'Projection is the precise, geometric, idempotent SPECIAL CASE within the broader family of reductions that abstraction names.' Projection drops the dimensions perpendicular to a chosen target (vs abstraction's free-form essence-extraction). Abstraction supplies the genus: Focus on core elements. Projection preserves that general structure while adding its differentia: Map a richer object onto a lower-dimensional target along a chosen direction, discarding the rest. 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.


Remove the jointly incompatible consequences and the temporary assumption has not been shown impossible, so the indirect proof cannot close. Contradiction supplies the empty-model witness; proof by contradiction adds the controlled assumption, derivation, and discharge sequence.

Proof by contradiction contains a derived contradiction as the discharge condition that makes rejecting the temporary negated assumption valid.


Deductive reasoning supplies truth-preserving consequence from premises. Proof by contradiction is its strict specialization that adds a temporary negated target, derives an impossibility from the augmented premise set, and concludes the target by discharging that assumption. Every proof by contradiction is deductive, while direct and constructive deductions need not use the indirect contradiction sequence.

Proof by contradiction is the deductive strategy that assumes a target's negation, derives impossibility, and discharges that temporary assumption.


Property rights are the specific shape boundary takes when what is demarcated is a resource and the demarcation criterion is enforceable exclusion of non-holders by a defined holder. The four boundary components map directly: the bounded entity is the resource, the demarcation criterion is the legal-enforcement rule, permeability is the bundle of entitlements (use, capture, exclude, transfer) governing crossings, and accountability follows from holder identification. Property rights are jurisdictional boundaries around resources, structured as separable entitlement bundles backed by enforcement.

Property rights are the specific shape boundary takes when the demarcated entity is a resource and the criterion is enforceable excludability with bundled entitlements.


Proportion and scale adds compositions, visual harmony, viewer-relative sizing, and aesthetic or functional judgment to the portable ratio relation; common rescaling preserves the underlying quotient.

Removing the art-and-design frame leaves the ordered ratio relation among relative dimensions and their reference quantity.


Proportion and scale is the specific shape scale takes when the band of interest is the relative sizing among elements within a single composition or work, rather than the level of aggregation at which a system is described. It is a structurally-particularized instance of treating scale as a first-class object, with the added commitment that the relevant quantity is ratio — golden ratio, perceptual relative size, dimensional relationship to the viewer — and that the aesthetic and functional payoff is governed by how parts relate to each other and to the whole rather than by absolute dimensions.

Proportion and scale is the specific shape scale takes when relative sizes among elements within a work are the operative concern.


Proportionality is the specific shape commensurability takes when the dimensions being placed on a common scale are a triggering cause and a response — a wrong and its sanction, a threat and a restriction, a contribution and a reward. It is a structurally-particularized instance of bringing heterogeneous quantities into a common metric, with the added commitment that the comparison yields a fitness verdict: the response is appropriate when its measured magnitude tracks the cause's measured magnitude, excessive when it overshoots, insufficient when it undershoots. Without commensurability's prior reduction to comparable units, the proportionality judgment has nothing to weigh.

Proportionality is the specific shape commensurability takes when comparing the magnitude of a response to the magnitude of its triggering cause.


Proportionality presupposes normativity because it is constituted as an ought-side standard: actions, sanctions, or restrictions are required to be calibrated in scale to the wrong, threat, or interest they address, and deviations from that fit are subject to criticism. Without the prior structure of evaluation against a standard, the claim that a response is too harsh or too lenient has no purchase. Proportionality inherits normativity's general machinery of correctness-claims and specializes it by making the standard a comparative one: the response must match the triggering cause in magnitude or weight.

Proportionality presupposes normativity because it specifies a standard of correctness — fit between response and triggering cause — for evaluating actions.


Both store content so a matching cue can retrieve it without a separate explicit address. Prospective memory fixes the stored content to an intended future action, the cue to an event or time condition, and successful retrieval to execution or routing of that action.

Prospective memory is associative memory specialized to retrieving an encoded future intention when its event or time cue is encountered.


Prototype_theory is 'a specific model of category structure — center-with-gradient' standing against the definitional (necessary-and-sufficient) model; classification is the broad activity of sorting by any rule. The two great models of what a category is; prototype_theory is one species of classification. Classification supplies the genus: Sorting entities into discrete categories by explicit rules, turning unbounded variation into a finite, reusable map for downstream reasoning and action. Prototype Theory preserves that general structure while adding its differentia: Categories are organized around their best examples rather than by necessary-and-sufficient definitions, modeling kinds as centers with gradients rather than boxes with edges. 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.


Remove the candidate-to-prototype degree of likeness and the center-with-gradient membership rule becomes unavailable: a privileged exemplar remains, but there is no structure that places members nearer or farther from it. Similarity Measure is therefore an internal constituent, not merely a common implementation.

Prototype membership is constituted by measuring a candidate's likeness to a privileged exemplar under weighted relevant features.


The provenance history records transfers or transformations through verifiable principal-and-artifact bindings.

An explicitly attested provenance chain uses each mark as an internal link binding a principal to a particular artifact state against a trust anchor. Documentary, observational, and reconstructed histories can still be provenance without formal or cryptographic attestation, so the relation is conditional.

Provenance contains Attestations when point-in-time principal-and-artifact bindings secure links in its multi-step history.


The tracked entity changes custody between successive holders.

When custody changes, provenance internally represents each transfer event as a link connecting outgoing and incoming holders, the object, triggering act, and transferred duties. Provenance can remain complete for an entity that never changes custodian, so the relation is conditional.

Custody-Transfer records are internal links in Provenance when the tracked entity passes between successive holders.


Provenance presupposes traceability because the documented record of an entity's origin, custody transfers, and transformations is the content claim that traceability's infrastructure makes verifiable. Without traceability's backward-and-forward linkage capability — the navigable chain from any element to its derivation history — provenance assertions would be unsupported claims about origin with no way to audit them. Traceability supplies the infrastructure; provenance supplies the specific content of authentic-origin claims that traceability's chain makes inspectable and assignable for credit, blame, or verification.

Provenance presupposes traceability because the documented chain of origin and custody requires the underlying infrastructure that links elements to their history.


