Collective Memory

Collective memory is the shared representation of the past that a group maintains through institutional, ritual, and communicative processes, constituting part of the group's identity and shaping present behavior. The concept encompasses: (1) a set of events, persons, places, and narratives held in common across group members as significant to collective identity, (2) institutional and material substrates that stabilize shared content over time (monuments, holidays, textbooks, rituals, archives, media, commemorative practices), (3) transmission processes through which each generation acquires the shared content, often in modified form (teaching, storytelling, public observance, family transmission, commemoration), and (4) a recursive relation to group identity: the memory partially constitutes what it means to belong, and membership partially determines what counts as accurate memory. Halbwachs 1925 established that remembrance is socially framed; individual memory exists within shared frameworks supplied by society<!-- FACT-D28-016 -->[^halbwachs-1925].

Representation

Collective memory is the specific shape representation takes when a group encodes its shared past through institutions, rituals, and narratives.

Collective memory is the specific shape representation takes when the target is a group's past — events, persons, narratives — and the medium is the distributed system of monuments, holidays, textbooks, rituals, and commemorative practices through which that past is held in common. It is a structurally-particularized instance of structured mapping from target to medium under a faithfulness convention, with the added commitments that the medium is socially distributed rather than individual, the mapping is reproduced across generations through transmission, and the representation feeds back to constitute the group's identity rather than merely standing for an external object.


Collective Systemic Learning

Collective Systemic Learning is the capacity of a multi-component system—an organization, team, research consortium, open-source community, or ecosystem—to deliberately or emergently collect experiences, detect patterns, update internal processes and structures, and continuously adapt or innovate as a whole, rather than remaining static or dependent on isolated individual learning<!-- FACT-D32-121 -->[^senge-1990]. The essential commitment is that learning occurs at the system level, not merely at the level of individual members, and is embedded in processes, structures, documentation, and culture that make learning organizational rather than personal and transient<!-- FACT-D32-122 -->[^argyris-schon-1978]; that collective learning requires mechanisms for knowledge capture (converting individual and localized experience into organizational knowledge), integration (connecting insights across sub-units and domains), and diffusion (propagating learning so it informs future decisions across the system)<!-- FACT-D32-123 -->[^nonaka-takeuchi-1995]; that systems capable of collective learning adapt faster to environmental change, recover more effectively from disruptions, develop more robust solutions (combining distributed expertise), and evolve capabilities that exceed what any individual member could develop independently<!-- FACT-D32-124 -->[^levitt-march-1988]; and that collective learning is distinct from aggregated individual learning: the organization becomes smarter than the sum of its members, developing organizational memory, shared mental models, and institutionalized practices that persist across individual turnover.

Learning

Collective systemic learning is a specialization of learning in which the agent doing the updating is a multi-component system rather than an individual.

Collective systemic learning is a kind of learning specialized by the locus of the durable update: the learning agent is an organization, team, consortium, or community rather than an individual mind. It inherits learning's general commitment to durable, experience-driven self-update of an agent's internal capability, and adds the specific machinery of system-level acquisition — knowledge capture, integration, embedded processes, structures, documentation, and culture — that makes the update organizational rather than personal and that lets the system as a whole adapt while individual members come and go.


Color Harmony

Color harmony is the deliberate, principled arrangement of colors within a palette or composition such that their relationships create aesthetic unity, emotional resonance, or visual coherence rather than discord or visual chaos. The essential commitment is to *relational color design*: not merely choosing colors in isolation, but orchestrating them according to structural principles (complementary opposition, analogous adjacency, triadic balance, or tetrad complexity) such that the viewer or user perceives them as a coordinated ensemble with psychological and aesthetic purpose. Every act of color harmony entails (1) the selection of a color theory framework (hue, saturation, value; the color wheel; tonal relationships) that constrains choice to a principled set, (2) the specification of dominant, secondary, and accent colors with clear functional hierarchy, (3) the establishment of visual unity through color repetition across elements while maintaining distinction through variation in saturation or value, (4) the psychological or emotional intent the color palette is meant to evoke or reinforce (calm, energy, sophistication, trust, danger), and (5) the recognition that color relationships are context-dependent—the same hue appears different against different backgrounds and alongside different neighboring colors. The deeper insight from Itten (1975), Albers (1963), and gestalt color perception is that color is fundamentally relational: colors do not have intrinsic properties independent of their context; a given blue appears cooler in the presence of orange, warmer in the presence of green. Color harmony thus requires understanding both color theory (the objective principles of hue, saturation, value) and color perception (the subjective, context-dependent ways colors interact). The practice originated in painting, drawing, and natural observation (Goethe's *Theory of Colours* linking color to natural phenomena; Munsell's systematic color notation) and has evolved into a foundational principle across visual design (graphic design, branding, fashion, interior design), user-interface design (digital color systems, accessibility requirements), data visualization (color mapping for distinctions and meanings), and psychology (color's effects on mood, behavior, and decision-making)<!-- FACT-D36-046 -->[^itten-1975-1].

Unity & Variety

Color harmony presupposes unity and variety because harmonious palettes balance shared color relationships against the differentiation needed for visual interest.

Color harmony presupposes unity and variety because its central achievement — a palette that reads as coordinated rather than discordant — operates by balancing unifying color relationships (analogous hues, shared saturation, consistent value range) against the variety needed to avoid monotony (complementary contrast, triadic span, accent introduction). Without unity-and-variety's prior structure of relational balance between coherence and differentiation, there is no evaluative dimension along which a palette can be judged harmonious. Color harmony inherits this balancing structure and specializes it to the hue, saturation, and value relations of a color set.


Commensurability

Diverse values expressed in common metric enabling comparison.

Commensurability is the structural property that enables diverse quantities or values to be expressed in a common unit or metric, allowing them to be compared, ranked, and traded off, a process Espeland and Stevens (1998) characterize as a fundamental social mode of valuation. <!-- FACT-D53-076 -->[^espeland-stevens-1998] Without commensurability, heterogeneous dimensions remain incommensurable—incomparable in principle. It is the prerequisite for any aggregation, ranking, or trade-off decision across multiple, initially disparate value dimensions.


Commitment Device

A self-imposed constraint that binds one's own future choices.

A commitment device is the structural pattern in which an agent, anticipating that a *later* self (or a later state of the world) will be tempted to deviate from a currently preferred course, deliberately alters the future choice set *now* — removing options, raising the cost of defection, or delegating the choice away — so that the tempting action becomes impossible or unattractive. The essential commitment is *strategic self-limitation against time-inconsistent preferences*: voluntarily shrinking one's own future freedom to make the desired behavior the path of least resistance, a logic Strotz (1955) first formalized in his analysis of how a rational agent who foresees the inconsistency of his future preferences will "precommit" by constraining the actions available to his later self. <!-- FACT-D54-211 -->[^strotz-1955] The pattern presupposes a divided agent — a present self who knows what it wants and a future self who, under the pull of temptation, immediate reward, or changed incentives, will want something different — and resolves the conflict in the present self's favor not by strengthening resolve but by foreclosing the option to renege, a move Schelling (1960) recognized as the strategic essence of binding oneself to gain credibility or self-control. <!-- FACT-D54-212 -->[^schelling-1960]

Constraint

A commitment device presupposes constraint because its function is to deliberately restrict the future feasible set of one's later self.

A commitment device works by deliberately altering the future choice set so that tempting deviations become impossible or costly — voluntarily imposing a binding restriction on one's later admissible actions. Without constraint's machinery of binding restriction on admissible configurations, there would be no structural difference between announcing an intention and locking in a course: the device's whole logic is to convert a soft preference into a hard constraint. The parent prime supplies the binding-restriction structure that the commitment device deploys against time-inconsistent preferences.

Temporal Inconsistency and Preference Reversals

Commitment devices presuppose temporal inconsistency because the strategic self-limitation only makes sense when a later self will be tempted to deviate.

A commitment device is a deliberate restriction of one's future choice set imposed by the present self to bind a later self against tempting deviation. The strategy is only intelligible when later preferences are expected to differ from current ones in a predictable way — when the agent anticipates preference reversal as the future becomes present. Temporal inconsistency names exactly this pattern: the same information and goals produce reversed preferences as horizon shortens. Commitment devices presuppose this dynamic as the threat they are designed to neutralize through preemptive self-binding.


Commutativity

Commutativity is the order-independence-of-inputs principle that: (1) **for an operation $\circ$ on a set, swapping the order of operands does not change the result** — formally, $a \circ b = b \circ a$ for all $a, b$ in the set; the simple axiom has profound consequences because it removes one dimension of sequencing that must otherwise be tracked, enabling reordering, parallelization, and algebraic manipulations that are unavailable in non-commutative settings; (2) commutativity is a property *of a specific operation on a specific structure*, not a property of a set alone — addition and multiplication of integers are commutative, but subtraction and division are not; matrix multiplication is non-commutative (in general $AB \neq BA$)[^cayley-1858]; function composition is typically non-commutative ($f \circ g \neq g \circ f$); string concatenation is non-commutative; quaternion multiplication is non-commutative, as Hamilton (1843) established in introducing the quaternion algebra in which $ij \neq ji$<!-- FACT-D39-001 -->[^hamilton-1843]; rotations in 3D are non-commutative (rotating about two different axes produces different results depending on order); (3) commutativity supplies **a standard reasoning pattern for reordering freedom and parallelization** — if an operation is commutative, terms in a summation, factors in a product, or operations in a pipeline can be reordered for clarity, optimization, or parallelization without affecting results; commutativity also underpins abelian algebraic structures (abelian groups, commutative rings, fields), as Boole (1847/1854) prefigured in formalizing the commutativity of conjunction and disjunction in the algebra of logic<!-- FACT-D39-004 -->[^boole-1847] which admit simpler theory than their non-commutative counterparts; the absence of commutativity forces careful sequencing and is itself meaningful — non-commutativity is a feature in contexts where order matters (time-ordered quantum mechanics, sequential message processing); (4) the concept generalizes across domains — **mathematics** (algebraic axioms; abelian structures; commutative diagrams in category theory, as Mac Lane (1971) systematizes in *Categories for the Working Mathematician*)<!-- FACT-D39-014 -->[^mac-lane-1971], **computer science** (parallelism — commutative updates parallelize without synchronization; CRDTs rely on commutativity of merge operations; commutative database transactions conflict less), **physics** (commuting observables in quantum mechanics share eigenstates; non-commuting observables satisfy uncertainty relations)[^heisenberg-1925], **linguistics** (word-order freedom in some languages; syntactic commutativity in coordinate constructions), **social dynamics** (some social interactions are order-independent — greeting protocols — while others are path-dependent) — all deploy the reorder-without-effect structural pattern.

