Exponentiation is a specialization of iteration. The general pattern is the repeated application of a step with state carried between rounds and progress measured across rounds. Exponentiation instantiates this with the per-iteration step being multiplication by a fixed factor, so the increment at each step is proportional to the current state rather than to a fixed quantity. This produces the constant-ratio successive values that distinguish exponential growth or decay from linear or polynomial accumulation. Compound interest, radioactive decay, and viral early-outbreak dynamics are the same iterative pattern under different per-step multipliers.

Exponentiation is a specific kind of iteration where repeated multiplication makes each round's increment proportional to the current state.


Exponentiation presupposes recurrence because b to the n is generated by reapplying multiplication-by-b at each step, exactly the structural recurrence x_{n+1} = b*x_n whose closed form is exponential. The constant-ratio-between-successive-values signature that distinguishes exponential from linear growth is a recurrence relation. Without recurrence's pattern of values reappearing across iterations under an identifiable rule, the per-step proportional growth has no generating structure; exponentiation is the family of solutions to the simplest multiplicative recurrence. Recurrence supplies the prerequisite condition: The property by which a state, event, or value reappears across time or iterations because the present state depends on prior states, distinct from mere repetition by its measurable lag structure. Exponentiation operates against that background: Repeated multiplication scaling. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.

Exponentiation presupposes recurrence because repeated multiplication is the iterated application of a constant-ratio rule across steps.


Risk supplies the prerequisite condition: Exposure to a known distribution of possible outcomes. Exposure Creep operates against that background: Between rare severe shocks, valuable assets accumulate inside a known hazard's impact zone because a quiet history reads as safety, so the next shock's loss is driven by the grown stake rather than by any change in the hazard. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.

Exposure Creep presupposes Risk, whose structure must already obtain for the child mechanism to be meaningful or operational.


The learner's internal state changes through repeated experience and the change persists into later prediction or behavior. The differentia is that the retained state encodes empirical frequencies or regularities of the exposure stream rather than a single association or skill.

Exposure-distribution learning is Learning specialized to durable frequency-sensitive updates from an encountered observation distribution.


The mechanism is identified by comparing an agent's post-exposure expectations with the statistics it repeatedly encountered. Without an internal representation that can encode those regularities, there is no model whose calibration can drift toward the exposure distribution.

A retained internal representation of the exposure distribution is a strict constituent of Exposure-Distribution Learning.


Risk supplies the prerequisite condition: Exposure to a known distribution of possible outcomes. Exposure Pathway operates against that background: The chain of links by which a hazard travels from source to vulnerable target, breakable at any link, turning risk into a graph search over severable routes. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.

Exposure Pathway typically presupposes Risk, whose structure must already obtain for the child mechanism to be meaningful or operational.


External analytic challenge contains feedback because its probes must return to alter or explicitly re-justify the next state of the work. Cut the challenge-to-response return path and the outsider can comment but cannot correct the work; the structure becomes observation or later judgment rather than pre-commitment challenge. parent_in_child


External analytic challenge presupposes a reversibility horizon because it must land before accumulated commitment makes correction costlier than carrying the work forward. If reversal cost does not change with timing, pre-commitment challenge has no structural advantage over post-commitment review and the defining scheduling constraint disappears. External challenge is a review arrangement timed relative to a commitment threshold, not a species of reversibility horizon.


External analytic challenge contains viewpoint because the challenger must occupy a station whose access, occlusion, and bias profile differ from the authoring frame. Remove the differently positioned station and a challenger sharing the same accumulated access and blind spots cannot provide the outside-frame correction the identity requires. parent_in_child


Allocation is the assignment of a limited supply across competing claimants subject to feasibility, with the question of who or what gets how much as the bare assignment itself. Externality is the particular shape this pattern takes when the assignment fails to incorporate third-party effects: a producer or consumer takes an action whose private cost or benefit diverges from the social cost or benefit, and the market — absent intervention — produces an allocation in which the unpriced residue lands on parties not in the transaction. A structurally-particularized instance of allocation whose specific defect is misassignment from unpriced flows.

Externality is the specific shape allocation takes when third-party effects of an action are not reflected in the price the decision-maker pays.


An externality is constituted as the unpriced residue of an economic action — the consequence to third parties that the market price fails to internalize. Without the price mechanism's role as the scalar signal that aggregates private costs and benefits into the coordinating signal between buyers and sellers, there would be no baseline against which to identify the externality's unpriced character. The externality is intelligible only against the background expectation that prices ought to convey full social cost, which the price-mechanism prime supplies.

Externality presupposes the price mechanism because the externality is defined by what falls outside the price signal that coordinates market exchange.


'externality is the side-effect pattern given a price-system framing' — the substrate-specific, priced, third-party instance. side_effect is the substrate-neutral parent; externality keeps its price_mechanism/allocation parents. Side Effect supplies the genus: An action's change to shared state beyond its declared interface. Externality preserves that general structure while adding its differentia: Spillover effects. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


Every admitted case carries a locally warranted competence or reliability claim beyond the sampled regime that bounded its evidence. The apparatus continues to present the output and confidence as though those scope conditions still held, creating the parent's reach-versus-warrant gap. Extrapolation adds a calibrated apparatus, an out-of-regime input, a self-blind confidence indicator, and an absent regime-exit detector.

Extrapolation beyond a sampled regime is Transferability Overclaim specialized to a calibrated apparatus that leaves its validated regime while continuing to display in-regime confidence.


The failure is not merely encountering a novel input. It is carrying a competence claim, calibrated confidence display, or rule validated on one regime into another where that evidence does not reach. Validation supplies the original claim and its legitimate evidential envelope.

Extrapolation beyond a sampled regime presupposes a validation claim whose evidential scope is bounded by the regime on which competence was established.


The pattern quantifies uncertainty about intersection between an accessible sample and a distinguished rare-target set. Its central claims — n/N for one target and the hypergeometric complement for k targets — require Probability as their formal substrate.

Extreme Capture Probability is a probability law over which rare targets a bounded selection includes.


Eyes on the street is the specific shape monitoring takes when observation is distributed, incidental, mutually-visible, and parasitic on other activity. 'a subspecies of monitoring with sharply different enabling conditions.'. Monitoring supplies the genus: Continuously observing a system's state to detect deviation from expected behavior and trigger a response, separating genuine signal from routine noise. Eyes On The Street preserves that general structure while adding its differentia: Safety and accountability produced as a byproduct of dense incidental observation by embedded participants, conditional on shared space, mutual visibility, and a low-cost intervention pathway. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.


Fabula (content/what) and syuzhet (form/how presented) is a specific instance of the form-content duality applied to narrative temporal sequencing. Form and Content supplies the genus: The relationship between a work's structure and its substance. Fabula And Syuzhet preserves that general structure while adding its differentia: The chronology of events and the order in which they are told are separable design objects, each optimizable for its own criterion. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


Exception: the chronology-versus-presentation split can organize non-narrative artifacts such as event logs, interfaces, curricula, and technical explanations that do not form a story.

Narrative supplies the canonical object in which fabula and syuzhet was identified: connected events can be reconstructed into an underlying chronology while being encountered in a deliberately chosen order. Yet the prime's portable structure is the separation between an underlying event order and an order of presentation, which can also organize logs, interfaces, curricula, and technical explanations that are not narratives in the stronger story-like sense. Narrative is therefore a typical enabling context rather than a universal containing whole.

Fabula and Syuzhet usually presupposes Narrative because the distinction originated as a way to separate a story's event chronology from its order of presentation, but the separation can transfer to non-narrative ordered representations.


Normativity supplies standards, reasons, permissions, prohibitions, and other ought-bearing claims. Remove that content and the fact-value distinction collapses into a classification among descriptive claim types; the child adds the descriptive contrast and the bridge discipline governing movement between the two.

Fact-Value Distinction contains Normativity because one side of the distinction must consist of genuinely evaluative, reason-giving, or ought-bearing content.


Cartesian Product supplies the genus: All combinations of independent dimensions, one choice per axis. Factorial Design preserves that general structure while adding its differentia: Multiple variables tested together. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.

Factorial Design is a specialization of Cartesian Product, retaining the parent's defining structure while adding the child's specific commitments.