Laundering operates on the relation between a present item and its origin through a custody or publication chain. Without a provenance claim to obscure, sever, or replace with a cleaner-looking chain, there is no laundering operation—only ordinary transfer.

Provenance laundering presupposes Provenance because the process is defined by making an item's origin and successive custody transfers harder to reconstruct.


Proxy–Target Fidelity supplies the genus: How faithfully an observable proxy tracks the unobservable target it stands in for — the degree to which acting on, optimizing, or inferring from the proxy is acting on the target itself. Proxy-Target Divergence preserves that general structure while adding its differentia: An apparatus calibrated against a proxy keeps operating on it after the proxy-target relationship has silently decoupled. 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.

Proxy-Target Divergence is a specialization of Proxy–Target Fidelity, retaining the parent's defining structure while adding the child's specific commitments.


Fidelity has no referent until a proxy is appointed to represent a target for some use. The live node then evaluates how well that standing-in relation holds across regimes and under optimization. Representation is the prerequisite mapping claim; proxy fidelity is its use-relative graded adequacy and substitution risk, not the mapping artifact itself.

Proxy-target fidelity presupposes a representation relation in which an observable stand-in is designated to carry selected information about a distinct latent target.


Selection supplies an eligible population, a use- or fitness-dependent basis, differential retention, and a changed survivor composition. Pruning inherits that structure and adds a specific temporal and mereological differentia: the candidates are surplus components of an already built system, the surplus was generated because the useful subset was not knowable in advance, and the non-selected components are removed to leave a leaner configuration.

Pruning is selection specialized to a previously over-generated component set whose under-used members are removed after use reveals which subset should persist.


Psychological safety presupposes trust because its core claim — that team members can speak up, admit error, and disagree without fear of ridicule or retaliation — requires trust's prior structure of confident reliance under vulnerability. Without the willingness to be vulnerable to others based on positive expectations of their ability, benevolence, and integrity, the interpersonal risk-taking psychological safety names is unavailable. Psychological safety inherits trust's vulnerability-under-incomplete-monitoring structure and specializes it to the team setting, where the shared belief that good-faith voice will be received without reprisal scales individual trust into a climate-level resource.

Psychological safety presupposes trust because it is the team-level condition in which members can be vulnerable in interpersonal risk-taking without fear.


Taxation, selective incentives, strong norms, repeated contribution, or an endowment can suppress observed free riding without changing the good's consumption properties.

Potential beneficiaries receive the non-rival benefit whether or not they pay, so withholding contribution is privately attractive while universal withholding defeats provision. Institutions can suppress the behavior without changing the defining non-excludability and non-rivalry.

Public Goods typically generate the Free Riding incentive that turns non-excludable benefit into under-contribution and under-provision.


Public vs. private contexts is the structurally-particularized form observability takes in the social-behavioral case: when an actor's choices are externally observable, internal preferences are inferable through the action; when private, the same preferences may produce divergent action. It inherits observability's commitment to the inferability of internal state from external outputs, particularized to the case where the actor anticipates the observer's inference and adjusts behavior accordingly, producing the systematic public–private behavioral gap Kuran formalized.

Public vs. private contexts is the specific shape observability takes when behavior's audience-visibility status systematically alters action.


Pub-sub routes through a named intermediary TOPIC/broker rather than to a recipient — 'the topic itself becomes an object,' a reified intermediary reference. It presupposes indirection (introducing an intermediary reference that decouples endpoints).


The threshold-breach burst is a tipping-point crossing; punctuated_equilibrium presupposes it as one constituent and adds the loading-phase, recurrence, and heavy-tailed increment distribution. 'the tipping point is one ingredient of the pattern, not the pattern.'. Tipping Points (or Phase Transitions) supplies the prerequisite condition: Abrupt state change. Punctuated Equilibrium operates against that background: Change runs bimodal in tempo: long intervals of near-stasis that load latent constraint, interrupted by short bursts of correlated structural reorganization. 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.


Purity and pollution presupposes contagion because the structural claim that pollution is removable only through cleansing rests on a prior commitment that pollution propagates contact-to-contact through a social network. It inherits contagion's pattern in which a state spreads from an affected element to a connected one and reproduces in each new host, particularized to symbolic-categorical taint rather than infection or behavior. Without contagion's transmission-by-contact structure, the binary classificatory defilement could not spread to threaten boundary integrity.

Purity and pollution presupposes contagion because pollution is treated as transmissible by contact, spreading the categorical taint through networks.


Purity and pollution sorts things into pure and polluting, treating pollution as contagious matter-out-of-place that defiles classificatory order and requires ritual cleansing. This is a particular case of symbolic boundaries: conceptual distinctions actors deploy to categorize the social field with substantial consequences. Symbolic boundaries supply the underlying classificatory operation that sorts the world into kinds. Purity and pollution specialize this by adding the contagion logic and the ritual-purification mechanism, defending the integrity of the categorial scheme against transgression. Without symbolic boundaries as substrate, there would be no classifications for pollution to threaten.

Purity and pollution presupposes symbolic boundaries because the pure-polluting partition is a particular classificatory operation defending cultural categories.


Quality control is a measure-compare-act feedback gate binding process variation to defined tolerances. Feedback supplies the prerequisite condition: Outputs influence inputs. Quality Control operates against that background: Checking output against a specification before release and rejecting or reworking non-conforming items, binding process variation to defined tolerances through a measure-compare-act feedback gate. 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.


Quality control is a kind of verification specialized to the production-to-customer interface: the object being checked is each unit of output, the specification is the defined tolerance, and the procedure is the inspection or sampling test that triggers rejection or rework when items deviate. It inherits verification's commitment to checking conformance against a stated criterion via an evidence-producing procedure yielding accept/reject verdicts, and supplies the specific feedback-gate function that binds process variation to defined limits before release, distinct from the prevention and improvement layers around it.

Quality control is a specialization of verification in which the conformance check operates as a release gate against manufacturing-style tolerance specs.


Predicate supplies the prerequisite condition: A testable yes-or-no property of an object, returning a truth value. Quantifier operates against that background: Specifies the scope of a claim over a domain — all, some, none, most, or exactly N. 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.