Invariance

Commutativity is a kind of invariance: the result of a binary operation is preserved under the swap-of-operands transformation.

Commutativity says that a o b equals b o a for all elements, so the result of the operation is unchanged under the transformation that swaps the operand order. That is the precise structure of Invariance: a named feature (the operation's value) preserved under a named family of transformations (operand permutation). Commutativity specializes invariance by fixing the operation as a binary combiner and the transformation as the order-swap on its two arguments.

Symmetry

Commutativity is a specialization of symmetry in which the transformation group permutes the operands of a binary operation.

Commutativity is a specialization of symmetry in which the symmetry group is the swap of operands and the operation is left invariant under that swap: a circ b equals b circ a for all operands. It inherits the general symmetry commitment that a system is invariant under a specified group action, and specializes by fixing the group to the two-element permutation of operands of a binary operation. When this swap symmetry holds, sequencing collapses one dimension and unlocks reordering, parallelization, and algebraic manipulations unavailable in non-commutative settings.


Comparative Advantage

Comparative advantage is the principle that an agent (country, firm, individual) should specialize in producing those goods or services whose production entails the lowest *opportunity cost* relative to alternative agents, even when that agent has no absolute advantage in any production, and that the resulting pattern of specialization and exchange yields mutual gains for all participants. The essential commitment is that the *relative* efficiencies — not absolute ones — determine the welfare-improving pattern of production, and that trade based on comparative advantage is (under the standard assumptions) positive-sum, with each party better off after specialization and trade than in autarky. <!-- FACT-D09-100 -->[^ricardo-1817] Every comparative-advantage articulation specifies (1) the agents under consideration — countries (the classical setting), firms, individuals, teams; (2) the goods or tasks that can be produced by either agent — typically at least two, to make the opportunity-cost comparison meaningful; (3) the technology of production — typically constant-returns (Ricardian) or with factor intensities (Heckscher-Ohlin); (4) the terms of trade between the goods that allow both parties to benefit — any price ratio strictly between the two agents' opportunity-cost ratios yields mutual gains; and (5) the institutional setting — free trade, tariffs, quotas, transport costs, transaction costs. The construct is associated with Ricardo (1817), who formalized it in his *Principles of Political Economy* with the canonical England-Portugal / cloth-wine example, though it builds on earlier work by Smith (1776) on absolute advantage, and it remains the foundational theoretical case for gains from trade in economics. <!-- FACT-D09-100 -->[^ricardo-1817]

Exchange

Comparative advantage presupposes exchange because the welfare-improving specialization it recommends only materializes when surpluses are actually traded.

Comparative advantage presupposes exchange because the principle recommends specialization based on relative opportunity costs precisely so that the specialized output can be exchanged for surplus from other specialists. Without exchange's bilateral conditional-transfer structure, specialization just produces lopsided autarkic outputs and no mutual gain. Exchange supplies the substrate on which the positive-sum claim is cashed out: the agents involved must trade for the comparative-advantage allocation to be welfare-improving rather than welfare-destroying, so the principle is parasitic on the availability of exchange.

Opportunity Cost

Comparative advantage is the specific shape opportunity cost takes when production decisions are compared across agents with different alternative-use profiles.

Comparative advantage is the specific shape opportunity cost takes when the choice context is the allocation of production across multiple agents, and the relevant comparison is each agent's opportunity cost of producing one good relative to another. It is a structurally-particularized instance of evaluating choices by the value of the best forgone alternative, with the added commitments that the comparison is interpersonal — not within one agent's options but across agents' relative trade-offs — and that the welfare result is positive-sum specialization-and-trade based on relative rather than absolute production efficiencies.


Comparative Method

comparative analysis
comparative-historical method

Systematically juxtaposing selected cases so that their similarities and differences do the causal-inference work that controlled experiments cannot.

Comparative Method is a family of research techniques characterized by (1) the systematic juxtaposition of multiple cases — societies, eras, organizations, phenomena — selected to permit inferences about what is common across the cases, what varies, and why, (2) a substitute-for-experiment logic in domains where controlled experimentation is impossible, such that case selection does the inferential work that randomization does in experimental science, (3) two classical designs (following Mill's methods of agreement and difference): most-similar design comparing cases that share most features and differ on the outcome of interest, and most-different design comparing cases that differ on most features but share the outcome, and (4) a characteristic set of failure modes (small-N inference limits, selection bias, unit-of-analysis problems) that mature practice addresses through explicit case-selection justification.<!-- FACT-D40-001 -->[^bloch-1928]

Comparison

The comparative method is the specific shape comparison takes when it becomes a substitute-for-experiment research design across selected cases.

The comparative method is the specific shape comparison takes when it becomes a systematic research strategy in domains where controlled experimentation is impossible. Comparison's general anatomy — comparands, shared frame, alignment rule, output relation — is structurally particularized into selected societies, eras, or organizations as comparands; Mill's methods of agreement and difference as alignment rules; and inferences about what varies and why as outputs. The general operation is preserved; the specific shape is its disciplined deployment as inferential substitute for randomization through deliberate case selection.


Comparison

Place items in a shared frame along chosen dimensions to read off a relation between them.

Comparison is the structural operation of placing two or more items — the *comparands* — under a shared frame, selecting one or more dimensions along which they will be co-considered, applying an alignment rule that makes them commensurable enough to relate, and reading off an output relation: same or different, greater or lesser, analogous or unmatched, ranked or unranked. The cognitive-science treatment by Holyoak and Thagard (1989) characterizes this as a constraint-satisfaction process running over structural, semantic, and pragmatic constraints — a formal model of the role-slots the operation requires.<!-- FACT-D56-181 -->[^holyoak-thagard-1989] It turns isolated properties of individual items into *relational information* between them. The operation is what cognitive scientists, philosophers of method, and statisticians have all converged on as a foundational move of structured thought — Tversky's (1977) feature-matching account treats similarity itself as the output of a comparison process over weighted feature sets, parameterized by direction and salience.<!-- FACT-D56-182 -->[^tversky-1977]


Compatibility

The relational condition under which two or more entities can coexist or compose without breakage, interference, or contradiction.

Compatibility is the capacity of two or more entities—systems, components, standards, formats, agents, processes—to coexist, interact, or compose without breakage, interference, or contradiction. It names a relational property: not an intrinsic quality of a single entity, but a condition between entities, an attribute Rogers (2003) places at the center of his classic account of how innovations diffuse through social systems. <!-- FACT-D52-106 -->[^rogers-2003] A plug and socket are compatible when their physical and electrical signatures align; a library version and an application are compatible when their API contracts align; a blood type and a recipient's immune system are compatible when immune rejection does not occur; an organizational culture and a new hire are compatible when social norms and values align sufficiently.


Competition

rivalry contest competitive_pressure vying

Rivalrous pursuit of a scarce prize where one party's gain is another's loss.

Competition is the structural pattern in which multiple agents pursue the same scarce resource, position, or reward under conditions where one party's gain reduces what remains for others — a *rivalrous payoff*. The essential commitment is *negatively coupled fitness*: success is relative rather than absolute, so each participant's outcome depends not only on its own performance but on the performance of every rival contesting the same prize. This coupling generates selective pressure that rewards relative advantage and drives continual adaptation, differentiation, or escalation. <!-- FACT-D54-226 -->[^darwin-1859] The concept emerges most cleanly from evolutionary biology, where Darwin (1859) framed the "struggle for existence" as the engine of natural selection, but it generalizes with remarkable fidelity across ecology, economics, sports, politics, attention markets, and computer science. <!-- FACT-D54-227 -->[^darwin-1859]


Completeness

The Cauchy criterion of 1821 (Cauchy, *Cours d'analyse*) is the originating articulation of the no-gaps idea in analysis: a sequence converges if and only if it is Cauchy, which characterises completeness as the structural property of a metric system in which internal sequence-processes terminate inside the system. **Completeness is the no-gaps-in-the-structure principle that names the condition under which a system's internal processes (convergence, deduction, coverage, the construction of canonical extensions) have their natural terminations *inside the system itself* rather than escaping to a larger ambient structure.** <!-- FACT-D39-062 -->[^cantor-dedekind-1872]<!-- FACT-D39-061 -->[^cauchy-1821]


