	Abstractions about how interfaces succeed or fail for users, including accessibility and Fitts's Law, biases like distinction bias, and specific failure modes such as mode errors, touch-target misses and progressive-disclosure breakdowns.
Vector Bundles & Classifying Constructions	11	Abstractions about vector bundles and constructions built from them — bundle types and structure (holomorphic, line, flat and inverse bundles, bundle metrics), bundle gerbes, and classifying spaces such as BO(n), alongside looser invariants and theorems (cohomological dimension, AD+, Arakelian's theorem).
Vector Spaces & Linear Structures	17	Abstractions that are built on vector spaces and linear structure — matrix and group classification (classical group, linear group, Frobenius normal form), core linear-algebraic operations (linear map, outer product, complex conjugate), and graded or multilinear extensions such as filtered algebra, triple system and W-algebra.
Visual & Cinematic Composition Techniques	26	Abstractions that shape how visual and narrative works are composed, depicted and read — cinematic techniques (Dutch angle, shot/reverse shot), pictorial depth and light cues (aerial perspective, shading, lighting ratio, motion lines), optical imaging effects (defocus, schlieren imaging), and contrast devices (foil, mise en abyme).
Visual Composition & Image Techniques	22	Abstractions about how images and moving pictures are made and perceived — color grading and color space, drawing and mark-making techniques like stippling and mass drawing, film-editing conventions such as the 180-degree rule and reaction shots — alongside perceptual effects like memory color and Troxler's fading.
Visual Perception & Media Representation	20	Abstractions about visual and cognitive phenomena that shape how images and interfaces are made and perceived — binocular rivalry, eye tracking, animation, cinematography, and graphical interfaces — and interpretive concepts like absolute metaphor, formalism, and visual rhetoric applied to art and media.
Warning Fatigue & Threat Response	12	Abstractions that loosely connect diminished or defensive responses to repeated warnings and threats, including habituation to alerts such as alarm fatigue, confirmation fatigue and public-warning fatigue, threat-driven social and psychological reactions like identity threat and culture of fear, and related concepts such as internal validity and balance of threat.
Wave Propagation & Elastic Media	20	Abstractions about how waves propagate, interact, and are measured in elastic and acoustic media, including named wave types and interface modes (Love wave, Stoneley wave, seismic anisotropy), boundary and transmission behavior (absorbing boundary condition, transmission coefficient, Zoeppritz equations), and coupling or attenuation effects (coupled mode theory, Manley-Rowe relations, anelastic attenuation factor).
Wave Propagation & Signal Sensing	13	Abstractions about how waves and signals propagate and are measured, covering acoustic phenomena (Acoustic Lobing, Acoustic Short Circuit, Phase Velocity), remote-sensing systems (Sodar, Radio Acoustic Sounding System, Photometric System), and signal-processing or exposure measures like Digital Down-Converter and Occupational Noise.
Wavelets & Function-Space Approximation	19	Abstractions about representing functions through transforms and structured bases, including wavelets and their duals, function spaces like Barron space, spectral methods, and capacity or ridge-function constructions used in approximation and decomposition.
Welfare Economics & Utility Theory	29	Abstractions about how economic value, welfare, and choice are modeled formally, including utility representations and preference structures (Leontief utilities, monotone preferences, multi-attribute utility), welfare and efficiency criteria (allocative efficiency, compensation principle, Atkinson index), and behavioral or strategic anomalies in decision-making (uncertainty effect, taste-based discrimination, signalling).
Welfare, Inequality & Well-Being Theories	7	Abstractions about social welfare and subjective well-being, including efficiency and equity principles like Kaldor-Hicks and Pigou-Dalton, happiness paradoxes like the Easterlin paradox and hedonic treadmill, and theories of inequality and preference.
Work, Care & Occupational Exclusion	6	Abstractions about how work demands, care responsibilities, and disability intersect with social structure, including measures and theories of labor participation (absence rate, compatibility-with-childcare theory, conservation of resources theory), workplace hazard control (hazard elimination), and structural exclusion from meaningful occupation (occupational apartheid, social model of disability).
Written Language & Typographic Convention	11	Abstractions about how written text is composed, formatted, and read — orthographic and shorthand encoding systems like spelling and the stroke count method, typographic layout conventions such as indentation, sentence spacing, and widows and orphans, and the cognitive processes of word recognition, guessing, and writing.