Quantifier presupposes Predicate, whose structure must already obtain for the child mechanism to be meaningful or operational.


The state is an output constituent rather than a genus of the quench operation. The qualifier excludes immutable copies and policy codification whose persistence is imposed externally rather than earned by basin-and-barrier geometry.

In kinetic-trapping branches, Quenching contains a locally persistent but globally nonpreferred captured state isolated by a mobility or activation barrier.


A fast transition in name alone is insufficient. Onset, duration, relaxation time, phase alignment, and the constraint-to-exploration ratio determine whether an in-flight state is actually captured and how much frustration is frozen in.

Quenching is defined by a race in which mobility suppression must outrun the system's relaxation, producing frozen, equilibrated, or mixed regimes by rate ratio.


Queueing is a specialization of allocation: it assigns a limited supply (server time at a finite-capacity resource) across competing claimants (arriving jobs, requests, customers) under a feasibility constraint (one job at a time per server) guided by a discipline (FIFO, priority, LIFO). It inherits allocation's structural commitment — finite stuff flowing to multiple sinks — and particularizes it to the temporal case where the assignment is by wait order rather than instantaneous division, with arrival and service processes setting the dynamics.

Queueing is a kind of allocation that distributes finite service capacity across arriving demands by determining who waits and for how long.


Queueing presupposes flow because its structural setting is a directional transfer of items from arrival to service to departure, with rates, conservation, and channel constraints all native to flow. Without the prior availability of flow as a continuous directional transfer through a system with defined source, channel, and sink, there is no inflow-and-outflow geometry against which finite service capacity can create accumulation. Little's law and the rest of queueing theory presuppose the flow conservation that ties arrival rate to throughput and time-in-system.

Queueing presupposes flow because waiting only arises when an inflow of work items meets a service capacity that constrains throughput.


Concurrency supplies the prerequisite condition: Manage simultaneous processes. Race Condition operates against that background: The outcome of a system depends on the uncontrolled relative timing of concurrent actions on shared state, so the order effects land — not the actions — determines the result. 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.

Race Condition presupposes Concurrency, whose structure must already obtain for the child mechanism to be meaningful or operational.


Competition supplies rival actors pursuing negatively coupled advantage over a scarce prize. Race to the Bottom adds a commonly ordered dimension, unilateral gain from moving downward on it, mobility of the prize toward the undercutter, response pressure on rivals, and convergence toward a lower bound that may dissipate joint value. Many competitions instead reward improvement, endurance, differentiation, or upward performance, so the specialization is strict.

A Race to the Bottom is the strict species of Competition in which relative advantage is gained by lowering a shared ordered dimension and thereby inducing reciprocal undercutting.


2A: random walk is a stochastic process (not always Markovian). Stochastic Process supplies the genus: A quantity indexed (usually by time) whose evolution is governed by randomness — an indexed family of random variables sharing one probability law. Random Walk preserves that general structure while adding its differentia: A trajectory built as the running sum of independent random increments, whose displacement grows like the square root of the number of steps. 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.


Randomization presupposes causality because its entire warrant is causal inference: random assignment severs the link between treatment and pre-treatment characteristics, so observed differences in outcomes can be attributed to the productive connection from cause to effect. Without causality's four-part structure — cause, effect, productive connection, modal robustness — there would be no target relation for the randomization to identify. Random assignment is precisely the procedure that licenses the counterfactual claim causality requires.

Randomization presupposes causality because its purpose is to identify causal effects by severing the link between treatment and confounders.


Randomization is the particular form experimental design takes for the assignment step: units are allocated to treatment conditions by an explicitly stochastic mechanism with specified probabilities independent of unit characteristics. This achieves the structural property that treatment groups are expected statistically equivalent on all pre-treatment variables — measured and unmeasured. The general architecture of principled comparison for causal inference is specialized here to the stochastic-assignment mechanism, with chance-driven allocation as the lever that neutralizes confounding and supports valid causal inference.

Randomization is the specific shape experimental design takes when treatment assignment is made stochastic to neutralize observed and unobserved confounders.


Randomization is the mechanism that physically realizes a confounder-severing intervention (severs every incoming edge at once). Add intervention as a parent; randomization keeps its causality/experimental_design/probability parents.


Randomization is the structurally-particularized form probability takes when a stochastic mechanism is purposefully used to assign experimental units to conditions, ensuring each unit's probability of any treatment is specified in advance and independent of its characteristics. It inherits probability's coherence apparatus — sample space, events, calibrated assignment of numbers in [0,1] — particularized to the assignment-procedure case. The expected statistical equivalence of treatment groups follows directly from the probability calculus applied to the assignment.

Randomization is the specific shape probability takes when the chance mechanism is deliberately injected to assign units to treatments.


Probability supplies the coherent distribution, moments, conditional events, and test baselines by which an ensemble is lawful. Randomness adds a generating source, predictor-relative unpredictability, source taxonomy, and application-specific quality certification.

A scoped Randomness claim requires a Probability law specifying the ensemble regularities beneath individually unpredictable outcomes.


Rank is undefined until the members of a comparison set are placed under an order relation. Order is therefore an internal constituent: it supplies the ordinal positions while Rank-Dependent Value adds a mapping from those positions to value and the rank-preserving-shift invariance. Remove the order and no first, median, percentile, or relative standing remains to carry value.

Rank-Dependent Value contains an ordering of the comparison distribution because ordinal position is the argument from which its positional component is computed.


Rashomon_effect is 'a diagnosis of abductive UNDERDETERMINATION' — the condition in which inference-to-the-best-explanation cannot converge (several internally-coherent accounts fit equally). It presupposes the abductive frame and names where it stalls. Abductive Reasoning supplies the prerequisite condition: Infer the hypothesis that would best explain a surprising observation, accepted provisionally and held defeasibly against better candidates. Rashomon Effect operates against that background: Multiple internally coherent but mutually inconsistent accounts of one event, underdetermined by the testimony set with no internal adjudication procedure. 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.