Complexity

Complexity is the intricacy-and-interaction principle that: (1) **a system is complex to the degree that describing its behavior, predicting its outcomes, or controlling its dynamics requires information, computation, or coordination disproportionate to the system's apparent size** — complexity arises from the number of components, the density and non-linearity of their interactions, the presence of feedback loops, and the emergence of system-level properties not present in components; distinct traditions give the concept distinct formalizations, yet they share a common core — that some systems resist compression, prediction, or closed-form analysis; (2) the concept has distinct formalizations that are equally-originated and not reducible to one another: **computational complexity** (resources — time, space, communication — required by algorithms to solve problems; complexity classes P, NP, PSPACE, EXP); **descriptive complexity** (Kolmogorov complexity — length of the shortest program that generates a string); **systems complexity** (complex adaptive systems with many interacting agents, feedback, emergence); **organizational complexity** (number of roles, interfaces, coordination requirements in organizations); **structural complexity** (graph or network metrics — diameter, clustering, modularity); (3) complexity supplies **a standard reasoning pattern for deciding how to tame or live with difficulty** — decomposition (finding near-independent modules and reducing inter-module complexity), abstraction (suppressing detail at appropriate levels), approximation (accepting bounded error to gain tractability), layering (nested levels of detail), heuristic or statistical methods (when exact solution is infeasible), simulation (when analytical solution is infeasible); (4) the concept generalizes across domains — **computer science** (algorithmic complexity, P vs. NP, complexity classes), **mathematics** (Kolmogorov complexity, entropy-based measures), **systems science** (emergent behavior, complex adaptive systems, chaos), **biology** (metabolic, neural, ecosystem complexity), **organizational management** (coordination costs, Conway's law, organizational design), **engineering** (software, aircraft, infrastructure complexity management), **economics** (market complexity, macroeconomic nonlinearity) — all diagnose some version of "this is harder than its surface suggests, and specific tools are needed."


Complexity (Time/Space)

Computational complexity measures how resource usage (time — number of elementary operations, space — memory consumed) scales with problem size, enabling prediction of feasibility and performance independent of machine-specific constants. The essential commitment is that asymptotic *growth rate* — not absolute execution time — determines whether an algorithm remains practical under increasing inputs, and that distinguishing polynomial-time from exponential-time problems provides a fundamental taxonomy of practical solvability.

Constraint

Computational complexity is a specific kind of constraint, binding admissible algorithms to those whose resource growth rate keeps problems practically solvable.

Computational complexity is a specialization of constraint. The general pattern restricts admissible configurations to those satisfying a binding condition, with the feasible set as a first-class object. Complexity instantiates this with the binding condition being asymptotic resource growth: algorithms whose time or space scales as polynomial in input size are admissible for large instances, while exponential-time procedures are practically infeasible. The polynomial-versus-exponential boundary partitions the algorithmic feasible set, supplying a machine-independent admissibility criterion that governs which problems can be solved at scale.

Scaling and Scale Dependence

Computational complexity is the specific shape scaling takes when the system is an algorithm and the resource cost grows with input size.

Computational complexity is the specific shape scaling and scale dependence takes when the system in question is an algorithm and the property changing qualitatively with size is resource usage -- time or space. The qualitative-shift signature that scale dependence names appears as the polynomial-versus-exponential boundary: an algorithm efficient at small inputs may be infeasible at large ones not from implementation error but from asymptotic growth rate. Big-O classification is the scale-dependence taxonomy of computational systems.


Composition

Arranges components into a cohesive whole.

Composition is the deliberate, structured arrangement of visual or conceptual elements into a unified whole such that their spatial relationships, visual weight distribution, rhythm, and directional flow create coherence, guide attention, and achieve aesthetic or functional intent. The essential commitment is to *relational design*: not merely placing elements on a surface or in a system, but orchestrating them such that the viewer or user perceives them as a structured ensemble rather than a collection of separate items. Every act of composition specifies (1) a primary organizing principle (symmetry, asymmetrical balance, diagonal tension, hierarchical centrality, modular repetition), (2) the visual or conceptual weight and spatial distribution of elements relative to a containing frame or field, (3) paths of movement or emphasis that guide the perceiver's eye or cognition through the work, (4) the intervals, ratios, and relational distances between elements that establish rhythm or harmony, and (5) a unity that emerges from the coherence of these relationships. The classical insight from Arnheim and Lauer-Pentak is that human perception is fundamentally relational—we perceive individual elements not in isolation but in relation to others—and composition is the discipline of making those relations intentional, transparent, and generative of meaning. The practice originated in painting and drawing (Renaissance studio training, rule-of-thirds conventions, tonal composition principles) and has evolved into a foundational pattern across visual design (graphic design, photography, film framing), spatial design (architecture, landscape, interior design), narrative and temporal arts (music structure, literary narrative flow, film editing), and information design (data visualization, dashboard layouts, user-interface hierarchies)<!-- FACT-D36-001 -->[^arnheim-1974].

Gestalt Principles

Composition presupposes Gestalt principles because deliberate arrangement of elements into a unified whole relies on the perceptual grouping rules Gestalt names.

Composition presupposes Gestalt principles because the orchestration of visual or conceptual elements into a perceived unified whole — its central commitment — works through the perceptual mechanisms by which observers group discrete stimuli into structured wholes: proximity, similarity, continuity, closure, figure-ground, common fate. Without Gestalt's prior grouping operations, the compositional arrangement would register only as a collection of separate items rather than as a coherent ensemble. Composition inherits Gestalt's grouping-rule apparatus and deploys it intentionally, treating the perceptual rules as design levers for guiding attention, weighting elements, and producing coherence.


Compositionality

Compositionality is the principle that: (1) the meaning or behavior of a complex expression is **determined** by the meanings or behaviors of *the constituent meanings* and the rules by which the parts are combined; (2) the determination is **systematic** — the same parts under the same rules yield the same whole — so a finite stock of parts and rules can generate an unbounded family of expressions; (3) the determination is **compositionally local** — *the combination rules* ensure each combination step depends only on its immediate constituents, not on the surrounding context or on the history of how those constituents were formed; (4) compositionality is simultaneously a design stance (build systems out of well-specified parts and combinators) and an explanatory claim (observed systems can often be *analyzed* this way).


Compression

Compression is the encoding of information in a representation shorter than the original, exploiting redundancy (statistical regularity, structural predictability, perceptual unimportance)<!-- FACT-D25-166 -->[^mackay-2003] to reduce the number of symbols, bits, or physical resources required to store or transmit it — either *losslessly* (exact reconstruction possible)<!-- FACT-D25-167 -->[^cover-thomas-2006] or *lossily* (controlled approximation, accepting some degradation for much greater reduction). The essential commitment is that raw information representations generally contain redundancy that can be eliminated without reducing — and often with corresponding increase in — their effective utility, and that the Shannon limit sets a hard lower bound on lossless compression (the entropy of the source) below which no lossless encoding can reach. Every compression articulation specifies (1) the source model — what is being compressed (text, image, audio, video, scientific data, code)<!-- FACT-D25-169 -->[^rissanen-1978] and its statistical or structural properties; (2) the loss discipline — lossless (exact reconstruction, bounded by entropy) or lossy (controlled fidelity loss, subject to distortion-rate tradeoffs); (3) the algorithm — entropy coding (Huffman, arithmetic, ANS)<!-- FACT-D25-170 -->[^huffman-1952], dictionary methods (LZ77, LZ78, LZW), transform coding (DCT, wavelet), predictive coding, perceptual models; and (4) the use context — storage vs transmission, one-shot vs streaming, latency-sensitive vs bandwidth-sensitive, correctness-critical vs approximable. The construct has roots in Shannon's 1948 foundational information theory<!-- FACT-D25-171 -->[^shannon-1948], Huffman's 1952 prefix code<!-- FACT-D25-172 -->[^huffman-1952], Lempel-Ziv's 1977/78 dictionary methods, and the rich subsequent literature on transform and neural compression.

Abstraction

Compression is a specialization of abstraction in which the retained structure is information-theoretic regularity and the discarded structure is the redundancy.

Compression is a specialization of abstraction in which the purpose-relative retention is reduction of representational length: keep the information-theoretic content needed for exact or approximate reconstruction, drop the statistical or perceptual redundancy. It inherits abstraction's general commitment to purpose-relative retention of structure with explicit naming of what is kept and dropped, and specializes by fixing the purpose to storage or transmission economy and the projection to one that shortens symbol count, with the Shannon limit setting the floor on lossless reduction.

Aggregation

Compression is a kind of aggregation: it collapses redundant detail into a unified shorter representation while retaining chosen structure.

Compression encodes information in a shorter representation by exploiting redundancy, deliberately losing or restructuring detail to retain the features that matter for reconstruction or downstream use. That is the move of Aggregation: collapsing many items into a unified form that keeps chosen features while suppressing granular detail. Compression specializes aggregation by tying the suppressed detail to redundancy or perceptual unimportance and by holding a reconstruction or fidelity criterion as the design constraint.

Optimization

Compression is a kind of optimization: it minimizes representation length subject to a reconstruction-fidelity constraint.

Compression seeks the shortest encoding of a source under a chosen fidelity criterion — exact reconstruction for lossless, bounded distortion for lossy — and trades coding cost against quality at the chosen operating point. That is the optimization triplet: decision variable (the encoding), objective (representation length), and constraint (fidelity). Compression specializes optimization to the encoding-length objective, with rate-distortion theory and entropy bounds setting the achievable frontier.