A factorial design varies multiple factors simultaneously at multiple levels in a single integrated experiment, exposing each factor's main effect and the interactions between factors. The whole experiment is broken into a structured set of parts — factors and their level combinations — that, properly combined, reconstitute the full design and license clean attribution of variation. That is the move of Decomposition, here specifically shaped as a multi-factor cross-classification that exposes both additive contributions and interaction structure invisible to one-factor-at-a-time designs.

Factorial Design is the specific shape decomposition takes when an experiment is structured into factors with main effects and interactions.


Factorial design is the particular form experimental design takes when several factors are crossed within one integrated experiment rather than varied one-at-a-time. The structure observes every combination (or a balanced subset) of factor levels, which both estimates main effects efficiently and reveals interactions — effects that depend on other factors' levels — that no single-factor design can detect. The general architecture of principled comparison under randomization is specialized here to multi-factor combinatorial assignment, trading one-at-a-time intuition for combinatorial efficiency and interaction-detection.

Factorial design is the specific shape experimental design takes when multiple factors are varied simultaneously to reveal main effects and interactions.


'Not generic decomposition — factorization adds a hard constraint decomposition lacks': the parts must be same-type and recombine under a NATIVE binary operation under which the kind is closed, recovering the original exactly. A specialization of decomposition (any split). Decomposition supplies the genus: Breaking a whole into parts that can be analyzed independently and recombined to reconstitute the whole, making complexity tractable through divide-and-conquer. Factorization preserves that general structure while adding its differentia: Expressing one object as a product of same-type factors under its native operation. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.


Fail-safe is a specialization of fault tolerance in which the response to failure is to drop into a pre-engineered least-harmful state rather than to continue providing service through redundancy or failover. It inherits the general fault-tolerance commitment that components will fail and that the system must be designed so individual failures do not cascade into system-level catastrophe, and specializes by fixing the strategy to safe-default-on-failure (brakes engage when power is lost, valves close when signal is lost) rather than to continued operational availability.

Fail-safe is a specialization of fault tolerance in which continued service is sacrificed and the post-failure default state is engineered to be the least harmful.


Fail-Safe arranges the system so that its default post-failure state is the least harmful available — gates default closed, brakes default engaged, valves default safe — rather than devolving into an uncontrolled state. Choosing such a default requires weighing which transitions are reversible (and so tolerable as a halt state) against which are irreversible (and so must be avoided). That is the apparatus of Reversibility and Irreversibility. Fail-Safe presupposes the reversibility distinction to identify which failure state to engineer toward.

Fail-Safe presupposes Reversibility and Irreversibility: design must classify which post-failure states are safe to settle into and which must be avoided.


FMEA decomposes a system or process into distinct failure modes, causes, local effects, and downstream effects for separate evaluation. After the engineering_design frame is stripped away, the retained structural roles are those of Decomposition: Breaking a whole into parts that can be analyzed independently and recombined to reconstitute the whole, making complexity tractable through divide-and-conquer. Failure Mode and Effects Analysis (FMEA) adds the local frame and commitments expressed in its identity: Identify failure modes. The parent pattern remains recognizable without that vocabulary, while the child is the framed realization of it. That preservation test establishes decomposition rather than taxonomic subsumption.


FMEA ranks prospective failure modes by risk-bearing consequences and likelihood or detectability dimensions. Risk supplies the prerequisite condition: Exposure to a known distribution of possible outcomes. Failure Mode and Effects Analysis (FMEA) operates against that background: Identify failure modes. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.


Fairness evaluates whether an allocation, procedure, or treatment respects equal regard and principled differentiation. Whatever fairness criterion is selected — equal shares, desert, need, or capability — it cannot count as fair if the outcome systematically depends on the identity of the party rather than on relevant features of the case. Impartiality supplies that baseline structural requirement: invariance under identity permutation, with like cases treated alike. Fairness then builds on impartiality by specifying which features count as relevant and how they should weight outcomes.

Fairness presupposes impartiality because any defensible standard of fair treatment requires that identity-irrelevant features not systematically move outcomes.


Reification supplies the genus: An abstraction designed to summarise a substrate is treated as the substrate itself, with the audit trail back to the original allowed to atrophy. Fallacy Of Misplaced Concreteness preserves that general structure while adding its differentia: Mistaking an abstraction — a model, statistic, or construct — for a concrete thing, then applying interventions licensed only for the particulars to the reified stand-in. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.

Fallacy Of Misplaced Concreteness is a specialization of Reification, retaining the parent's defining structure while adding the child's specific commitments.


Fallback is context-triggered switching among maintained operating routes with failure or insufficiency as the cue and priority ordering as its differentia. A controller detects a context condition and selects one maintained mode or route from a discrete repertoire rather than constructing a response anew. The modes are asymmetrically primary and secondary, and the trigger is the primary route's inability to meet a minimum functional requirement.


Fallback Path is the ordered primary-secondary species of diverse pathways that can realize the same minimum function. At least two non-identical pathways can each deliver the specified minimum function, so loss or inadequacy of one need not eliminate it. One path is preferred, another is secondary, and an explicit failure or insufficiency condition governs the handoff.


Partition supplies the prerequisite condition: A division of a set into non-overlapping, collectively exhaustive blocks. False Dilemma operates against that background: A partition of a rich option space is presented as exhaustive when it is not, so reasoning proceeds inside cells while real alternatives have been suppressed. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.

False Dilemma presupposes Partition, whose structure must already obtain for the child mechanism to be meaningful or operational.


The paradox 'is an application of Bayes' rule' — posterior odds = prior odds x likelihood ratio — but 'a single, sharp corollary' (low-prior PPV collapse), not the whole machinery. A specialization of bayesian_updating. Bayesian Updating supplies the genus: Update beliefs with evidence. False Positive Paradox preserves that general structure while adding its differentia: Under a rare base rate, most positive flags are wrong even when the detector is highly accurate. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.


Each concept fixes the contrast class of the other within empirical claim-evidence relations. Falsifiability requires at least one stable forbidden observation; Unfalsifiability denies that any admissible observation has stable claim-defeating force. Neither is a subtype or component of the other, so the relation is strict and mutual.

Falsifiability and Unfalsifiability are co-defining complements distinguished by whether a stable claim-defeating observation exists.

Within empirical claim-evidence relations, falsifiability and unfalsifiability are co-defining complements distinguished by whether a stable forbidden observation exists. Falsifiability identifies a nonempty stable set of claim-defeating observations; unfalsifiability identifies its absence. Specifying either requires the same claim, observation space, and defeat relation. Directing the complement as subsumption in either direction leaks polarity: a claim exposed to a stable refuter is not a kind of a claim immune to every refuter, and the reverse is equally false.


Fault tolerance keeps systems serviceable when components fail by drawing on redundant components, spare capacity, error-correction overhead, and standby paths designed to absorb failures without service loss. All of those mechanisms are surplus capacity held beyond nominal need, exactly the Reserve pattern — deliberately maintained slack whose value lies in its availability when expected conditions are exceeded. Fault tolerance presupposes reserve as the substrate that the failover, error-correction, and degradation mechanisms consume when faults strike.

Fault Tolerance presupposes Reserve: continued operation under failures draws on redundancy and capacity held beyond expected need.


Fault tolerance specializes robustness by fixing the perturbation class to component failures: hardware breakage, software bugs, network partitions, adversarial corruption. Where robustness names maintained function across a broad envelope of input conditions and disturbances generally, fault tolerance focuses specifically on internal-component failure as the perturbation type, deploying redundancy, monitoring, failover, and graceful degradation as its characteristic mechanisms — a particular shape robustness takes when the threats targeted are the failures of the system's own constituent parts.

Fault tolerance is a specialization of robustness focused on continued operation specifically under component failures rather than across all perturbations.


Feature engineering deliberately TRANSFORMS the representation of raw observations so a latent regularity becomes legible to a downstream consumer; it presupposes representation and acts on it. Also leans on transformation.