The ratchet effect is 'a specific path-dependent mechanism: direction-asymmetric, monotone, lock-driven'; 'many path-dependent systems are not ratchets (they can reverse); the ratchet is the one-way subclass.' A strict specialization of path_dependence. 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. Ratchet Effect preserves that general structure while adding its differentia: Direction-asymmetric coupling plus a locking element produces accumulating one-way displacement under bidirectional forcing. 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.


Rate Coding specializes the general representation-and-recovery scheme to identical discrete events. The encoder places magnitude in event frequency and the decoder recovers it through windowed counting, with the integration window trading temporal resolution against precision.

Rate Coding is an Encoding and Decoding scheme in which magnitude is carried by identical-event frequency over an integration window.


A rate limit is a temporal constraint on consumption (units per time per actor); a specialization of constraint. Constraint supplies the genus: Limits possibilities to guide outcomes. Rate Limiting preserves that general structure while adding its differentia: Cap the temporal rate at which an identifiable actor consumes a resource. 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.


'It is one specific tool — meter, window, budget, response — within the broader discipline of provisioning and scheduling resources, not the whole of it.' The per-actor-per-time cap within resource_management. Resource Management supplies the genus: Allocation of finite assets. Rate Limiting preserves that general structure while adding its differentia: Cap the temporal rate at which an identifiable actor consumes a resource. 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.


Comparison supplies the genus of placing quantities in one declared frame. Ratio adds ordered quantitative roles, a nonzero reference denominator, division, and a quotient interpreted multiplicatively or per unit.

Ratio is comparison specialized to a multiplicative or per-unit relation obtained by dividing an ordered numerator by a nonzero denominator.


Reactance is a motivational state triggered specifically by the perceived restriction of a behavioral freedom: without a constraint imposing itself on the admissible set of actions the individual believes they possess, there is no threat-to-freedom event, no aversive arousal, and no freedom-restoration motivation. The four-component process presupposes that the structural feature being responded to is a binding restriction on what one is allowed to choose — the very situation constraint names — and reactance is the psychological reaction to that situation.

Reactance presupposes constraint because the motivational state only arises when a perceived freedom is threatened or restricted by an external limit.


Reactance is the homeostatic particularization for the variable of perceived behavioral freedom: when external constraint threatens to push the variable below its acceptable band, an aversive motivational state arises and drives corrective behavior aimed at restoring the freedom. Where homeostasis names closed-loop self-regulation that holds a variable within a setpoint range generally, reactance fixes the regulated variable as autonomy and the corrective action as freedom-restoration motivation — a particular sensor-comparator-actuator loop operating on the psychological variable of choice.

Reactance is the specific shape homeostasis takes when perceived autonomy is the regulated variable and freedom-restoration is the corrective response.


Back-action is the SUBSPECIES of externality where the peripheral harm does not stay with the third party but is metabolized by a downstream channel and RETURNS to the causer after a delay. externality is the genus; the return path is the differentia. Externality supplies the genus: Spillover effects. Reaction-Channel Back-Action preserves that general structure while adding its differentia: Peripheral harm from an action is metabolized by a downstream system and returned to the original actor as operational cost, after a delay. 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 reaction intermediate is the named transient INTERIOR STATE of a multi-step transformation (absent at both endpoints), whose formation/consumption rates govern throughput; it presupposes a transformation to have an interior of. Transformation supplies the prerequisite condition: A rule-governed mapping that restructures an input into a different output, holding certain invariants fixed while altering others. Reaction Intermediate operates against that background: A multi-step transformation passes through a named transient state, absent at both endpoints, whose formation and consumption rates govern throughput and form a distinct intervention surface. 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.


Reality monitoring is the use-time CLASSIFICATION of each stored item by source class (internally-generated vs externally-perceived) from source-correlated features — a specialized classification with its own signal-detection (d'/criterion) structure. Classification supplies the genus: Sorting entities into discrete categories by explicit rules, turning unbounded variation into a finite, reusable map for downstream reasoning and action. Reality Monitoring preserves that general structure while adding its differentia: A system holding items from multiple source classes must, at use-time, attribute each item to its source — most basically internally-generated versus externally-perceived — with characteristic errors when the cues mislead. 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.


Set and Membership is internal to the prime's defining construction: the possibility collection, realized collection, subset relation, and omitted members are the objects being compared. The child adds a generating process, model-constructed possibility boundary, observed realization, gap shape, and intervention logic.

Realized vs Possible Outcomes contains a possibility set, a realized subset, and the membership and inclusion tests that expose their gap.


The coverage footprint and its falloff define the local jurisdiction whose tiling composes system-wide coverage; remove the inside-outside demarcation and the field is no longer bounded or receptive selectively.

A receptive field contains a boundary in input space separating stimuli that can affect the unit from those that cannot.


Receptor saturation specializes boundedness by fixing the bounded quantity as available binding sites or interaction slots and the consequence as an asymptotic response ceiling. Where boundedness names the general property that some structural feature is contained within a finite envelope, receptor saturation specifies that the envelope is the count of available sites and that approaching this envelope produces hyperbolic or sigmoidal saturation in the response — a particular shape boundedness takes when finite interaction capacity caps the input-to-output mapping at a hard ceiling.

Receptor saturation is a specialization of boundedness in which finite binding-site capacity caps the maximal achievable response regardless of further input.


Receptor saturation describes a system whose response approaches an asymptote because the population of binding sites is finite and eventually fully occupied. The number of sites is a binding restriction on admissible response magnitudes: no configuration with response above the saturation ceiling is reachable, regardless of input intensity. That is exactly the structure of a constraint — a hard cap on the feasible set — specialized to capacity ceilings imposed by fixed interaction substrate.

Receptor Saturation is a kind of constraint: a finite count of binding sites caps the system's response regardless of further input.


Reciprocity presupposes cooperation because its content — responding in kind to others' contributions — is intelligible only against the prior tension cooperation names: the gap between collective optimum and individual incentive in which costly contributions must be sustained against defection. Without that gap, in-kind return is just trade; with it, reciprocity becomes the structural device that converts a one-shot defection problem into a repeated game where contribution can be rewarded and defection punished. Reciprocity inherits cooperation's structural situation and supplies one of the principal mechanisms by which the cooperative outcome is stabilized.