Conceptual Blending

Conceptual blending is the cognitive operation of constructing a new integrated mental space — the "blend" — from two or more input mental spaces, by selectively projecting elements from the inputs into the blend and allowing emergent structure and meaning to arise in the blend that is not present in any single input. The essential commitment is that the blend is not a union, intersection, or analogical copy of the inputs but a genuinely new cognitive construction with its own structure, running pattern, and inferences, causally connected to the inputs through a generic space that captures what they share structurally. Every blending claim specifies (1) two or more input spaces with distinguishable elements and relations, (2) a cross-space mapping identifying correspondences between input elements, (3) selective projection from inputs into a blended space, and (4) emergent structure in the blend — composition, completion, and elaboration that yields meaning beyond what any input provides.

Analogy

Conceptual blending presupposes analogy because cross-space projection into a blended space relies on prior structural mapping between the input domains.

Conceptual blending presupposes analogy because constructing a blended space by selectively projecting elements from two or more input spaces requires a cross-space mapping that identifies correspondences between elements — exactly the structural role-alignment that analogy supplies. Without analogy's relational mapping between source and target domains, there would be no correspondence structure to feed selective projection, and the blend could not preserve a coherent generic space capturing what the inputs share. Analogy supplies the mapping operation; blending adds the further move of constructing a new integrated space with emergent structure not present in either input alone.


Concurrency

Concurrency is the ability of a system to manage *multiple independent or interdependent processes occurring simultaneously*, often requiring explicit coordination, synchronization, or conflict resolution. The essential commitment is that separate loci of execution or activity proceed in time-overlapping fashion, raising questions of *ordering, resource contention, and logical correctness* under concurrent interleaving.


concurrent engineering
simultaneous cross-functional teams
integrated team-based development
parallel collaboration

Concurrent, Cross-Functional Collaboration is an organizing principle and practice for product development and complex project work characterized by (1) the simultaneous engagement of specialists from different functional disciplines (design, engineering, manufacturing, marketing, operations, quality assurance) from the earliest phases of the project, rather than sequential handoff from one function to the next, (2) the establishment of tight communication feedback loops and shared decision-making authority among those specialists such that insights and constraints from each function inform design decisions in real time, (3) the explicit commitment to discovering and resolving integration conflicts before they are embedded in downstream work, and (4) the recognition that the cost of rework and delay from sequential discovery of conflicts far exceeds the cost of upfront coordination. The deeper insight is both temporal and epistemic: temporal, in that waiting for one phase to complete before the next begins guarantees that discoveries in later phases will necessitate expensive rework in earlier phases; epistemic, in that no single function has complete knowledge of the problem — a designer may create beautiful interfaces that the operations team cannot support, an engineer may design mechanisms that manufacturing cannot produce economically, and a business team may commit to timelines that ignore technical reality. Only through concurrent, real-time collaboration can these conflicts surface early enough to be resolved through redesign rather than through costly after-the-fact patches. The practice originated in concurrent engineering (1980s–1990s, driven by Japanese manufacturing emphasizing parallel development of product and process) and formalized through cross-functional team structures, agile development, and product development process methodology (Clark and Fujimoto 1991, Wheelwright and Clark 1992). The mechanism works because information flow is bidirectional and immediate: a manufacturing engineer's insight about process constraint shapes the designer's part geometry; the designer's early concept shapes what manufacturing expertise is required; the marketer's understanding of customer need shapes both; and feedback occurs before irreversible commitments are made<!-- FACT-D35-016 -->[^clark-fujimoto-1991].

Coordination

Concurrent cross-functional collaboration is a specialization of coordination — specifically, coordination among diverse-discipline specialists working simultaneously on a shared design problem.

Concurrent cross-functional collaboration is a specialization of coordination in which the actors being aligned are specialists from different functional disciplines and the alignment occurs simultaneously rather than through sequential handoff. Where coordination names the active alignment of independently controlled actors toward a coherent collective outcome generally, this specialization fixes the actor composition (cross-functional), the temporal structure (concurrent), and the medium of alignment (tight communication loops with shared decision authority around design integration).

Task Interdependence

Concurrent cross-functional collaboration presupposes task interdependence because its simultaneous engagement is justified only when functional tasks have reciprocal couplings.

Concurrent cross-functional collaboration is justified only when the tasks being performed are reciprocally interdependent — when design, manufacturing, and operations decisions iteratively shape one another rather than feeding forward in a fixed sequence. Without task interdependence's machinery of workflow coupling, the simultaneous engagement of multiple specialists would be wasteful: tasks that are merely pooled or sequential need only sequential handoff. The reciprocal interdependence supplies the structural condition that makes concurrent engagement the efficient coordination form.


Conditioning (Behavioral)

Behavioral conditioning is a family of learning mechanisms by which an organism detects statistical contingencies between environmental events and adjusts internal state and behavior to reflect those contingencies. The family comprises four structural components: (a) *stimulus-response pairing or contingent reinforcement* — events are linked in time or by consequence, establishing a predictive or instrumental association; (b) *response strengthening through consequence pairing* — repeated pairings modulate the probability and vigor of the response; (c) *generalization and discrimination* — the learned association extends to similar stimuli or contexts (generalization) and narrows when reinforcement is withheld for non-target stimuli (discrimination); and (d) *extinction under non-reinforcement* — withdrawal of the contingent outcome weakens the association, though complete erasure does not occur (spontaneous recovery demonstrates this persistence). conditioning comprises four core mechanistic components: stimulus-response pairing, response strengthening, generalization-discrimination, and extinction-recovery.<!-- FACT-D18-016 -->[^baum-2017]

Learning

Behavioral conditioning is a specialization of learning; it is the family of contingency-detection mechanisms that durably update behavior through pairing.

Learning is the process by which an agent durably updates an internal capability — knowledge, skill, model, or behavior — as a result of experience. Behavioral conditioning is the specific family of learning mechanisms that detect statistical contingencies between environmental events (stimulus-response pairings, contingent reinforcement) and adjust behavior accordingly, with generalization, discrimination, and extinction as characteristic features. It inherits learning's durable-experience-driven-self-update structure and adds the specific mechanism — contingency detection through pairing — that produces the update. A specialization of learning keyed to associative contingency.

Feedback

Behavioral conditioning presupposes feedback because learned associations are forged by routing the consequence of a response back to modulate the response itself.

Behavioral conditioning depends on the closure of a loop between behavior and consequence: the organism emits a response, the environment delivers reinforcement or punishment, and the returned signal modulates the probability of the response on the next cycle. Without the feedback arrangement — output measured, returned along a path, coupled with a sign that strengthens or weakens — the contingencies that conditioning detects could not be detected, and the response-strengthening and extinction dynamics could not arise. Feedback is the structural substrate on which conditioning operates.


Confidence Intervals

A confidence interval is the interval-estimate-with-calibrated-coverage principle that: (1) **a confidence interval is an interval [L(X), U(X)] computed from sample data X that, under repeated sampling from the same data-generating process, covers the true unknown parameter value θ with a pre-specified long-run frequency 1−α (typically 95%, sometimes 90% or 99%) — formally, P(L(X) ≤ θ ≤ U(X)) ≥ 1−α under the assumed probability model and sampling design; the coverage probability is a property of the procedure (the construction rule for L and U), not of any particular realized interval once data are observed, and it is this long-run frequency calibration that distinguishes frequentist confidence intervals from Bayesian credible intervals (which have direct probability interpretations for the specific observed data given a prior)**; the canonical modern formulation is due to Jerzy Neyman 1937 ("Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability," *Philosophical Transactions*), though earlier work by Fisher on fiducial intervals and by Laplace on inverse-probability intervals anticipated aspects; Neyman's construction — invert a family of hypothesis tests to produce the interval of parameter values not rejected at level α — provides the general recipe, and the duality between confidence intervals and hypothesis tests (#434) is fundamental: a 95% CI excludes a null value if and only if a two-sided test of that null rejects at α = 0.05; (2) the concept has **several identifiable components and distinctions**: *confidence coefficient or confidence level* (1−α, the nominal long-run coverage), *confidence interval width* (range of plausible values, reflecting precision; narrower for larger samples and lower variability), *one-sided versus two-sided intervals* (bounded above, below, or both), *exact versus approximate intervals* (exact under assumed model versus asymptotic normal-theory approximations), *Wald interval* (point estimate ± z × SE — the common but sometimes-poor approximation), *likelihood-ratio interval* (inverting likelihood-ratio tests), *score interval* (Wilson interval for binomial proportions; inverting score tests), *exact interval* (Clopper-Pearson for binomial; Fisher's exact for contingency tables), *bootstrap interval* (percentile, bias-corrected, BCa — resampling-based intervals that relax parametric assumptions), *simultaneous interval* (Scheffé, Tukey, Bonferroni-adjusted — joint coverage across multiple parameters), *prediction interval* (covers a future observation, not the parameter — wider than CI for mean), *tolerance interval* (covers a specified proportion of the population with specified probability), and *credible interval* (Bayesian alternative with direct probability interpretation of parameter given data and prior — conceptually distinct but sometimes numerically similar); (3) the deeper logic is that **a confidence interval communicates both a point estimate and its uncertainty in a single integrated summary, supporting both statistical inference (does the interval exclude a null value?) and effect-size characterization (what is the range of plausible effect magnitudes?) — combining in one quantity what p-values and effect sizes provide separately**; the CI's information advantage over the dichotomous reject/do-not-reject p-value result is substantial: a 95% CI that just barely excludes zero conveys weaker evidence than one that clearly excludes zero, information that a binary "significant" label suppresses; a 95% CI that includes zero but is narrow conveys meaningful evidence of a small-or-zero effect, while a CI that includes zero but is very wide conveys uninformative data; the ASA 2016 and 2019 statements, the New Statistics movement (Cumming 2014 "The New Statistics: Why and How," *Psychological Science*), and many discipline-specific methodological reforms have advocated for CI-centric reporting over p-value-centric reporting for exactly these reasons; the limitation, persistently misunderstood, is that the confidence level refers to the procedure's long-run frequency behavior, not to the probability that the specific realized interval contains the parameter — this frequentist-interpretation subtlety is the source of most CI misinterpretation, paralleling the p-value's transposed-conditional confusion; (4) the concept appears across domains — **clinical trials and biomedicine** (95% CIs around treatment effects as standard primary-result reporting; CONSORT reporting standards; meta-analysis forest plots showing CIs across studies), **epidemiology and public health** (risk-difference, risk-ratio, and hazard-ratio CIs as standard; disease-surveillance point estimates with CIs), **public opinion polling** (margin of error as 95% CI on proportions; pre-election poll reporting), **physics and metrology** (measurement uncertainty reported as "± 1σ" or equivalent; particle-mass and fundamental-constant measurements with CIs; CODATA recommended values), **economics and econometrics** (regression coefficient CIs; GDP-growth estimates with CIs; central bank fan charts showing forecast uncertainty), **engineering and quality control** (process-capability CIs; reliability estimates with confidence bounds; tolerance intervals in manufacturing), **machine-learning evaluation** (bootstrap CIs on accuracy, precision, recall; model-comparison CIs), **climate science** (IPCC uncertainty ranges for climate-sensitivity estimates and projected warming; attribution CIs), **finance** (Value-at-Risk with confidence level; portfolio-return CIs), **survey statistics** (official statistics with published CIs; ACS estimate CIs at various geographic levels) — across these, the interval-estimate-with-calibrated-coverage principle is shared, with domain-specific implementation (Clopper-Pearson for small-sample proportions; bootstrap for complex statistics; likelihood-based for non-normal models).