Anticipation without an inspectable or encoded surrogate is guessing; the upstream model is the internal constituent that lets predicted consequences modify the action. Representation supplies an internal constituent: Model complex ideas. Feedforward requires that role within this mechanism: A predictive model of an action's consequences is interposed upstream of commitment, so the actor pre-corrects rather than waits for a deviation to feed back. Remove the parent-role and the child loses a required internal operation, even though the parent can exist outside the child. The child is therefore built from the parent rather than being a taxonomic kind of it.

Feedforward contains a predictive representation mapping intended action and disturbance to expected consequence before commitment.


Feedforward inhibition is inhibition specialized to the case where the SAME go-signal drives both the activator and a parallel brake (pre-committed, not error-tuned). inhibition is the genus (the general external/applied brake on a transformation); this candidate is the same-input parallel-path special case. NOTE inhibition is also a candidate in THIS batch -> a candidate-to-candidate parent edge. Inhibition supplies the genus: An external agent actively slows, blocks, or reduces an otherwise-active transformation by occupying or counteracting the mechanism that would carry it forward. Feedforward Inhibition preserves that general structure while adding its differentia: The same input that activates a downstream element simultaneously recruits a brake on it along a parallel path, so the response is shaped by their difference. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.


Gestalt Principles supplies the genus: Perceptual grouping rules. Figure-Ground preserves that general structure while adding its differentia: Perceptual organization of a field into salient figure and receding ground. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.

Figure-Ground is a specialization of Gestalt Principles, retaining the parent's defining structure while adding the child's specific commitments.


Calls opportunity_asymmetry the prime's genus: first-mover advantage is the species where the asymmetry is TEMPORAL and order-indexed (the same move pays differently by its rank in a sequence). opportunity_asymmetry is the parent. Opportunity Asymmetry supplies the genus: Agents possess unequal access to actions and favorable outcomes. First Mover Advantage preserves that general structure while adding its differentia: When a contest rewards early arrival, the same move yields a different return depending on when in the sequence it is taken. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.


The same move yields a different return by sequence position, locking in early arrivals — path dependence in a rewarded contest. Path Dependence supplies the genus: Outcomes are shaped by the specific historical sequence of past choices, which lock in consequences and foreclose alternatives that persist despite present incentives to change. First Mover Advantage preserves that general structure while adding its differentia: When a contest rewards early arrival, the same move yields a different return depending on when in the sequence it is taken. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


The input structure maps to a curved output under load while connectivity is invariant; the hinge, stress regime, and bend-rather-than-break condition supply the child's differentia.

A fold is transformation specialized to stress-induced bending that changes shape while preserving continuity.


Foreseeing (prediction) is a specialization of foresight. Specifically, it instantiates the structured-future-anticipation stance in the point-estimate-with-uncertainty mode: an explicit predictive model maps current state and historical pattern to a projected future state with attached confidence, closed by a calibration loop comparing predicted to realized outcomes. Like other foresight methods, it serves present perception and choice under uncertainty; unlike scenario planning, it commits to specific outcome claims with probability rather than mapping a plural space of possibilities.

Foreseeing (prediction) is a specialization of foresight that targets specific future-state claims with calibrated uncertainty rather than scenario sets.


Foreseeing is a specialization of inductive reasoning. The general pattern is ampliative inference from specific observations to conclusions whose content exceeds what the premises logically guarantee, with quality measured by support strength, calibration, and coverage. Prediction instantiates this with the conclusion being a future state and the premises being the current state plus historical pattern; the predictive model is the inductive bridge, and the calibration loop is precisely the quality test inductive reasoning's framework requires. Prediction carries the characteristic uncertainty of induction because the future may always depart from the observed regularity.

Foreseeing is a specific kind of inductive reasoning, drawing a future-state conclusion from observed patterns whose support strength is calibrated.


Foreseeing forms a structured belief about a future state, specifying not just what will happen but the range of plausible outcomes with confidence or probability attached. This presupposes uncertainty: the structural condition of incomplete knowledge about a future state, with the commitment to specify the unknown, the evidence base, and the form of unknowing. The future is the canonical unknown variable; the predictive model is a tool for navigating it; the projected range with attached probability is the uncertainty quantification itself. Without uncertainty's framing of incomplete knowledge as a structured object, prediction collapses into mere assertion.

Foreseeing presupposes uncertainty because predicting a future state requires the incomplete knowledge that makes the future an unknown to be characterized.


Form and content presupposes representation because the dualism that separates the message from its manner of presentation operates only where a structured mapping from a target onto a medium is in play. Representation supplies the target-medium-faithfulness machinery within which the medium's structure (form) shapes how the target's structure (content) is conveyed. Without representation's mapping, there is no medium whose form could constrain or constitute the received content. The form-content distinction is the explicit acknowledgment that representation's medium-side choices are not inert — they channel, distort, and partly constitute what the target conveys.

Form and content presupposes representation because the dualism separating what is conveyed from how it is structured operates within representational mappings between target and medium.


'Not formalization — formalization is the PROCESS, a formal_system is the ARTIFACT that process aims at.' The finished four-component package presupposes (is the product of) the formalization process. Formalization supplies the prerequisite condition: Rendering informal practice into explicit, codified, rule-governed form. Formal System operates against that background: Symbols, formation rules, axioms, and inference rules closed under mechanical derivation. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.


The formal-versus-informal duality requires that some practices be rendered explicit and codified into rules, charters, and policies — the very move that formalization names. Without the formalization machinery — making tacit practice statable, checkable, and transmissible — there would be no formal layer to contrast with the informal layer; the distinction would collapse into a single tier of uncodified practice. Formalization is the structural operation that produces the formal half of the duality, and is therefore presupposed by the dual structure.

Formal vs informal structures presupposes formalization because the formal layer is by definition the codified, rule-governed counterpart to the informal practice.


Formal-versus-informal structures distinguishes codified roles, procedures, and authority from the emergent practices through which a system also operates. Social norms commonly constitute part of that informal layer by supplying shared behavioral expectations and decentralized sanctions absent from the formal chart. The relation is typical rather than strict because an informal layer can also be organized through personal networks, tacit knowledge, reputation-based influence, or improvised workarounds without a clearly norm-governed component.

Social norms commonly form part of the informal layer that interacts with an organization's codified formal structure.


Formalization is the move up the explicitness gradient — replacing tacit know-how with codified notation, axioms, or statutes — and that move only operates inside a representational medium. To articulate a previously implicit rule one needs symbols, schemas, or formal language that map onto the practice being captured under a faithfulness convention. Representation supplies the structured mapping of target to medium that formalization then sharpens into mechanically operable, audit-checkable form, so formalization cannot get off the ground without a representational substrate already available.

Formalization presupposes representation because making practice explicit requires a medium in which axioms, notation, and rules can stand for the target.


Formalization is the particularization of transformation to the explicitness gradient: the input is tacit, conventional, or intuitive practice; the rule is articulation into notation, axioms, statutes, or schemas; the output is explicit, checkable, transmissible system. Where transformation names structured input-to-output mapping with preserved invariants generally, formalization specifies that the invariant targeted is the substantive content of the practice while the degree of freedom being reshaped is its representational explicitness — moving up from implicit know-how to codified knowledge.

Formalization is the specific shape transformation takes when tacit practice is restructured into explicit, codified, rule-governed form.


Formative assessment implements a measure-compare-act feedback loop routing learning evidence back to instruction. Feedback supplies the prerequisite condition: Outputs influence inputs. Formative Assessment operates against that background: Ongoing feedback. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.


Formative assessment is a specialization of monitoring: continuous in-process observation (quizzes, exit tickets, think-pair-share, draft reviews) accumulates evidence about student learning to detect deviation from expected progress and trigger instructional response. It inherits monitoring's commitment to continuous or periodic observation with threshold comparison and corrective action, particularized to the pedagogical case where the monitored variable is learning state and the response is adjustment of teaching strategy rather than final summative judgment.

Formative assessment is a kind of monitoring whose continuous evidence-gathering informs in-flight instructional decisions rather than final judgment.


Formative assessment is a specialization of pedagogy whose distinctive move is continuous, in-process evidence-gathering whose purpose is to inform teaching and learning decisions during the instructional cycle rather than render a final verdict. It inherits pedagogy's commitment to deliberately structuring the learner's encounter with content for durable capability change, and adds the specific machinery of assessment-for-learning: quick checks, exit tickets, draft reviews, and feedback loops that let the instructional agent adjust sequencing and support based on evidence of where each learner currently stands.