Reciprocity presupposes cooperation because the in-kind return that defines reciprocity is the mechanism by which costly cooperative contributions are sustained.


Reciprocity is the specific shape symmetry takes when the invariance is between actions and their returns within a social relationship: help is met with help, harm with harm, contribution with contribution. It is a structurally-particularized instance of transformation-group invariance, where the transformation is the role-swap between giver and receiver and the property preserved is the kind or magnitude of the action. The added commitment is that the symmetry is enforced across time through expectations and norms rather than as an instantaneous geometric balance, and that violations carry social consequences ranging from withdrawal to retaliation.

Reciprocity is the specific shape symmetry takes when actions in an ongoing relationship are returned in kind across parties.


It inherits the judgment of treatment under a defensible standard and adds a prior representational gate: whose identity is intelligible, whose testimony is credible, and which injuries count as injuries before distribution or procedure is assessed.

Recognition justice is fairness specialized to whether parties and their harms enter the evaluative frame with equal standing.


Reconsolidation is memory consolidation specialized to re-storing a previously consolidated item after retrieval makes it malleable again. Memory Consolidation supplies the genus: Converting a newly encoded trace from a fragile, overwritable form into a durable, interference-resistant one through a slow post-encoding stabilization process. Reconsolidation preserves that general structure while adding its differentia: A stored item returns to a malleable state when retrieved and must be re-stored, so every retrieval is a read-modify-write and a potential edit of the original. 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 stale authoritative record is a proxy that has decoupled from the reality (target) it describes while still driving decisions, fitting the named-children pattern (alongside Goodhart, sensor drift, etc.). Proxy-Target Divergence supplies the genus: An apparatus calibrated against a proxy keeps operating on it after the proxy-target relationship has silently decoupled. Record-Reality Divergence preserves that general structure while adding its differentia: An authoritative record of an external state drifts from the reality it describes while remaining the basis for downstream decisions. 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.


A typed cross-system sameness verdict (equivalent/near-match-with-loss/ambiguous/no-match) that deliberately BLOCKS the transitive closure an equivalence_relation enjoys; presupposes the equivalence machinery precisely to control where it must not apply across two sets. Equivalence Relation supplies the prerequisite condition: Groups elements into equivalence classes. Record Reconciliation operates against that background: Matching records across two naming systems and declaring, for each pair, a typed sameness verdict with explicit conditions of preservation and loss. 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.


It inherits measurable dispersion across instances and adds a sensitive entry window, weak control by current stock, lifespan persistence, and age-structured echoes. Variability supplies the genus: Differences across instances. Recruitment Variability preserves that general structure while adding its differentia: A stock replenished by discrete cohorts whose size is set by environmental conditions at an early sensitive window — not by current stock — develops persistent, age-structured echoes from which cohorts were lucky. 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.

Recruitment variability is variability specialized to externally driven differences among discrete incoming cohorts whose signatures persist through a stock.


Amplification supplies the genus: Increase signal or disturbance. Recursive Attenuating Amplification preserves that general structure while adding its differentia: A one-shot input recirculating through a leaky operator with sub-unit retention produces a bounded total response of input/(1−k). 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.

Recursive Attenuating Amplification is typically a specialization of Amplification, retaining the parent's defining structure while adding the child's specific commitments.


Strategic red teaming is external analytic challenge strengthened with an adversarial brief, institutionally separated role, protected authority, and contracted pre-commitment response. Both install a competent outside challenge to expose assumptions and failure modes while the primary work can still change, with findings routed back before commitment. Red teaming requires an explicit adversarial perspective, protected organizational authority, role separation, and capture-resistant reporting that the broader genus does not.


After the military_strategic_studies frame is stripped away, the retained structural roles are those of Wargaming: Rehearse a plan against an adaptive opponent, turn by turn, to surface the assumptions it hid. Red Teaming In Strategy adds the local frame and commitments expressed in its identity: Build an independent, role-protected adversary whose job is to attack the plan before reality does. 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.

Red Teaming In Strategy is the framed or domain-specific realization of Wargaming; removing the local frame leaves the parent's structural relation intact.


Redundancy is a specialization of reserve. The general reserve pattern is a deliberately maintained surplus of capacity beyond expected need, valuable precisely because available when demand exceeds expected. Redundancy specializes this by giving the surplus a particular form: duplicated components whose failure-independence allows any one to maintain function if others fail. The same hold-surplus-against-shock logic of reserve applies, with component duplication as the specific implementation and fault tolerance as the specific shock to absorb.

Redundancy is a specialization of reserve in which the maintained surplus takes the form of duplicated components that can substitute on failure.


Self-checking uses redundancy (the partially-independent path) and adds a comparator that extracts an error signal. After the systems_cybernetics frame is stripped away, the retained structural roles are those of Self Checking: A system detects errors in its own output by computing the answer through partially-independent paths and comparing. Redundancy adds the local frame and commitments expressed in its identity: Duplicate critical components. 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.


Maintaining two oppositely-optimised persistent substrates presupposes redundancy (the duplicate path), adding a periodic transfer mechanism that consolidates rather than masks. After the systems_cybernetics frame is stripped away, the retained structural roles are those of Two-Store Architecture: A fast interference-prone store and a slow integrated store coupled by a periodic transfer mechanism, paying for both speed and integration by maintaining two oppositely-optimised substrates. Redundancy adds the local frame and commitments expressed in its identity: Duplicate critical components. 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.


'Refactoring is a transformation, but a BEHAVIOR-PRESERVING one — it is the specific member of the transformation family constrained by the equivalence invariant.' A clean specialization of transformation. Transformation supplies the genus: A rule-governed mapping that restructures an input into a different output, holding certain invariants fixed while altering others. Refactoring preserves that general structure while adding its differentia: Change internal structure while preserving observable behavior. 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.


Feedback supplies the prerequisite condition: Outputs influence inputs. Reference Cadence Exceeds Tracking Bandwidth operates against that background: When the signal a closed loop must track changes faster than the loop's bandwidth, persistent error follows that no amount of executor effort can close. 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.