Uncertainty

Confidence intervals are a specific kind of uncertainty quantification, supplying interval estimates with calibrated long-run coverage.

Confidence intervals are a specialization of uncertainty. The general pattern is the structural condition of incomplete knowledge about a parameter, with the commitment to specify the unknown, the evidence, the form of unknowing, and the calibration. Confidence intervals instantiate this with the evidence being sample data, the form being a sampling-distribution-derived interval, and the calibration being the pre-specified long-run frequency with which the procedure covers the true parameter. It is uncertainty formalized as a procedure-level coverage claim about the unknown, distinct from but complementary to Bayesian credible intervals over the parameter directly.

Statistical Inference

Confidence intervals presuppose statistical inference because they are an interval-estimate procedure whose calibrated coverage is defined within the inferential framework.

A confidence interval is a procedure that produces interval estimates with a pre-specified long-run coverage probability under repeated sampling — a structure intelligible only within statistical inference's machinery of treating observed data as one draw from a probability model and reasoning about underlying parameters under sampling variability. Without that inferential framework, the long-run frequency interpretation that gives the interval its calibration would be vacuous, and the procedure would degenerate to bare data summarization. Statistical inference supplies the sampling-framework substrate the confidence-interval procedure operates in.


Confirmation Bias

Confirmation bias is the structural claim that reasoners systematically favor information processing that supports *the prior belief* or hypothesis over information processing that tests the belief symmetrically. This bias manifests across three principal channels: *the biased search*, in which reasoners selectively seek sources, witnesses, or test cases that tend to return confirming evidence while neglecting or avoiding those that might disconfirm; *the biased interpretation*, in which ambiguous or mixed evidence is read as consistent with the held hypothesis while disconfirming details are explained away or discounted; and *the biased memory*, in which supporting instances are retrieved from memory more readily and with higher salience than disconfirming ones.

Bias

Confirmation bias is a specialization of bias in which the systematic displacement favors processing that supports the prior belief.

Confirmation bias is a specialization of bias. Specifically, it instantiates the systematic-displacement-from-the-true-value pattern in the information-processing subclass: biased search, biased interpretation, and biased memory together skew evidence accumulation in the direction of the held hypothesis. It exhibits bias's defining signature -- a sign and direction surviving the accumulation of more data -- with the offset traced to the asymmetric handling of confirming versus disconfirming evidence, distinguishing this class within the broader catalog of cognitive biases.

Heuristic

Confirmation Bias is a kind of heuristic: a fast rule favoring belief-consistent processing yields systematic error in evidence evaluation.

Confirmation bias is the systematic tendency to favor information processing that supports prior belief — through biased search, biased interpretation, and biased recall — over symmetric testing. Functionally it is a fast rule that economizes on the costs of fully balanced evaluation at the price of characteristic directional error. That is the heuristic profile: a simplified procedure whose value depends on the trade-off between speed and accuracy. Confirmation bias specializes heuristic to belief-protecting evidence processing.


Conflict of Interest

A conflict of interest arises when a person or institution holds multiple duties, relationships, or financial interests that pull in incompatible directions, such that pursuit of one duty or interest undermines or compromises the other, as Davis and Stark (2001) develop in their cross-professional analysis of conflict of interest in the professions.<!-- FACT-D49-061 -->[^davis-stark-2001] The core tension is between loyalty to different principals, or between self-interest and fiduciary duty. Conflicts need not involve corruption; they exist whenever incentive structures create a pull toward suboptimal decision-making from the perspective of at least one stakeholder.

Role Conflict

Conflict of interest presupposes role conflict because incompatible duties and interests pulling one agent in different directions instantiates the multi-role strain pattern.

Conflict of interest arises when a person or institution holds multiple duties, relationships, or financial interests pulling in incompatible directions, such that pursuing one undermines another. The structure is a particular case of role conflict: a single agent simultaneously occupies positions whose embedded expectation-sets cannot all be satisfied. Role conflict supplies the underlying multi-incumbency-with-incompatible-expectations pattern. Conflict of interest specializes it to fiduciary and incentive contexts, where the incompatible roles concern duties to principals or self-versus-other interests, with the same structural impossibility of simultaneous full compliance.


Conformity

Aligning one's behaviour or beliefs to a group standard.

Conformity is the structural pattern in which an individual adjusts its expressed belief, judgment, or behavior toward a perceived group standard, sometimes overriding its own private information or preference, in response to either *normative* pressure (the desire to be accepted, to avoid sanction or exclusion) or *informational* pressure (treating the majority as evidence about reality). The essential commitment is *individual yielding to the aggregate*: a unit-level decision is pulled toward a population-level signal, which in turn strengthens that signal for the next individual. The phenomenon was first isolated experimentally by Asch (1956), whose line-judgment paradigm showed that subjects with intact perception nonetheless conformed to a unanimous but wrong majority on roughly a third of critical trials. <!-- FACT-D54-241 -->[^asch-1956]


Confounding

Confounding is the third-variable-common-cause-of-association principle that: (1) **confounding occurs when the association between a putative cause X and an outcome Y is distorted — either fabricated, exaggerated, attenuated, or reversed — because of a third variable Z that is a common cause of both X and Y or is otherwise non-causally linked to both in a way that contaminates the apparent X-Y relationship; formally in modern causal-inference terms, Z is a confounder if it is a cause of Y (or a proxy thereof) and is associated with X through a non-causal path, such that conditioning on Z is required to identify the causal effect of X on Y — and failing to account for Z yields biased causal estimates**<!-- FACT-D25-022 -->[^pearl-2009]; the concept has deep historical roots, articulated by John Stuart Mill 1843 in his methods of experimental inquiry (the method of difference requiring the treated and untreated cases to agree in all circumstances except the one being investigated), and elaborated through the 20th century by R.A. Fisher (randomization as defense against confounding in experimental contexts), Jerome Cornfield (epidemiological reasoning about smoking and lung cancer)<!-- FACT-D25-023 -->[^cornfield-1959], Austin Bradford Hill (Hill's criteria for causal inference in observational epidemiology, including consideration of confounding), David Cox, Donald Rubin (potential-outcomes framework), and Judea Pearl (causal-graph-based definitions using d-separation and back-door criterion)<!-- FACT-D25-024 -->[^pearl-2009] — the concept spans experimental-design/statistics origins with substantial co-development in medical/epidemiological research, warranting the `multi_origin_equal` flag for statistics and medicine; (2) the concept has **several identifiable components and distinctions**: *confounder* (a variable Z that is a cause of Y and is associated with X through a non-causal path, satisfying the back-door criterion in causal-graph terms), *confounding bias* (the distortion in the X-Y association produced by failing to adjust for Z), *measured versus unmeasured confounding* (confounders that the analyst has data on versus those that exist but are not measured — the latter is the canonical weakness of observational inference), *residual confounding* (confounding that persists even after adjustment, due to measurement error in the confounder or incomplete adjustment), *time-varying confounding* (confounders whose values change over time in response to treatment, requiring g-methods for proper adjustment), *collider bias* (distinct from confounding — a variable caused by both X and Y; conditioning on a collider *creates* bias rather than adjusting for it), *selection-into-exposure* and *selection-into-study* (related but conceptually distinct sources of association distortion), *simple confounding* (X → Z, Z → Y path, plus direct X → Y) versus *common-cause confounding* (Z → X, Z → Y paths with no direct X → Y), and *confounding-by-indication* in medicine (the indication for treatment is associated with outcome independent of treatment effect); (3) the deeper logic is that **confounding is a fundamental epistemological challenge in causal inference from observational data: the association observed between X and Y reflects the combination of any true causal effect and any non-causal paths linking the two, and there is no observational test that can distinguish these without additional assumptions — either experimental intervention (randomization breaks all back-door paths), or untestable observational assumptions (no unmeasured confounders, instrumental-variable conditions, regression-discontinuity conditions) that permit identification of the causal effect from observed data**; this is why randomization is the primary defense (and the `tight_pair_with_randomization` flag reflects the mutual-definition character of the two concepts — randomization is the procedure that eliminates confounding in expectation; confounding is the bias that randomization is designed to prevent); observational causal-inference methods (matching, stratification, regression adjustment, propensity-score methods, inverse-probability weighting, instrumental variables, regression discontinuity, difference-in-differences, synthetic controls) each rest on specific assumptions about confounding structure that are testable only imperfectly; the rise of modern causal-inference methodology (Pearl 1995 causal graphs; Rubin potential-outcomes framework; Hernán-Robins *Causal Inference: What If* 2020) provides formal frameworks for reasoning about confounding that go beyond the informal "control for confounders" advice of classical epidemiology; (4) the concept appears across domains — **epidemiology and public health** (smoking as confounder of coffee-disease associations; socioeconomic status as confounder across many exposure-disease associations; confounding by indication in pharmaco-epidemiology), **medicine and clinical research** (age, sex, comorbidity as confounders in observational treatment-outcome studies; Bradford Hill criteria for causal inference; modern causal-inference epidemiology), **economics and econometrics** (omitted-variable bias as econometric name for confounding; instrumental-variables methods; natural experiments; regression-discontinuity designs; credibility revolution), **social sciences** (socioeconomic status, selection-into-education, unobserved ability as persistent confounding challenges; quasi-experimental methods), **technology and A/B testing** (selection-into-variant confounding when randomization is compromised; cohort-effect confounding in observational user studies), **ecology and conservation biology** (environmental-factor confounding of species-habitat correlations; temperature confounding many biological associations), **industrial and quality control** (process-variation confounding of cause-effect investigation; operator-effect as confounder), **legal and forensic science** (selection-into-arrest, population-substructure in forensic statistics), **behavioral sciences** (unobserved psychological traits as confounders; instrument-effect in survey research), **machine-learning and data science** (spurious correlations in training data; distribution-shift as confounding-analog; fairness and selection-into-data) — across these, the third-variable-common-cause-of-association principle is shared, with domain-specific instantiations (confounding-by-indication in medicine; omitted-variable bias in economics; selection in tech; environmental variables in ecology).