Formative assessment is a specific pedagogy that gathers in-process evidence of learning to inform ongoing instructional and learning decisions.


Founder effect is one specific path-dependence mechanism: a small high-variance initial sample conservatively amplified into durable identity. names path_dependence as its genus; sibling of critical_juncture and lock_in. Path Dependence supplies the genus: Outcomes are shaped by the specific historical sequence of past choices, which lock in consequences and foreclose alternatives that persist despite present incentives to change. Founder Effect preserves that general structure while adding its differentia: A small unrepresentative initial subset starts a new population through a narrow gate, and its idiosyncratic composition is amplified into the descendant's durable identity. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.


Fractal geometry studies sets whose detail repeats, exactly or statistically, across scales, with non-integer dimension quantifying space-filling roughness. This presupposes recurrence: the structural property by which a pattern, condition, or value reappears across iterations or instances. Self-similarity is recurrence operating along the scale axis rather than the time axis: zooming in reproduces, exactly or statistically, the same form. The recursive generating rules that produce Mandelbrot sets and the statistical scale-invariance of coastlines both rely on the same reappearance-of-pattern structure that recurrence names as foundational.

Fractal geometry presupposes recurrence because scale-invariant self-similar structure is recurrence operating across scales rather than time.


Fractal geometry is the structurally-particularized instance of scale in which structure does not change qualitatively across scales but instead repeats, exactly or statistically, so that a single scale-invariant description applies across the range. It carries forward scale's general commitment that properties and behaviors vary as size or resolution changes, and gives this idea its specific shape: the change across scales is itself a self-similarity transformation, and the appropriate quantitative measure is a non-integer Hausdorff or box-counting dimension capturing roughness and space-filling capacity.

Fractal geometry is the specific shape scale takes when structure repeats across scales and dimension itself becomes non-integer.


Scale Invariance supplies the genus: Behavior unchanged under scaling. Fractal Geometry preserves that general structure while adding its differentia: Self-similar patterns. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.

Fractal Geometry is typically a specialization of Scale Invariance, retaining the parent's defining structure while adding the child's specific commitments.


Fractal geometry presupposes self-organization because the natural and physical instances it catalogs (coastlines, vascular networks, lungs, large-scale structure, asset-price series) acquire their scale-repeating roughness through local interaction rules under their own dynamics rather than from an externally imposed blueprint. Self-organization supplies the causal architecture by which macro-order emerges from micro-rule; fractal geometry then provides the quantitative vocabulary, especially fractal dimension, for measuring the recursive structure that self-organizing processes characteristically generate across scales.

Fractal geometry presupposes self-organization because the recursive scale-invariant structures it studies typically arise from local rules without a central designer.


This preserves the source's decisive initiation-versus-propagation separation. Defect is not an internal arrest mechanism or a genus of toughness; it is the required damaged initial condition against which the toughness property is defined.

Fracture Toughness begins after a localized defect already exists and asks whether the substrate arrests or permits its coupling-mediated spread.


The threshold is an internal decision boundary in the toughness property, not a background assumption. Its coordinates vary by substrate, but below-versus- above reversal of propagation outcome is invariant.

Every Fracture Toughness claim contains a critical defect length, energy, reproduction number, or blast-radius boundary separating arrest from runaway spread.


A change of frame requires specifiable old and new frames plus the mapping and invariants by which their assignments can be compared. The parent can occur independently, but without it the child’s mechanism is undefined, establishing prerequisite dependence.


Frame Change is Transformation specialized to preserving a referent while substituting the organizing frame that assigns its coordinates or meaning. The parent supplies the genus and can occur without the child; the child preserves it while adding commitments the parent does not require.


They are siblings, not parent/child. (Listed here only to flag the considered-and-rejected relation.). Viewpoint supplies the genus: A position fixes an access set, an occlusion set, and a bias profile. Frame of Reference preserves that general structure while adding its differentia: Observational perspective. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.

Frame of Reference is typically a specialization of Viewpoint, retaining the parent's defining structure while adding the child's specific commitments.


The frame is precisely the set of represented facts licensed to persist under a transformation while only direct effects and relevant ramifications are recomputed. Invariance supplies an internal constituent: Properties unchanged under transformation. Frame Problem requires that role within this mechanism: After a change, the challenge of bounding which facts now need re-derivation and which persist by default, without re-checking everything. Remove the parent-role and the child loses a required internal operation, even though the parent can exist outside the child. The child is therefore built from the parent rather than being a taxonomic kind of it.

Facts held unchanged under the current action form a constitutive invariant region of every frame-problem solution.


Without an explicit or implicit world model there is no bounded fact set over which an action's consequences and default persistence can be computed. Representation supplies the prerequisite condition: Model complex ideas. Frame Problem operates against that background: After a change, the challenge of bounding which facts now need re-derivation and which persist by default, without re-checking everything. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.

The frame problem presupposes a represented state whose facts can persist, change, or require re-derivation.


'a frame is a deliberately set context' — framing is the chosen/active special case of context. Context supplies the genus: Surrounding state that selects which content a fixed focal signal carries. Framing preserves that general structure while adding its differentia: Presentation shapes perception. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


Framing is the structural claim that presentational choices — what is salient, what reference point is used, what vocabulary applies — systematically shape evaluation even when underlying facts are equivalent. The construct presupposes that there is a presentation in the first place: a structured mapping of target onto medium under conventions, with selected features foregrounded and others dropped. Representation supplies that substrate — the structured mapping with its faithfulness claim and selection of features. Framing specializes representation by analyzing how the variable choices within that mapping move judgment, exploiting the selection-and-configuration latitude representation always contains.

Framing presupposes representation because configuring a presentation that shapes evaluation requires a representational medium whose features can be configured.


Free riding presupposes social dilemma because the act it names — benefiting from a collectively-produced good without contributing proportionately — is the prototypical defection move in the dilemma's incentive structure: when the good is non-excludable and individual benefit exceeds individual cost-share, withholding contribution is privately dominant while universal withholding leaves everyone worse off. Without the social dilemma's prior conflict between individually rational and collectively optimal action, free riding would not be a structural pathology but merely an accounting irregularity. Free riding instantiates the dilemma in the specific setting of non-excludable goods.

Free riding presupposes social dilemma because exploiting collective provision is the characteristic individually-rational defection in a public-goods dilemma.


Both retain a deliberately false no-perturbation reference and interpret real departures through separately named forces. Frictionless Benchmark Reasoning adds a theorem-like result—an invariance, irrelevance, conservation, or efficiency claim—and uses that sharp result as the fixed origin for an organized research program. Zero-Force Null Baseline remains broader because its reference may instead yield another exact distribution, level, trajectory, or equilibrium without that invariance-style differentia.

Frictionless Benchmark Reasoning is the Zero-Force Null Baseline subtype whose idealized case yields a sharp invariance, irrelevance, conservation, or efficiency result that becomes the program's coordinate origin.


Functional redundancy specializes redundancy by relaxing the duplicate-component constraint: instead of identical replicas, multiple non-identical mechanisms each suffice for the critical function, so the loss of any one leaves the function intact. Where redundancy names deliberate duplication for fault tolerance with independence of failure as the central design variable generally, functional redundancy specifies that the duplicates are structurally diverse pathways, which both reduces common-mode failures and broadens the operating envelope across conditions where any single mechanism might be impaired.

Functional redundancy is a specialization of redundancy in which the duplicated elements are non-identical pathways that converge on the same function.


The fundamental attribution error is a specialization of bias. The general bias pattern is systematic, signed displacement of a process's outputs from a true or fair value, persisting despite more data. The FAE specializes by giving the displacement a specific direction: explanations of others' behavior systematically over-weight dispositional causes and under-weight situational ones, with asymmetric application to self versus other. The same systematic-rather-than-random-displacement logic of bias applies, with dispositional-versus-situational attribution as the specific dimension and observer-actor asymmetry as the specific signature.

Fundamental attribution error is a specialization of bias in which dispositional explanations are systematically over-weighted relative to situational ones.