Reference Cadence Exceeds Tracking Bandwidth presupposes Feedback, whose structure must already obtain for the child mechanism to be meaningful or operational.


Reference-point dependence presupposes comparison because an outcome obtains its sign and value only through contrast with the selected baseline. Remove the outcome-to-reference comparison and no signed departure exists, so moving the reference cannot change the outcome's classification or value. Reference-point dependence is an evaluation regime built on a comparison, not every comparison or a taxonomic species of comparing.


Proxy-Target Divergence supplies the genus: An apparatus calibrated against a proxy keeps operating on it after the proxy-target relationship has silently decoupled. Reference Standard Decay preserves that general structure while adding its differentia: A measuring apparatus keeps scoring against a reference standard that has silently drifted, so its numbers stay stable while their meaning shifts. 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.

Reference Standard Decay is a specialization of Proxy-Target Divergence, retaining the parent's defining structure while adding the child's specific commitments.


Refinement is the iterative sharpening of a candidate through repeated cycles of evaluation and adjustment, which structurally requires that the output of each round (the current candidate's quality) be routed back to shape the next round's input. Without feedback's closed loop — output measured, signal returned, input modified — there would be no mechanism by which iterations could accumulate progress; refinement would collapse into one-shot creation or undirected variation rather than the directed convergence that defines the pattern.

Refinement presupposes feedback because each iterative improvement requires evaluating the current candidate and routing that judgment back to adjust the next pass.


Refinement is the convergence-toward-fitness particularization of iteration: each cycle takes a current candidate, evaluates it, and produces a sharpened successor that becomes the input to the next cycle. Where iteration names repeated application of a step with cumulative use of prior outputs generally, refinement fixes the progress notion as monotone improvement toward precision or fitness, the state carried as the current candidate, and the operation per cycle as evaluation-and-adjustment — a particular shape iteration takes when an initial approximation is being progressively sharpened.

Refinement is the specific shape iteration takes when each cycle progressively sharpens the precision, quality, or fitness of a candidate.


It caps one identifiable unit's action rate over time, inheriting the structural effect of a temporal budget. Its differentia are that the limit is imposed by the unit's own post-action state, starts immediately after firing, and expires after a recovery interval rather than being administered by an external counter.

A refractory period is intrinsic rate limiting specialized to an automatic post-action interval during which the same unit cannot act again.


Frame Change supplies the broader genus: a referent is preserved while an operative coordinate, classificatory, tonal, or interpretive frame is replaced and bridged. Reframing preserves that structure and adds an interpreting agent or community plus a change in meaning, salience, evaluation, or action. Non-interpretive frame changes can occur without Reframing, establishing strict subsumption.

Reframing is the interpretive species of Frame Change, preserving a referent while replacing the frame that assigns its meaning and implications.


Framing supplies a presentational or contextual structure that changes what an observer notices, infers, or values. Reframing is the strict specialization that starts with an already active frame, substitutes another frame over substantially the same referent, and compares the changed meaning or action implications. Every reframe therefore performs framing, while an initial framing need not replace anything and is not yet a reframe.

Reframing is framing specialized to a before-and-after operation in which the referent stays fixed while a replacement frame changes how it is interpreted.


Regime Change retains the general before-state, transition, and after-state structure and adds a change between stable operating regimes whose feedback, attractor, or governing-response structure differs qualitatively. The broader parent admits ordinary state changes without that regime-level discontinuity.

Regime Change is a State Transition between qualitatively distinct stable regimes with altered governing dynamics.


Diminishing Returns supplies the exhaustion arm of the conjunction. If additional use of the incumbent strategy still produced undiminished gains, the system would not be stalled between regimes; it would merely have an optional future capability to develop. The plateau identity therefore requires diminishing returns inside it, while adding the absent, qualitatively different successor-capability arm that Diminishing Returns alone does not contain.

A regime-transition plateau necessarily contains declining marginal gains from the strategy that powered the first regime.


A successful first regime commonly leaves specialized assets, routines, skills, evaluation criteria, and beneficiaries that raise the cost of building its successor. This history-shaped constraint deepens many transition plateaus, but it is not universal: a successor capability may simply be unavailable or slow to mature even when the inherited path is easy to abandon.

Prior-regime investments and beneficiaries typically constrain the pivot, although an exogenous capability gap can produce the plateau without strong historical lock-in.


Register shifting is the structurally-particularized form accommodation takes in the sociolinguistic case: the system (the speaker) modifies internal structure (lexical, syntactic, phonological selections) in response to external pressure (formality, audience, mode) to remain coherent without rupturing identity. It inherits accommodation's commitment to selective internal adjustment that preserves the system under external demand, particularized to the case where what is adjusted is style position along a register continuum.

Register shifting is the specific shape accommodation takes when speakers selectively adjust linguistic form to context, audience, or task.


The specific three-party form of indirection — provider, consumer, and a registry that is its own addressable entity — whose payoff is turnover survival (a provider can relocate without consumer change). Indirection is the abstraction's structural parent; registry-mediated discovery uses indirection but adds the registry, the stable-name/mutable-location split, and turnover survival. Indirection supplies the genus: Introduces intermediary references. Registry-mediated discovery preserves that general structure while adding its differentia: Agents find each other through a shared registry rather than by direct reference: a named indirection mapping stable identifiers to current locations, so coupling survives turnover. 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.


Regression to the mean presupposes bias because failing to account for the regression effect when selecting on extreme initial values produces a systematic displacement: extreme observations re-measure closer to the mean, and treating the change as causal effect introduces an offset proportional to (1 minus correlation) times the initial deviation. Without bias's framing of systematic-rather-than-random displacement, the regression phenomenon would be mere noise; instead it is a predictable directional offset that survives averaging, generating spurious causal claims (drug works on the sick, second-novel slump) unless corrected.

Regression to the mean presupposes bias because uncorrected use of extreme-selected observations yields a systematic offset away from the underlying mean.