Bias

Confounding is a kind of bias: it produces a systematic, non-averaging displacement of the estimated causal effect from the true effect.

Confounding distorts the estimated relationship between cause and effect in a consistent direction set by the common cause's structure, with the displacement persisting and often growing as samples accumulate rather than averaging out. That is the defining contrast between Bias and noise: bias is a persistent offset that more data does not erase. Confounding specializes bias to the causal-inference case, where the offset arises from non-causal paths between treatment and outcome rather than from estimator construction.

Causality

Confounding presupposes causality because the third-variable distortion is defined relative to the true causal relation it obscures.

Confounding presupposes causality because the very claim that an observed association is distorted -- fabricated, attenuated, or reversed -- requires a true causal relation against which the distortion is measured. The confounder Z is a common cause of X and Y in the causal graph, and adjustment is required to recover the genuine X-to-Y causal effect. Without causality's four-component structure of cause, effect, productive connection, and counterfactual sensitivity, there is no causal target to be confounded and no formal criterion separating spurious association from genuine effect.

Experimental Design

Confounding presupposes Experimental Design: identifying and controlling third-variable common causes is the central problem the design must address.

Confounding occurs when a third variable that is a common cause of putative cause and effect distorts the observed association, fabricating, exaggerating, attenuating, or reversing it. The concept is meaningful only against a design that seeks to license causal or comparative inference: randomization, blocking, stratification, and matching all exist precisely to neutralize confounders. Confounding presupposes Experimental Design as the framework whose ambitions it threatens and whose protocols it forces.


Conjugate Variables

Conjugate Variables are the structural pattern where (1) a system admits **two complementary descriptions** parameterized by variables (x, p) whose combined behavior is governed by a **fundamental coupling** — *the Poisson-bracket relation* {x, p} = 1 classically <!-- FACT-D13-080 -->[^poisson-1809], *the canonical commutation relation* [x̂, p̂] = iℏ quantum-mechanically <!-- FACT-D13-081 -->[^dirac-1930], or an integral transform kernel (e.g., Fourier pairing) in signal analysis <!-- FACT-D13-082 -->[^fourier-1822] — (2) the two descriptions are **mutually determining but jointly under-determined**: fixing one sharpens while the other broadens, and vice versa <!-- FACT-D13-083 -->[^heisenberg-1927], (3) a **canonical transformation or integral transform** mediates between them, preserving the essential physics or information content while exchanging which features are local and which are distributed <!-- FACT-D13-084 -->[^hamilton-1834], and (4) the pair admits a quantifiable **lower bound on joint resolution** (Heisenberg σ_x σ_p ≥ ℏ/2 <!-- FACT-D13-085 -->[^heisenberg-1927], Gabor limit σ_t σ_f ≥ 1/4π) that is not a measurement limitation but a structural property of the representation <!-- FACT-D13-086 -->[^schrodinger-1930].

Invariance

Conjugate variables presupposes invariance because the canonical transformation between the two descriptions preserves the underlying physical content.

Conjugate variables couple two descriptions of a system through a canonical transformation that preserves essential physics or information content while exchanging which features are local. This presupposes invariance: a named feature remaining unchanged under a named family of transformations, with the joint commitment to what is preserved and which operations preserve it. The conjugate transformation preserves the action functional, the commutator structure, or the total signal energy; what is preserved (the invariant) is what makes the two descriptions equivalent for physical purposes despite their different sharpness in different variables.

Measurement Uncertainty and Complementarity

Conjugate variables presuppose measurement uncertainty and complementarity because the pair only acquires its joint under-determination through complementary measurement structure.

Conjugate variables presuppose measurement uncertainty and complementarity because the defining feature of a conjugate pair, beyond a formal coupling like a commutator or Fourier kernel, is that sharpening one side necessarily broadens the other. That joint under-determination is precisely what complementarity names: a structural trade-off in what can be simultaneously specified, not a contingent instrumental limit. Without the prior commitment that certain observables are complementary in this irreducible sense, the canonical pairing would reduce to a routine change of variables with no inherent measurement constraint.

Symmetry

Conjugate variables presupposes symmetry because the canonical transformation mediating between the two complementary descriptions is a symmetry of the underlying physics.

Conjugate variables couple two complementary descriptions of a system via a canonical transformation or integral transform that preserves the essential physics while exchanging which features are local. This presupposes symmetry: invariance under a specified group of transformations, with the algebraic commitment that the stated transformation leaves the system unchanged in a specified sense. The canonical transformation is precisely such a structure-preserving group action on phase space; the Fourier kernel is a unitary transformation preserving total content. Without symmetry's transformation-group framework, the equivalence between conjugate descriptions has no algebraic substrate.


Consent

Consent is the normative-ethical concept of *the consenting agent capacity* <!-- FACT-D21-060 -->[^faden-beauchamp-1986] exercising autonomous authorization over a domain (body, data, property, decision) in which another party proposes to act. The essential commitment is fourfold: (1) **the consenting agent** — a person or party with cognitive and legal capacity for autonomous decision, capable of understanding implications and expressing will; (2) **the action or transfer requiring legitimation** <!-- FACT-D21-061 -->[^locke-1689] — a proposed action, use, or relational engagement that would be a violation of autonomy or rights without authorization; (3) **the informational-competence precondition** <!-- FACT-D21-062 -->[^faden-beauchamp-1986] — valid consent requires information (the consenting party understands what is authorized and its material implications), voluntariness (free from coercion, undue pressure, or deception), and capacity (cognitive and legal standing to authorize); and (4) **the legitimating-transformative effect** <!-- FACT-D21-063 -->[^belmont-report-1979] — consent transforms what would otherwise be impermissible into permissible, making the act authorized rather than a violation.

Authority

Consent presupposes authority because consent operates by granting another party legitimate authority over a domain that would otherwise be off-limits.

Consent presupposes authority because its essential function is to confer legitimate decision-making power over a domain — body, property, data, action — that the consenting agent would otherwise control exclusively. Without authority's prior structure of recognized right-to-decide, the act of consenting would have nothing to transfer or authorize. Consent inherits authority's general apparatus of legitimate power to bind and supplies the specific mode by which that power can arise from below: through the autonomous, informed, voluntary authorization of the party whose domain is at stake, generating an obligation the recipient could not otherwise claim.


Conservation Laws

A conservation law is a statement that a specifiable quantity associated with a system remains constant in time whenever the system is isolated from external flows of that quantity — any apparent change must therefore be accounted for by exchange across the system boundary, transformation into other forms, or accumulation in reservoirs. The essential commitment is that certain quantities have a bookkeeping character: they cannot arise or disappear within a closed region, so any change in the amount present entails an identifiable flow or transformation elsewhere. Every conservation law specifies (1) the conserved quantity, (2) the system boundary across which flows are tracked, (3) the transformations among related quantities (energy into different forms, matter into different species) that remain bookkeeping-consistent, and (4) the symmetry or structural reason underlying the conservation. The deep theoretical anchoring of conservation laws comes from Noether's theorem <!-- FACT-D10-032 -->[^noether-1918], which establishes that every continuous symmetry of a dynamical system's Lagrangian generates a corresponding conservation law; this unifies the classical intuitions with quantum mechanics and relativistic field theory.