Fundamental attribution error presupposes responsibility attribution because it is defined as a characteristic distortion in how the assignment from outcome to agent is performed: over-weighting dispositional sources and under-weighting situational ones, with an asymmetric self-other pattern. Without the prior operation of mapping observed behavior back onto candidate causes and apportioning credit or blame, there is no assignment for the bias to skew. The error is parasitic on the attribution machinery; it specifies which input weights get systematically miscalibrated when agents perform the directed assignment from effects to responsible sources.

Fundamental attribution error presupposes responsibility attribution because it names a systematic bias inside the very act of assigning causes to agents.


Fungibility is the APPLIED equivalence-class claim: within a class individuation drops out of every downstream computation (balance, not inventory). It is an equivalence_relation plus losslessness + identity-erasure.


Calls fungibility 'a strict, symmetric strengthening of substitutability' — the lossless, symmetric, any-for-any case. Substitutability supplies the genus: One component replaces another without functional degradation. Fungibility preserves that general structure while adding its differentia: Any unit of a class substitutes for any other without loss, erasing individual identity in favor of type and quantity. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


Per-stage attrition is meaningful only when a population moves through a defined sequence with countable entry and exit at each boundary. Pipeline supplies that ordered stage structure; Funnel Analysis supplies the diagnostic accounting that localizes loss and identifies the binding stage.

Funnel analysis presupposes an ordered pipeline whose stage boundaries let entrants, exits, and conditional survival be attributed to particular transitions.


A future/promise is a reified placeholder interposed between consumer and eventual value, matching indirection's definition of an interposed reference decoupling access from binding. Indirection supplies the genus: Introduces intermediary references. Future Or Promise preserves that general structure while adding its differentia: A first-class placeholder for a value committed to be supplied later. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


'Not state_and_state_transition in general — a future has a CONSTRAINED state machine': a single irreversible transition pending -> fulfilled|rejected. A specialization of state_and_state_transition (general machines cycle/revisit). State and State Transition supplies the genus: Captures system condition and evolution. Future Or Promise preserves that general structure while adding its differentia: A first-class placeholder for a value committed to be supplied later. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.


A future wheel is the specific shape causality takes when the causal relation is unfolded forward as a branching cascade: a triggering event sits at the center, first-order consequences radiate from it, each first-order consequence then generates second- and higher-order consequences in successive concentric layers. It is a structurally-particularized instance of cause-and-effect with productive connection and counterfactual robustness, with the added commitments that the mapping is exhaustive across orders rather than tracing a single chain, the structure is graphical-radial, and the value lies in surfacing indirect higher-order effects that linear analysis misses.

A future wheel is the specific shape causality takes when consequences are mapped outward in concentric layers from a triggering event.


Futures literacy presupposes foresight because it is defined as the underlying capability that enables effective use of foresight methods — scenario planning, horizon scanning, backcasting — along with reflexive awareness of the anticipatory assumptions in play. Without foresight as the object-domain of structured future-anticipation, there is no skill content for the literacy to be literacy in. Foresight supplies the practices, stances, and outputs that futures literacy then becomes capable of deploying critically, distinguishing it from any specific method by being the capability dimension underneath the methods stack.

Futures literacy presupposes foresight because it is the developed capability to use foresight methods reflexively and well.


Futures literacy is the structurally-particularized form modal reasoning takes in the future-anticipation case: the structured space of alternatives is the set of plural possible futures, the modal operators are "could," "would," and "should," and the truth of a futures claim is grounded in the set of accessible scenarios in which an inner proposition holds. It inherits modal reasoning's apparatus of operators quantifying over alternatives, particularized by the reflexive awareness of the anticipatory assumptions shaping each scenario set.

Futures literacy is the specific shape modal reasoning takes when the structured space of alternative possibilities is plural possible futures.


Fuzzing is the generate-broadly-then-select-on-anomalies pattern aimed at falsification: inject controlled (wider-than-designed) variation, watch an oracle, iterate. A specialization of variation_strategies (deliberately inject variation + select from the results), specialized to surfacing latent failures.


Gain control is a specific adaptive mechanism: a slow secondary loop measures recent input statistics and retunes the forward path's input-output SLOPE to keep it in range. A specialization of adaptation (system adjusts to conditions). Loosest defensible genus; not feedback (different regulated quantity). Adaptation supplies the genus: Systems adjust to conditions. Gain Control preserves that general structure while adding its differentia: A slow secondary loop continuously retunes the gain of a fast forward signalling pathway so it stays in its useful range across changing input statistics. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


Gain control is homeostatic regulation whose regulated variable is signalling gain, held in useful range by a slow secondary loop. Homeostasis supplies the genus: Maintain internal stability. Gain Control preserves that general structure while adding its differentia: A slow secondary loop continuously retunes the gain of a fast forward signalling pathway so it stays in its useful range across changing input statistics. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


Gains from trade is the positive-sum outcome that arises when parties specialize and exchange, but the welfare improvement depends on the prior structural fact that the parties differ in relative opportunity cost — comparative advantage. Without the underlying commitment that relative efficiencies determine the welfare-improving specialization pattern, the specialization that generates gains would have no basis: parties with identical opportunity-cost ratios produce no surplus from trade. The comparative-advantage structure is what makes the exchange positive-sum rather than zero-sum.

Gains from trade presupposes comparative advantage because the welfare improvement requires that parties specialize according to their relative opportunity costs.


Gains from trade presuppose exchange because the surplus produced by specialization is only realized when the specialized parties transfer their output to each other on mutually agreeable terms. Without exchange's bilateral conditional-transfer structure, specialization yields autarkic stockpiles, not mutual gain. Exchange supplies the substrate on which comparative advantage can be cashed out: parties produce where opportunity cost is lowest precisely because they expect to swap surpluses, and the swap is what converts production differences into the strictly-better consumption possibilities the gains-from-trade claim asserts.

Gains from trade presuppose exchange because the positive-sum surplus only realizes when specialized parties actually transfer outputs to each other.


Gains from trade arise from specializing according to comparative advantage, which is itself defined in terms of relative opportunity costs — the value of the next-best alternative production each party gives up. Without opportunity cost's machinery of valuing alternatives foregone under scarcity, the comparison of parties' relative production capabilities collapses: there would be no metric by which to identify who should specialize in what, and the welfare improvement of exchange would have no basis. Opportunity cost supplies the comparative metric on which gains-from-trade rests.

Gains from trade presupposes opportunity cost because the relative efficiencies that drive specialization are differences in the value of alternatives foregone.


A game-theoretic strategy is the specific shape function takes when the input is the player's observed history up to an information set and the output is the action prescribed at that point. It is a structurally-particularized instance of a deterministic single-valued rule from domain to codomain, with the added commitments that the domain is the set of information sets reachable in a fully described game, the codomain is the player's action set at each, and the rule must be specified at every contingency — including off-equilibrium paths — because rational analysis requires behavior closed under counterfactual play.

A game-theoretic strategy is the specific shape function takes when the mapping is from observed game history to a chosen action at each information set.


Root declaration, eligible-reference walking, and visited-state marking are constitutive parts of reachability-bounded garbage collection; the traversal exposes the live set before the unreachable complement can be reclaimed.

Garbage collection contains a reachability traversal from declared roots to distinguish live resources from reclaimable ones.


GIGO is a quality-MONOTONICITY constraint on a transformation (fidelity to ground truth cannot rise across a single-input map — the data-processing inequality); it presupposes the transformation whose output quality it bounds. transformation is its genus, GIGO 'a constraint on one dimension of it'. Transformation supplies the prerequisite condition: A rule-governed mapping that restructures an input into a different output, holding certain invariants fixed while altering others. Garbage In, Garbage Out operates against that background: The quality of a transformation's output is bounded above by the quality of its inputs; no downstream sophistication can repair defects already present in the input. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.


Gatekeeping inherits Selection's input population, passage basis, differential continuation, admitted output, and excluded complement. It adds a single choke-point topology, an identifiable or accountable arbiter with discretion, asymmetric power over senders, and a downstream audience that sees the admitted stream but not the rejected one. Economic Screening is not the genus: its canonical identity is menu-induced self-revelation by privately informed agents, a mechanism a gate need not use.