Regression to the mean is a specialization of probability: it follows directly from the calibrated quantification of uncertainty when observations decompose into a stable component plus a transient random component. It inherits probability's coherence apparatus — sample space, conditioning, expectation — and particularizes it to the conditional-expectation case where an extreme initial draw, conditioned on, predicts a less extreme re-measurement. The magnitude (1−r) times the initial deviation is a direct consequence of bivariate distribution structure.

Regression to the mean is a kind of probability phenomenon in which extreme observations re-measure closer to the population mean due to transient noise.


Regret is the difference an agent registers between the outcome obtained and the better outcome a forgone alternative would have produced. Computing that gap requires placing the actual and counterfactual outcomes under a shared evaluative frame and reading off a greater-lesser relation. Without Comparison as the underlying operation, no value gap can be formed, so regret presupposes the alignment-and-difference machinery that comparison supplies, applied retrospectively to chosen versus unchosen paths.

Regret presupposes Comparison: it is the value gap measured between the realized outcome and a counterfactual alternative.


Regret is meaningful only after an agent has selected one alternative from a set and foreclosed the others; it then evaluates the realized path against unchosen counterfactuals. Without a prior Decision — the act of collapsing deliberation into commitment — there is no chosen-versus-foregone pair to compare and no commitment whose costs can be registered. Regret therefore presupposes the decision event as the structural precondition of its own evaluative geometry.

Regret presupposes Decision: there must have been a prior commitment among alternatives before retrospective evaluation can register a gap.


Regret presupposes modal reasoning because its defining structure is retrospective comparison of the realized outcome against the better outcome a forgone alternative would have produced. That comparison requires quantifying over a space of possible-but-unrealized alternatives and evaluating a counterfactual conditional, which is exactly what modal reasoning supplies via its operators over accessible alternatives. Without the prior availability of structured reasoning over what could-have-been, regret reduces to a brute affective response with no benchmark against which to register the gap between actual and alternative.

Regret presupposes modal reasoning because the value gap it registers is a comparison between the actual outcome and a counterfactual alternative.


Regularization is 'a MODIFICATION of the objective — adding a penalty term — that changes which extremum is sought; it presupposes an optimization but is not one.' Presupposes-parent. Optimization supplies the prerequisite condition: Finds best solution under constraints. Regularization operates against that background: Add a tunable soft penalty on the complexity of a candidate solution to a fitting procedure, trading data-fit against complexity by an explicit weight chosen for out-of-sample performance. 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.


Regulatory capture presupposes institution because the dynamic operates on the durable rule-complex Stigler analyzes: a regulator is an institution -- a self-reproducing set of rules, roles, and shared expectations enforcing a mandate -- and capture is the redirection of that institutional apparatus to serve private rather than public interests. Without institution's framing of enduring rule-enforcement structure beyond individual actors, capture collapses into mere corruption. Capture is institutional precisely because the rule-complex itself becomes the instrument, not just particular officials.

Regulatory capture presupposes institution because it is the redirection of an institution's rule-enforcement apparatus toward the interests it should regulate.


'Capture is one instance of rent-seeking — an agency taken over by the interests it regulates'; rent_seeking names the direction-of-effort criterion wherever an allocation channel exists. rent_seeking is the genus, regulatory_capture the species. Add rent_seeking as parent. Rent Seeking supplies the genus: Expending real resources to capture a larger share of existing value by working the rules that govern allocation, rather than to produce new value. Regulatory Capture preserves that general structure while adding its differentia: Regulated agents gain influence over institution redirecting it. 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.


Both expend effort before failure to preserve future function. Rehearsal adds a particular intervention: rerun the whole action in a lower-stakes but behaviorally faithful setting, observe performance, and correct between iterations. It is distinct from bare refresh in Maintenance Rehearsal.

Rehearsal is maintenance specialized to preserving a capability through repeated near-live execution and feedback before it is needed at full stakes.


Reification is a failure that befalls an abstraction: the constructed summary is identified with its substrate and the audit trail atrophies. Presupposes an abstraction to corrupt; the pathology is the lost provenance, not the abstracting. Abstraction supplies the prerequisite condition: Focus on core elements. Reification operates against that background: An abstraction designed to summarise a substrate is treated as the substrate itself, with the audit trail back to the original allowed to atrophy. 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.


Reinforcement is the OPERANT core of conditioning (action-strengthening-by-consequence); conditioning_behavioral is the broader umbrella (incl. Pavlovian). Conditioning (Behavioral) supplies the genus: Learning via association. Reinforcement preserves that general structure while adding its differentia: An action's consequence selectively changes the probability of that action recurring under similar conditions. 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.


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. Reinforcement preserves that general structure while adding its differentia: An action's consequence selectively changes the probability of that action recurring under similar conditions. 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.

Reinforcement is a specialization of Natural Selection, retaining the parent's defining structure while adding the child's specific commitments.


Reinforcement may be specified through direct consequence contingencies or schedules without an explicit reward predictor and computed temporal-difference error.

In prediction-based reinforcement systems, the loop computes received reward or bootstrapped return minus expected value and uses that internal signal to change action probability or value. The error is a constituent of the larger consequence-driven process, not the whole process and not its taxonomic genus.

Reward prediction error is a common internal teaching signal in reinforcement, updating value or action strength from expected-versus-received reward.


The exposure is measured by the restoration or redeployment gap between the asset's inside value and next-best outside value. Preserving reversibility reduces specificity and forfeits surplus; committing irreversibly creates quasi-rent and closes alternative paths—the prime's exact choice spectrum.

A relationship-specific investment contains an irreversible commitment decision: resources are sunk into a configuration and cannot be costlessly restored or redeployed once the partner-specific asset exists.


Asset specificity is the specific condition that ELEVATES transaction-cost frictions into a hold-up problem; high specificity CAUSES high transaction costs via appropriable quasi-rents. A driver presupposing the transaction-cost frame (Williamson). Transaction Costs supplies the prerequisite condition: Frictions in exchange. Relationship Specific Investment operates against that background: Resources spent to build an asset whose value is highest inside one specific relationship and drops sharply outside it, creating asymmetric hold-up exposure. 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.


The child retains the general pattern of intrinsic capacity, an actively suppressive constraint set, a composite prior baseline, and removal or separation from the suppressor. It adds explicit home and recipient contexts, non-portability of the constraint set, a transfer boundary, and the joint-attribution error that mistakes the constrained home equilibrium for an actor-only property.