Constraint

(1) **A constraint is a condition that restricts the set of admissible configurations, choices, or behaviors of a system to those satisfying it: the essential commitment is that the restriction is *binding for the purpose at hand* — anything violating the constraint is not an allowable candidate, regardless of other merit — and that the feasible set (the admissible subset) is a first-class object of analysis, separate from the objective that ranks within it.** (2) The distinctive focus is on *the binding restriction as a first-class structural object*, distinguished from the objective (which ranks admissible candidates rather than restricting admissibility), from a preference (which orders softly rather than forbidding), from a boundary in the territorial sense (see `boundary`; a wall is both boundary and constraint but the concepts are conceptually distinct), from a trade-off (see `trade_offs`; trade-offs arise *after* constraints have defined the feasible set), and from an impossibility proof (a constraint can be tightened enough to empty the feasible set, but the constraint itself remains a statement about admissibility, not an infeasibility theorem). (3) Every constraint specifies (i) the domain over which it applies (what kind of object or decision it acts on), (ii) the condition that must hold (equality, inequality, logical predicate, conservation law), (iii) the modal status of the restriction (hard vs soft, negotiable vs inviolable, binding vs slack), and (iv) the origin of the condition (physical law, regulatory mandate, budget, moral principle, prior commitment, design envelope). (4) The deeper abstraction is that **constraint reasoning is the structural prerequisite for all disciplined decision-making under restriction: Lagrange's 1788 *Mécanique Analytique*[^lagrange-1788] introduced Lagrange multipliers as the calculus of constrained optimization, treating constraints as first-class citizens in the variational principles that govern classical mechanics; Dantzig's 1947 simplex method[^dantzig-1947] turned linear constraints into the algorithmic core of operations research, enabling industrial-scale optimization of production, logistics, and resource allocation; Karush's 1939 master's thesis[^karush-1939] and its 1951 independent rediscovery and extension by Kuhn and Tucker[^kuhn-tucker-1951] established the KKT necessary conditions for constrained nonlinear optimization, generalizing Lagrange's framework to inequality constraints and remaining the foundational result of modern optimization theory; Rockafellar's 1970 *Convex Analysis*[^rockafellar-1970] consolidated the theory of convex constraints and the duality between feasible sets and supporting hyperplanes; Montanari's 1974 formalization[^montanari-1974] and Mackworth's 1977 arc-consistency algorithms[^mackworth-1977] founded constraint-satisfaction as a distinct computer-science subfield; Floyd's 1967 "Assigning Meanings to Programs"[^floyd-1967] and Hoare's 1969 axiomatic semantics[^hoare-1969] recast program correctness as the preservation of logical invariants under each program step, treating invariants as constraints on reachable states; Dijkstra's 1976 *A Discipline of Programming*[^dijkstra-1976] organized the entire practice of correct program derivation around constraint-based weakest-precondition reasoning; and Goldratt's 1984 *The Goal* and Theory of Constraints[^goldratt-1984] brought constraint-first thinking into operations management as the Five Focusing Steps for improving system throughput — these are the same structural move across domains that otherwise share nothing, and it is the move that distinguishes constraint-aware reasoning from unstructured "we want many things" decision-making.**


Constructivist Learning

Constructivism posits that learners actively construct knowledge through direct experience, reflection, and social interaction, rather than passively receiving pre-formed information from external authorities, an epistemology Piaget (1952) developed in *The Origins of Intelligence in Children* through his analysis of assimilation and accommodation. <!-- FACT-D48-046 -->[^piaget-1952] Learning is fundamentally an act of meaning-making where the learner's internal cognitive processes transform environmental stimuli into coherent mental models. This contrasts sharply with transmission models in which knowledge flows unidirectionally from instructor to student; instead, constructivism emphasizes bidirectional engagement—the learner acts upon the world, observes consequences, reflects on the gap between expectation and reality, and reorganizes understanding accordingly. The theory draws from developmental psychology (Piaget's assimilation and accommodation), sociocultural learning (Vygotsky's zone of proximal development, articulated in *Mind in Society*, Vygotsky 1978),[^vygotsky-1978] cognitive apprenticeship (Bruner's scaffolding, developed in *The Process of Education*, Bruner 1960),[^bruner-1960] and radical constructivism (von Glasersfeld's viability principle, set out in *Radical Constructivism*, Glasersfeld 1995),[^glasersfeld-1995] synthesizing them into a unified epistemology: knowledge is viable when it enables effective action within the learner's experiential world.

Learning

Constructivist learning is a specialization of learning that frames the durable update as active meaning-making rather than passive reception.

Constructivist learning is a kind of learning specialized by its account of how the durable update happens: the learner actively constructs knowledge through direct experience, reflection, and social interaction rather than receiving pre-formed content from an authority. It inherits learning's general commitment to durable, experience-driven self-update of an agent's internal state, and adds the specific epistemological commitment that meaning is produced bidirectionally through the learner's assimilation and accommodation of environmental encounters — contrasting with transmission models that treat the learner as a passive recipient.

Mental Model

Constructivist learning presupposes mental model because active knowledge-construction by the learner produces and revises internal representations of the domain.

Constructivist learning posits that learners actively construct knowledge through experience, reflection, and social interaction, building internal cognitive structures rather than receiving pre-formed information passively. The construction-and-revision activity requires that there be internal representations to construct: simplified, manipulable stand-ins for domain workings that support simulation and prediction. Mental model supplies that structural object. Without mental models as the target of construction, the assimilation-and-accommodation dynamic would have nothing to operate on and the bidirectional engagement between learner and world would have no internal substrate to revise.


Contagion

Spread of a state from element to element through contact.

Contagion is the structural pattern in which a state — an infection, a behavior, a default, a belief, or a failure — spreads from an affected element to a connected one through *direct contact or transmission*, and then *reproduces* in each new host so that the new host can in turn infect its own neighbors. The defining commitment is that propagation is contact-mediated and self-reproducing across a network, governed by a transmission rate and a contact topology, with a critical threshold separating two qualitatively different fates: a self-sustaining outbreak when each case produces on average more than one new case (R > 1), and burnout to extinction when it produces fewer (R < 1). <!-- FACT-D54-256 -->[^kermack-mckendrick-1927] This is not the same as a substance flowing downhill or diffusing along a gradient; what travels in contagion is a *state* that copies itself on contact, so the affected population can grow super-linearly rather than simply redistributing a fixed quantity. <!-- FACT-D54-257 -->[^hethcote-2000]


Containment

Holding a hazard, process, or agent within a deliberately maintained perimeter to prevent its spread or uncontrolled interaction with the surroundings.

Bounded isolation of an entity, process, hazard, or condition within a defined perimeter to prevent its spread or uncontrolled interaction with the surrounding environment, as Lewis (1977) develops in the context of multi-barrier defense-in-depth for nuclear reactor safety. <!-- FACT-D52-121 -->[^lewis-1977] Containment is the act of drawing a boundary and maintaining the integrity of that boundary; it presupposes that something uncontrolled would propagate or cause harm if left unchecked, a presupposition Anderson and May (1991) make explicit for infectious-disease propagation. It appears wherever an agent, energy, infection, or consequence must be held in place: reactor vessels holding radioactive material, quarantine zones holding disease vectors, sandboxed software holding untrusted code, detention facilities holding individuals deemed dangerous, and therapeutic frames holding traumatic affect. <!-- FACT-D52-122 -->[^anderson-may-1991]

Constraint

Containment is a kind of constraint: a maintained perimeter restricts the admissible reach of an entity, process, or hazard.

Containment draws and maintains a boundary that prevents a contained entity, process, or hazard from spreading or interacting uncontrolled with its surroundings. The perimeter functions as a binding restriction on admissible configurations: any state in which the contained item has escaped is ruled out regardless of other merit. That is the defining structure of a Constraint, here specialized to spatial-or-relational isolation of a propagating agent, energy flow, or contagious condition.

Boundary

Containment presupposes boundary because holding something within a perimeter to prevent spread requires that perimeter as a first-class structural object.

Containment is the bounded isolation of an entity, process, or hazard within a defined perimeter to prevent uncontrolled interaction with surroundings. The operation constitutively requires a boundary: a demarcation between contained and external with maintained integrity and controlled permeability. Boundary supplies the structural object — bounded entity, demarcation criterion, permeability — that containment then makes operative as a barrier to propagation. Without a boundary as first-class structure with maintained integrity, containment has no perimeter to defend and no inside-outside distinction to enforce.


Contextual Mode Switching

Contextual Mode Switching is the higher-order abstraction by which an agent — human, organizational, or machine — systematically maintains *the available modes* of communication, behavior, or processing, each optimized for a class of contexts. This phenomenon is grounded in modern usage-based linguistics (Bybee, Croft) and reflects how cognitive systems organize communicative repertoires across contexts[^bybee-2010] rather than maintaining a single default behavior.<!-- FACT-D23-135 -->[^bybee-2010]

Adaptation

Contextual mode switching is a specific kind of adaptation where the agent shifts among pre-built behavioral repertoires in response to context cues.

Contextual mode switching is a specialization of adaptation. The general pattern is a process by which a system changes its internal structure or behaviour in response to environmental change, preserving or improving fit. Mode switching instantiates this with the adaptation being movement among a maintained inventory of context-tuned modes (vocabulary, tone, procedure, tooling) triggered by contextual cues. The system maintains the modes as standing capacity rather than constructing each response from scratch, so the change-to-fit is realized as selection from a repertoire rather than incremental modification of a single default behaviour.