Gatekeeping is selection specialized to a choke point where an arbiter controls passage and the downstream audience cannot directly observe the rejected stream.


Gauge invariance is a specialization of invariance. Specifically, it names the case in which the family of transformations is a local symmetry group acting on unobservable internal degrees of freedom (phase, color, spacetime reparameterization) and the preserved feature is the set of physical observables. Like every invariance claim, it commits jointly to what is preserved and under which operations; gauge invariance is the subclass where the operations form a Lie group acting locally and physical states correspond to entire gauge-equivalence classes rather than individual configurations.

Gauge invariance is a specialization of invariance whose preserved feature is observable physics and whose transformation group is local gauge transformations.


Gauge invariance is a specialization of symmetry. The general pattern is invariance of a system under a specified group of transformations: applying the action leaves the system unchanged in a specified sense. Gauge invariance instantiates this with the transformation group acting locally on unobservable internal degrees of freedom (phase, color index, reparameterization), so physical observables correspond to equivalence classes under the action. The structural commitment is precisely symmetry's algebraic claim, with the particular feature that the group action is local and the invariant content is the gauge-equivalence class.

Gauge invariance is a specific kind of symmetry where the invariance is under a group of local transformations of unobservable internal degrees of freedom.


Superposition, cross-cutting, inclusion, and overprint are meaningful as chronology only relative to time's ordering dimension; geometry supplies evidence for that order but is not itself the temporal relation.

Geometric chronology presupposes temporal succession because its spatial rules recover an earlier-later relation among events.


Gestalt organization begins with discrete elements but makes the organized whole the primary percept and gives it shape, motion, figurehood, and meaning not present in the elements independently. Holism is the exact substrate-neutral irreducibility core; Gestalt adds a perceiver, a field, automatic parallel grouping rules, and perceptual-economy commitments.

Removing the automatic-perception and named-grouping-rule frame from Gestalt principles leaves holism's claim that whole-level relational properties are not recoverable from isolated part properties.


Goal congruence is a specialization of coordination in which the elements being aligned are not actions in real time but the underlying objectives, incentives, metrics, and decision criteria of individuals, teams, and departments. It inherits coordination's general structure of independently controlled actors combining into a coherent collective outcome, and specializes by fixing the alignment target to the objective functions agents pursue. When goals point in mutually reinforcing directions, local optimization contributes to global success; when they diverge, agents coordinate locally but produce collective failure — so goal alignment is the upstream condition that makes downstream coordination productive.

Goal congruence is a specialization of coordination in which the aligned elements are the objectives, incentives, and metrics of separate units.


'attention is the broad allocation of a scarce processing resource; goal shielding is its specifically goal-protective application — the active denial of that resource to competing goals while one is held.' attention is the genus. Attention supplies the genus: The selective allocation of a fixed processing capacity to some inputs while the rest are filtered out, surfacing scarcity upstream of every decision. Goal Shielding preserves that general structure while adding its differentia: While pursuing an active goal, suppressing access to competing goals that would compromise it, releasing the suppression only once the active goal ends. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


Goal Shielding controls rival access around an already selected goal; it does not itself explain why that goal retains active status until completion, abandonment, or swap. Open-Goal Persistence supplies the maintained selection and release event. Shielding adds asymmetric inhibition of alternatives and the interrupt policy governing what can break through.

Goal Shielding presupposes Open-Goal Persistence because competitors can be suppressed during pursuit only while one selected goal remains active across the execution interval.


The model may be explicit or encoded in policy, weights, rules, or structure, but removing representational correspondence destroys the theorem's invariant. Representation supplies an internal constituent: Model complex ideas. Good Regulator Theorem requires that role within this mechanism: Every effective regulator of a system must be, or must contain, a model of that system. Remove the parent-role and the child loses a required internal operation, even though the parent can exist outside the child. The child is therefore built from the parent rather than being a taxonomic kind of it.

The theorem's necessity claim is that every effective regulator contains a behaviorally adequate representation of the system it regulates.


The proxy's pre-intervention correlation with the construct is an implicit calibrated model. Using that relationship to allocate reward, penalty, or control changes agent behavior toward the cheapest proxy-improving actions, so the relationship no longer transports into the targeted regime. Goodhart specializes the parent with a proxy, construct, exploitable wedge, and metric-directed optimization.

Goodhart's Law is Intervention-Induced Model Invalidation specialized to a proxy relationship that breaks because the proxy is placed under binding optimization pressure.


Proxy-Target Divergence is the umbrella for any decoupling between an operational measure and the underlying target. Goodhart's Law fixes the mechanism to a control loop that rewards or penalizes the proxy, causing effort to move into the exploitable proxy-target wedge until the relationship collapses.

Goodhart's Law is Proxy-Target Divergence specialized to the mechanism in which binding optimization pressure on the proxy destroys its correlation with the construct.


Governance is the durable architecture of authority, accountability, and decision rights through which a collective system is steered. Accountability is one internal element: it identifies who must answer for an action or outcome, to whom, and through what review or sanction mechanism. Authority without accountability would allocate power while omitting the answerability structure that Governance explicitly includes.

Accountability is an internal element of Governance, assigning who must answer for decisions, conduct, and outcomes.


Governance is defined as the durable architecture of authority, accountability, and decision rights. It allocates, channels, limits, and legitimates binding decision power as part of its internal design. Accountability is a separate internal element whose own Authority dependency does not replace this direct constituent relation.

Authority is an internal element of Governance, distributed and bounded through roles, rules, legitimacy sources, and decision rights.


Gradual deterioration is the accumulation of many small, individually-tolerable damage events — fatigue cycles, corrosion increments, information losses — into a single trajectory of declining functional capacity. The downstream measurement collapses the granular history into a summary state (remaining strength, residual fidelity, remaining life). That is the move of Aggregation: many items collapsed into a unified form that retains chosen features and suppresses granular detail. Gradual deterioration specializes aggregation to summed micro-damage and its macroscopic functional reading.

Gradual Deterioration is a kind of aggregation: integrated stress accumulates many small damage increments into a single decaying functional capacity.


Gradual deterioration is the structural pattern in which small persistent stressors accumulate to erode functional capacity over time. This presupposes the more general pattern of temporal decay and degradation: that system properties systematically diminish through use, exposure, or natural processes following predictable functional forms. Without the underlying time-driven degradation pattern as a frame, the accumulation of microscopic damage below the failure threshold has no destination to converge toward; gradual deterioration is the slow, sub-threshold realization of the broader one-way tendency that temporal decay names.

Gradual deterioration presupposes temporal decay because incremental accumulation of damage only makes sense against the broader pattern of time-driven degradation.


Gradual deterioration is decay accumulated as stress is applied across temporal duration, with the present capacity a function of integrated history. The very content of the prime — that small persistent stressors below the immediate failure threshold accumulate into substantial decline — requires Time as the ordered dimension along which the stressors are distributed and the accumulation runs. Without temporal extent there is no integration interval and no gradual pattern; deterioration presupposes time as its supporting dimension.

Gradual Deterioration presupposes Time: incremental decay is by definition the integration of stress over temporal extent.


Narrative is the structural pattern of selecting, sequencing, and causally connecting events into a whole with an interpretive arc. A grand narrative or metanarrative is the specific case where the story is scaled to cover history, society, or a whole domain under a single trajectory or logic — progress, emancipation, rationalization, salvation. It inherits the basic emplotment machinery of narrative and adds commitments to comprehensive scope, directional teleology, and a legitimating function that organizes many local narratives under a common trajectory.

A grand narrative is a specialization of narrative; it is a story-structure scaled up to give a unifying account of history or a whole domain.


Partition supplies the genus: A division of a set into non-overlapping, collectively exhaustive blocks. Graph Coloring preserves that general structure while adding its differentia: Conflict-free labeling so that no two items joined by a conflict edge share a label. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.

Graph Coloring is a specialization of Partition, retaining the parent's defining structure while adding the child's specific commitments.


Great Man Theory attributes major historical outcomes to the actions and characteristics of exceptional individuals rather than to structural or sociological forces, treating those individuals as causally efficacious in ways structural accounts cannot reduce. The position is a particular application of responsibility attribution: mapping outcomes back to agents, with counterfactual-dependence as the test. Responsibility attribution supplies the underlying directed-assignment-from-effects-to-sources operation. Great Man Theory specializes it by concentrating the assignment heavily on individual agents and privileging their counterfactual significance over structural variables in the historical case.

Great Man Theory presupposes responsibility attribution because it concentrates causal credit for historical outcomes onto exceptional individuals.


'Not heuristic in general — greedy is a specific heuristic schema (local-best, irrevocable, no-backtrack) with a sharp optimality theorem (matroids) most heuristics lack.' A specialization of heuristic. Heuristic supplies the genus: Mental shortcuts. Greedy Algorithm preserves that general structure while adding its differentia: Committing irrevocably to the locally best choice at each step, with no lookahead. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.


Calls cooperation the genus: green-beard is one specific sustaining mechanism within it (a tag-keyed conditional disposition recognized one-shot), distinct from kin selection and reciprocity. cooperation is the parent. Cooperation supplies the genus: Agents bear individual costs to produce a shared benefit. Green-Beard Effect preserves that general structure while adding its differentia: Cooperation is sustained by a single observable marker that is both correlated with the cooperative disposition and recognizable by fellow carriers. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.


Natural Selection supplies the genus: A population of varying, heritable variants is filtered by a selection pressure so that the better-performing variants differentially reproduce or persist, shifting the population's composition over rounds — variation, selection, and retention as a substrate-neutral engine. Green-Beard Effect preserves that general structure while adding its differentia: Cooperation is sustained by a single observable marker that is both correlated with the cooperative disposition and recognizable by fellow carriers. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.

Green-Beard Effect is typically a specialization of Natural Selection, retaining the parent's defining structure while adding the child's specific commitments.


Gresham's Law contains Selection's eligible population, operative pressure, differential continuation, and shifted output composition. Heterogeneous goods enter a parity-constrained channel; the parity makes holders pass the lower-quality units while retaining, diverting, or converting the higher-quality units, so the circulating population changes. Gresham adds an imposed nominal parity, holder choice, a directional withdrawal-and-concentration result, and re-emergence of the better grade in a channel where quality can be priced. Adverse Selection is a sibling under Selection, not the genus: its differential participation is caused by hidden type rather than an imposed rule.

Gresham's Law is selection specialized to an enforced nominal parity that gives lower-quality goods greater passage through a channel and higher-quality goods greater retention outside it.


A reference channel cannot function as ground truth merely by being trusted. It must observe or assign the target in a frame comparable with the system being evaluated. Measurement supplies that value-producing and comparison-ready apparatus; Ground Truth adds the asymmetric authority designation and its known fallibility.

Ground truth presupposes measurement because the designated reference must produce a comparable observation against which another channel can be scored.


Forget the inverse requirement from a Group and its carrier, closed associative operation, and two-sided identity still satisfy every Monoid commitment. Monoid can occur without universal inverses, while Group adds that strict differentia, establishing the non-flattened subsumption chain Group → Monoid → Semigroup.

A Group is exactly a Monoid in which every element additionally has an inverse.


Internal binding is distinguishable from adhesion or external coupling only once a system boundary separates members from nonmembers. The boundary need not be social or cognitively represented; it may delimit a droplet, ecological guild, code module, or team.

Cohesion presupposes a Boundary that identifies which elements are bound internally and what fragmentation of the unit would mean.


Groupthink is the structurally-particularized form conformity takes under specific antecedent conditions: high cohesion, insulation, directive leadership, member homogeneity, and stress combine to amplify the individual-yields-to-aggregate pull until private information is suppressed and consensus precedes deliberation. It inherits conformity's pattern of individual judgment pulled toward group standard under normative and informational pressure, particularized to the small-group decision-making case where the eight Janis symptoms diagnose the pathology.

Groupthink is the specific shape conformity takes when high cohesion and directive leadership suppress dissent and produce premature consensus.


Automaticity supplies low-supervision execution; habit adds a learned cue-action binding and the diagnostic of outcome-devaluation insensitivity, so every habit is automatic but not every automatic process is a habit.

A habit is a specialized automatic regime in which a recurring cue selects a learned action that persists even after its outcome has been devalued.


A habit is the installed result of (operant) conditioning — the durable cue-action binding that conditioning writes; it presupposes the conditioning process. Conditioning (Behavioral) supplies the prerequisite condition: Learning via association. Habit operates against that background: A cue-triggered, automatically executed action sequence that persists under outcome devaluation. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.


Both require repeated or sustained exposure to reduce a capable receiver's response. Habituation adds a history of inconsequential stimulation plus the diagnostic differentia of stimulus specificity, spontaneous recovery, and dishabituation, excluding receptor damage, undifferentiated fatigue, and static insensitivity admitted by the broader response-tolerance family.

Habituation is tolerance specialized to learned, stimulus-specific response decrement that can recover after a pause or reverse under a novel stimulus.


Both require repeated exposure to reduce response as a stimulus proves unworthy of its initial recruiting force. The child adds a finite-specificity signal channel, base-rate degradation, rational posterior collapse, and the operator pathology of adding more alarms.

Habituation to repeated signal is general habituation specialized to a condition-flagging channel whose false-positive history also degrades the receiver's posterior and creates an ignore equilibrium.


Habitus is the system of durable, transposable dispositions that an individual acquires through sustained social exposure and that operates as the pre-reflective structuring principle of perception, judgment, and action. The dispositions guide behavior without being available for explicit articulation — agents act as though they know rules they cannot state. Implicit knowledge supplies precisely that structural commitment: knowledge influencing performance without verbal accessibility. Habitus specializes implicit knowledge to socially-acquired class-and-context-specific dispositions, with the social conditions of acquisition as the specific source of the implicit content.

Habitus presupposes implicit knowledge because its durable, transposable dispositions operate pre-reflectively without explicit articulation by the agent.


Habitus is the specific shape internalization takes when the external item being taken inward is the structuring effect of a social position — class, family, profession — and what becomes endogenous is a durable, transposable system of dispositions: perceptual schemes, evaluative categories, bodily comportments. It is a structurally-particularized instance of an external governor crossing into the interior and becoming part of how the agent simply is. The added commitment is that what gets internalized is not a discrete norm but a whole generative grammar of practice, operating beneath reflection across contexts unlike those in which it was acquired.

Habitus is the specific shape internalization takes when durable social-positional dispositions become the pre-reflective principle of perception and action.


Half-life is the time required for a first-order decay process to reduce a quantity to half its initial value, with the defining property that this time is constant regardless of the starting amount. The named feature (the halving time) is preserved under the named family of transformations (rescaling of the initial amount). That is precisely a claim of Invariance. Half-life specializes invariance by fixing the preserved feature as the characteristic halving duration and the transformation as initial-amount rescaling.

Half-Life is a kind of invariance: the time to halve a quantity is preserved across all starting amounts for first-order processes.


Half-life presupposes recurrence because its defining property is that for a first-order process the time to halve recurs with constant value regardless of starting amount: each successive halving event takes the same characteristic time. Recurrence supplies the general structural pattern of reappearance with predictable spacing across time, iterations, or instances; half-life is a quantitative parameter of one particular recurrence pattern (the geometric sequence of halvings) that characterizes any exponentially decaying process and lets one infer remaining quantity from elapsed time.

Half-life presupposes recurrence because halving repeats at constant intervals, producing a recurrent equal-spacing pattern across the decay trajectory.


Half-life provides the characteristic temporal scale of a first-order decay process — the natural unit at which the system's dynamics are most ergonomically described and across which population reductions of one-half, one-quarter, one-eighth are read off cleanly. That is exactly the role Scale plays: the specification of the size or resolution at which the system is naturally described, with behavior best understood at that band. Half-life presupposes scale as the dimension whose value it picks out for decay processes.

Half-Life presupposes Scale: it sets the characteristic time at which the process is naturally described and at which decay regimes change.


Distortion supplies the genus: Systematic, mapping-induced deviation of an output from a faithful rendering of its input. Harmonic Distortion preserves that general structure while adding its differentia: Passing a signal through a nonlinear transfer function generates new frequency components — harmonics and intermodulation products — absent from the input, an artifact of the nonlinearity itself rather than of any sampling or discretization. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.