State and State Transition

Contextual mode switching presupposes state and state transition because switching between mode-bundles requires a discrete state space of available modes.

Contextual mode switching organizes an agent's behavior as a repertoire of discrete modes, each a coherent bundle of vocabulary, tone, and procedure, with contextual cues triggering transitions between them. This is structurally a state-transition system: the modes are states, the cues are transition triggers, and the switching rule is the transition relation. Without an underlying commitment to discrete states with rule-governed transitions, the mode-bundles would not be separable nor the switches identifiable. Mode switching presupposes the state-machine architecture as its substrate.


Continuity

**Continuity is the no-sudden-jumps principle: a mapping or process for which arbitrarily small changes in input produce arbitrarily small changes in output, formally captured by the epsilon-delta condition for real-valued functions (`∀ε > 0, ∃δ > 0 : |x - x₀| < δ ⟹ |f(x) - f(x₀)| < ε`) due to Cauchy (1821) and Weierstrass (1872)<!-- FACT-D38-091 -->[^cauchy-1821][^weierstrass-1872] and by the preimage-of-open-is-open condition in general topology, as systematically presented by Munkres (2000)<!-- FACT-D38-092 -->[^munkres-2000], with the consequence that the mapping preserves limits and intermediate values.** The essential commitment is that continuity is the gateway property for the entire analytical toolbox of differentiation, integration, differential equations, fixed-point theorems, and intermediate-value reasoning — none of which apply to a mapping that admits arbitrary jumps — and that it is structurally distinct from but tightly paired with [`discreteness`](discreteness.md), where the two together cover the topological organization of how a system's states relate. Every continuity articulation specifies (1) the *domain and range* — the input and output spaces under consideration; (2) the *notion of closeness* — a metric, topology, or at minimum a neighborhood structure that distinguishes small changes from large; (3) the *mapping or process* — the function, operator, or transformation being analyzed; (4) the *continuity property and its scope* — pointwise continuity at a specific point, continuity on the entire domain, uniform continuity (a single `δ` works across the domain), or Lipschitz continuity (`|f(x) - f(y)| ≤ L|x - y|` for some constant `L`); (5) the *discontinuity catalog* — the explicit named locations and types of discontinuity (jump, removable, essential, oscillatory) where the property fails, together with the substrate explanation for each; and (6) the *analytical use* — which tool-class the continuity unlocks (intermediate-value theorem, extreme-value theorem, Brouwer or Banach fixed-point theorem, gradient methods, perturbation analysis, differential-equation solution theory). **Without all six parts the continuity claim is at risk of being an unspoken modeling assumption that breaks where it matters most; with them, the diagnostic spans real analysis, topology, dynamical systems, control engineering, signal processing, economics, and policy design within one structural skeleton — and the question "is this system continuous in its inputs, where, and what does that buy us?" becomes prosecutable rather than rhetorical.**

Invariance

Continuity presupposes invariance because the epsilon-delta condition is the preservation of nearness under the mapping.

Continuity presupposes invariance because the no-sudden-jumps condition is exactly the claim that a specific feature -- nearness between input points -- is preserved under the application of the mapping. The preimage-of-open-is-open formulation makes this explicit: the topological structure of openness is the named feature, and continuous maps are the family of transformations that preserve it. Without invariance's joint commitment to what-is-preserved and under-which-operations, the continuity condition has no structural content; continuity IS topological invariance under the map.


Continuity vs. Rupture

gradualism vs. revolution
incremental vs. radical change

Continuity vs. Rupture is the interpretive dimension along which (1) an observed change in a system is located between two idealized endpoints: fully continuous gradual evolution on one end, fully discontinuous sharp break on the other, (2) the location is determined by examining whether the state variables describing the system change smoothly or jump across a boundary, and whether the causal structure on the far side of the change preserves or severs the one on the near side, (3) the judgment is partially a function of the observer's time-resolution and variable-choice — what looks continuous at centennial resolution can look like rupture at annual resolution, and vice versa — and (4) the resulting assessment is used to classify the change as evolutionary, revolutionary, or mixed, with different explanatory and prescriptive implications attached to each class, as Foucault (1969) developed in his archaeological method. <!-- FACT-D41-016 -->[^foucault-1969]


Contrast

Contrast is the *perceptually and cognitively emphasized difference between two or more elements* — visual, auditory, conceptual, structural, temporal, or contextual — that enables discrimination, clarification, and inference. As Saussure (1916) put it, value (meaning, identity) emerges only through systems of difference — terms gain their content from what they are not.<!-- FACT-D51-271 -->[^saussure-1916] The abstraction operates across perception (where the visual system detects differences in light intensity, color, motion, texture, and spatial orientation), cognition (where comparison-based reasoning extracts meaning from juxtaposed concepts, categories, or arguments), signal processing (where edge detection and anomaly identification depend on difference-magnitude), and scientific method (where experimental-versus-control contrast is the foundational inferential mechanism).

Comparison

Contrast presupposes comparison because emphasizing a difference requires the prior operation of placing items under a shared frame.

Contrast presupposes comparison because foregrounding a difference between elements requires them first to be brought under a shared frame and aligned along some dimension where the difference can register. Comparison supplies the relational machinery — comparands, dimensions, alignment rule — that makes any two items commensurable enough to register as different. Contrast then specifies that the output relation is one of perceptually or cognitively emphasized difference rather than mere relation; without the prior comparative operation, there is no shared axis along which the heightened difference can be read.


Controllability

Controllability is the structural property that determines whether an agent's available inputs can steer a system's state into any desired region such that: (1) **a system is controllable when, for any initial state $x_0$ and any target state $x_1$, there exists an admissible input trajectory $u(t)$ that drives the system from $x_0$ to $x_1$ in finite time** — formally, for a linear time-invariant system $\dot x = Ax + Bu$, controllability reduces to the rank condition on the controllability matrix $\mathcal{C} = [B, AB, A^2 B, \ldots, A^{n-1} B]$ (full rank $\Leftrightarrow$ controllable); for nonlinear systems, the analogous condition uses Lie bracket algebra (Chow's theorem, Sussmann's controllability criterion); practical operational definitions in management contexts test whether "interventions of specified type-and-magnitude can move this system's key variables through the desired range"<!-- FACT-D35-106 -->[^kalman-1960-ctrl]; (2) controllability is **the information-theoretic dual of observability** (see #390) — observability asks "do outputs reveal state?"; controllability asks "can inputs steer state?"; Kalman's 1960 seminal work established this duality via $(A, B) \text{ controllable} \Leftrightarrow (A^T, B^T) \text{ observable}$, making the two reciprocal structural properties of the same state-space model; (3) controllability delivers **the structural precondition for intervention, healing, policy, and goal-directed action** — without controllability, desired states are structurally unreachable no matter how clever the strategy; software systems without deployable fixes cannot be healed; patients without effective treatments cannot recover; policies without available levers cannot reshape outcomes; organizations without change-authority cannot execute transformations; recognizing uncontrollability prevents wasted effort on impossible goals and redirects attention to structural redesign; (4) the concept generalizes across domains — **control engineering** (Kalman controllability, pole-placement via state feedback, linear-quadratic regulator design, reachability analysis for safety-critical systems)<!-- FACT-D35-107 -->[^kalman-1960-ctrl], **software engineering and infrastructure** (deployability, rollbackability, feature-flag control surfaces, deployment authority structure; controllability-of-production as a core SRE concern; circuit-breakers, rate-limiters, and admin APIs as controllability levers)<!-- FACT-D35-108 -->[^sre-controllability-2018], **medicine and public health** (medication effects, surgical interventions, behavior-change levers — each a controllability claim; uncontrollable conditions trigger different strategies — palliation rather than cure), **policy and governance** (which economic variables can tax-and-subsidy policy actually move? Which social variables resist all known interventions?), **game theory and economics** (controllability of outcomes in principal-agent games, information-asymmetric markets), **biology** (controllability of cellular and organismal states via genetic, pharmacological, or developmental interventions; network controllability in systems biology — Barabási-Liu-Slotine 2011), **climate and earth systems** (controllability of climate via anthropogenic intervention is limited; geoengineering debates are partly controllability questions) — all deploy the "can intervention move the state to the target?" structural question.


Controlled Reentry

Re-establishing a suspended activity or state through staged, monitored steps with the capacity to abort, because returning to normal is a separate engineered process and not a simple reversal of the exit.

Staged, monitored re-establishment of activity, state, or contact after a deliberate suspension or isolation period, with defined criteria for progression and capacity to re-suspend if failure signals appear, as Travis (2005) frames the structure for prisoner reentry. <!-- FACT-D52-136 -->[^travis-2005] The pattern emerges from aerospace engineering (orbital reentry under extreme heat and structural stress) but generalizes to software deployment after rollback, prisoner reintegration after incarceration (Petersilia, 2003), monetary policy normalization after stimulus, gradual end-of-quarantine protocols, addiction recovery re-exposure, post-incident system restoration, and ceasefire-to-peace transitions. <!-- FACT-D52-137 -->[^petersilia-2003] Controlled reentry embodies a fundamental insight, articulated in spacecraft mission design (Wertz, Everett, & Puschell, 2011): we left normal mode for a reason; getting back is a separately engineered process, not a simple reversal of the exit mechanism. <!-- FACT-D52-138 -->[^wertz-everett-puschell-2011]