Harmonic Distortion is a specialization of Distortion, retaining the parent's defining structure while adding the child's specific commitments.


Hashing is a deterministic many-to-one function from an unbounded input space to a short fixed-size token (a bounded codomain), used as the object's handle. A specialized function_mapping (deterministic, many-to-one-by-design, with a chosen sensitivity property).


Learning supplies the genus: Durable, experience-driven update of an agent's internal state that carries forward to alter later behavior or prediction. Hebbian Learning preserves that general structure while adding its differentia: A connection between two units strengthens as a function of their correlated activity, through a local, correlational, unsupervised, cumulative update. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.

Hebbian Learning is a specialization of Learning, retaining the parent's defining structure while adding the child's specific commitments.


Both identities require an introduced activity to consume the finite substrate on which an incumbent activity depends. The child fixes that substrate to coordinator attention and adds unsolicited pro-social presentation, per-unit handling cost above operational value, a social cost of refusal, and a volume threshold at which apparent help becomes displacement.

Helpful-inflow displacement is crowding out specialized to unsolicited pro-social inflow consuming the coordinator attention needed for the primary work.


Both make a unit's expressed choice depend on a perceived aggregate rather than only on its private judgment. Herding fixes the aggregate signal to others' visible choices and foregrounds imitation under uncertainty; Conformity also admits alignment driven by sanction, belonging, or a group norm. Information Cascade remains a separate sequential strict child and is not an alias.

Herding is conformity specialized to alignment with the crowd's visible choices under uncertainty, usually through informational rather than purely normative pressure.


The hermeneutic circle is the specific shape interpretation takes when the representational substrate is a complex whole whose meaning depends on its parts and whose parts depend on the whole. Interpretation's general operation — recovering meaning from a substrate given a constraining framework — is structurally particularized into iterative movement between part-reading and whole-reading, with the interpreter's fore-structure revised at each pass. The general activity of producing a constrained reading is preserved; the specific shape is the spirally-convergent loop with no terminal closure that this interdependence forces.

The hermeneutic circle is the specific shape interpretation takes when understanding the whole and the parts must be revised against each other iteratively.


The hermeneutic circle is the interpretive particularization of iteration: each pass reads parts in light of a provisional whole and re-reads the whole in light of refined parts, with the fore-structure carried as state between passes and convergence measured by interpretive coherence. Where iteration names repeated application of a step with cumulative use of prior outputs generally, the hermeneutic circle fixes the step as interpretation, the state as the evolving fore-understanding, and the progress notion as tightening coherence between part-readings and whole-readings.

The hermeneutic circle is the specific shape iteration takes when interpretation alternates between part and whole, with each pass revising both.


The hermeneutic circle presupposes sensemaking when deployed as an organizational interpretive practice because constructing a plausible working account of ambiguous events relies on iteratively revising part-understandings against whole-understandings as new cues arrive. Sensemaking supplies the broader cognitive-social process of cue-extraction, bracketing, and commitment to a working frame; the hermeneutic circle supplies the specific part-whole iteration mechanism that makes the working frame refinable rather than fixed at the first pass. The two operate together: sensemaking under ambiguity needs the circle's iterative coherence-tightening to converge on usable interpretation.

The hermeneutic circle presupposes sensemaking because its part-whole revising operation supplies the iterative refinement that working accounts under ambiguity require.


A heuristic is a kind of approximation specialized to decision and inference under cognitive or computational constraint: a simplified rule yields a good-enough judgment much faster than exhaustive analysis at the cost of accuracy in some cases. It inherits approximation's commitment to substituting a tractable surrogate for an intractable target while accepting a bounded, named error in exchange for tractability, and supplies the specific case where the intractable target is optimal reasoning and the surrogate is a fast rule whose ecological fit determines whether the error budget is acceptable.

A heuristic is a specialization of approximation in which a tractable rule of judgment is substituted for exhaustive optimal analysis.


Trade-offs is the general structural situation in which improving one valued dimension requires worsening another within a feasible set. A heuristic is the particular shape this pattern takes for decision and inference rules: speed and cognitive-or-computational cost are improved at the price of accuracy in some cases and systematic error in others, with the rule's value defined by the favorable trade in its actual deployment environment. It is a structurally-particularized instance of trade-off whose specific dimensions are speed-cost-accuracy and whose feasible set is the available rule space.

Heuristic is the specific shape trade-offs take in inference, where speed and cognitive cost are gained at the price of accuracy.


Hidden path and barrier crossing names transitions through classically forbidden regions with calculable probability, whether via quantum tunneling amplitudes or stochastic rare-event escape over an activation barrier. This presupposes probability: the calibrated quantification of uncertainty assigning numerical values to events under coherence rules. The transmission factor in the WKB approximation and the Arrhenius escape rate are both probability assignments to events that classical analysis would assign zero. Without probability's framework for numerical event-likelihood that obeys additivity and conditioning, the hidden-path transition has no quantitative content.

Hidden path and barrier crossing presupposes probability because barrier transit is a calculable transmission amplitude over forbidden regions.


Hidden path and barrier crossing describes transitions between system states through a classically forbidden region — quantum tunneling, thermal-fluctuation escape — with calculable probability. The phenomenon is constitutively a state-to-state transition: there is an initial state on one side of the barrier, a final state on the other, and a transition rate governed by the barrier shape. State-and-state-transition supplies that substrate: a state space and transition rules. Without an underlying notion of distinct states and rule-governed transitions between them, there is nothing for the hidden path to connect.

Hidden path and barrier crossing presupposes state and state transition because tunneling and rare-event escape are transitions between states across a barrier.


A string that ENCODES A PATH THROUGH a hierarchy, fusing identity and tree-position into one self-locating token; presupposes the containment hierarchy and adds the string-encoding (and its restructuring fragility) the bare relation lacks. Hierarchy supplies the prerequisite condition: Organizes elements into levels or ranks. Hierarchical Address operates against that background: A single string whose substring structure encodes a path through a tree, so the identifier simultaneously names an entity and locates it within a containment hierarchy. If the parent condition is removed, the child relation becomes undefined or loses the mechanism asserted by this edge; the parent can obtain independently, so the relation is presupposition rather than subsumption.


Hierarchical decomposability presupposes hierarchy's ranked-levels structure and adds within-level-dominates-cross-level coupling as a refinement. Hierarchy supplies the genus: Organizes elements into levels or ranks. Hierarchical Decomposability preserves that general structure while adding its differentia: Nested decomposition where within-level coupling dominates over cross-level coupling, making complex systems tractably analyzable one scope at a time. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


The Hierarchy and Network dossiers independently state this genus relation. Every hierarchy has nodes and edges whose pattern is first-class; the child adds an antisymmetric level order, direction-sensitive cross-level flow, and a tree-to-DAG-to-heterarchy restriction axis.

Hierarchy is the restricted kind of Network whose edges impose asymmetric, transitive levels rather than an unrestricted connection pattern.


Hierarchy retains the general ordering relation and adds explicit ranked levels, transitive asymmetric cross-level semantics, and often rooted parent structure. The order entry explicitly treats hierarchy as a kind of order rather than every order as hierarchical.

Hierarchy is order with explicit levels and asymmetric cross-level structure.


'Not function_mapping — a function-mapping is the FIRST-ORDER layer (data to data); a higher-order function operates on the NEXT layer up, taking or returning functions themselves... a STRATIFIED EXTENSION of function_mapping.' A specialization where inputs/outputs are themselves mappings. Function (Mapping) supplies the genus: Relates inputs to outputs. Higher Order Function preserves that general structure while adding its differentia: Treating a rule itself as a first-class object that other rules consume or produce. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association.


Historical determinism is a specialization of determinism: it asserts that the present state of a society plus the underlying forces (economic base, technological trajectory, geographic endowment) fix the trajectory of historical outcomes via lawful regularity. It inherits determinism's structural thesis — state plus laws yields unique successor — particularized to the macro-historical case where the relevant state and laws operate over civilizational rather than physical variables, with the corresponding deflation of contingency and agency.

Historical determinism is a kind of determinism in which historical outcomes are held to be fixed by underlying lawful forces independent of individual agency.