Release From Controlling Context is Constraint Release specialized to an actor separated from its home regulators by transfer into a recipient context lacking them.


Both preserve selected structure from a predecessor across a discontinuous migration into a successor. Remediation adds a medium change, quoted older forms used as legitimacy scaffolding, progressive shedding of substrate-bound conventions, and divergence through affordances unavailable to the predecessor.

Remediation is legacy integration specialized to a successor medium that selectively carries forward an older medium's conventions while exploiting new substrate affordances.


Interarrival, survival, and hazard functions require a probability measure over event times. The parent can occur independently, but without it the child’s mechanism is undefined; this is prerequisite dependence rather than subsumption.


A renewal process is recurrence specialized by reset events and distributed interarrival times. The parent supplies the genus and can occur without the child; the child preserves that structure while adding commitments the parent does not require.


Renormalization coarse-grains shorter-scale degrees of freedom and rescales to produce an effective description in which irrelevant couplings flow away and only the load-bearing structure remains. That is the move of abstraction: a purpose-relative projection from a concrete original onto the features that matter for the reasoning at hand, with the rest deliberately dropped. Renormalization specializes abstraction by tying the projection to a scale-flow and a universality argument about what survives.

Renormalization is a kind of abstraction: it retains only the long-distance structure that matters for the use at hand and discards the rest.


Renormalization-group flow drives the effective theory through a space of couplings, and its fixed points are precisely the loci where the theory is unchanged under further rescaling. The universal critical exponents and long-distance behaviors observed across disparate microscopic systems are features preserved under the rescaling transformation. That makes renormalization a specialization of invariance: a named family of transformations (the RG flow) leaves a named feature (the fixed-point physics) unchanged.

Renormalization is a kind of invariance: universal long-distance behavior is preserved across the flow's rescalings at a fixed point.


Renormalization is the structurally-particularized instance of scaling and scale dependence in which the dependence is captured by a concrete procedure: integrate out shorter-scale degrees of freedom, rescale, and read off how the effective theory's couplings change with scale. It carries forward the general scaling-and-scale-dependence commitment that dominant physics, mechanisms, and bottlenecks shift qualitatively as scale changes, and gives this idea its specific apparatus: a flow in theory space whose fixed points, attractors, and relevant or irrelevant perturbations determine which microscopic features survive at macroscopic scales.

Renormalization is the specific shape scaling and scale dependence takes when coarse-graining defines an explicit flow of effective theories across scales.


Strip the source of the captured sequence, the biological or computational storage medium, and the particular offline window. The preserved role is a post-encoding process that reactivates a fragile trace so it becomes more durable and interference-resistant: Memory Consolidation. Replay names one exact mechanism for it.

Removing hippocampal, software-buffer, simulation, and review framing from replay leaves post-encoding stabilization that converts a fragile trace into durable structure.


It retains Selection Bias's defining mismatch between the target population and the systematically selected observed sample, then fixes the selection mechanism to a sequence of reporting or ascertainment stages. Each stage admits a non-random fraction of the events surviving the previous stage, so both the total and composition of the final count can diverge from the true event population.

Reporting-Pyramid Undercount is Selection Bias specialized to an ordered sequence of non-random inclusion gates whose capture fractions multiply.


Representation is the structured mapping of a target system onto a medium that preserves selected features under a stated convention while deliberately dropping others. The selection of which features to preserve is itself an abstraction — purpose-relative retention of structure that keeps what matters for a given use and discards what does not. Abstraction supplies the prior judgment about what is load-bearing; representation then mechanizes that judgment as a faithfulness-claiming mapping. Without the abstract selection in place, the representational mapping has no principle by which to choose what features its medium should carry.

Representation presupposes abstraction because mapping a target onto a medium requires first deciding which features of the target to retain.


Representational modality is a specialization of representation. Specifically, it instantiates the target-to-medium mapping by fixing attention on which medium carries the encoding -- visual, auditory, tactile, olfactory, multimodal -- and on how the choice of medium reshapes what can be expressed, what is easily understood, and what actions become available. Like every representation, it commits to a faithfulness claim under stated conventions; modality is the subclass that varies the substrate while holding the represented system constant, exposing differential cognitive load and behavioral consequences.

Representational modality is a specialization of representation that focuses on the medium (visual, auditory, tactile) through which content is encoded.


Representational Structure Mismatch presupposes a representation whose target, medium, mapping, and purpose-relative faithfulness claim can be compared at the level of relations. Representation supplies the prerequisite condition: Model complex ideas. Representational Structure Mismatch operates against that background: A representation preserves its target's elements but misstates one or more task-relevant relations among them, so content can appear complete while its shape licenses the wrong traversal, inference, or action. 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.


Reproducibility and replicability are a kind of verification specialized to scientific findings: the object being checked is a reported result, the specification is the claim made about an effect, and the procedure is independent repetition — computational reproduction with the same data or replication with fresh data under similar conditions. They inherit verification's commitment to checking conformance against a stated criterion via a defined evidence-producing procedure, and supply the particular evidence-source — repeated independent execution — that constitutes valid checking in the scientific domain.

Reproducibility and replicability are a specialization of verification in which the conformance check is repeating the study to confirm the finding.


Reputation is the specific shape feedback takes when the output is an agent's conduct and the return path runs across time and across observers. The agent's behavior at t feeds into a public record; that record shapes how third parties treat the agent at t+1, which feeds back into the agent's incentives for behavior at t+1. The loop closure feedback requires is realized through the information channel third parties maintain, and the present value of future reputation premiums disciplines current quality through the same input-from-prior-output structure feedback names.

Reputation is the specific shape feedback takes when an agent's prior conduct loops back through third parties to shape future treatment.


Requisite variety holds that a regulator must possess at least as much internal variety as the disturbances it absorbs. Sustaining that match across novel disturbances requires the regulator to draw on a reserve of latent states, flexibilities, and learning mechanisms it can reconfigure when current responses are exhausted. That reserve is exactly Adaptive Capacity. Requisite variety presupposes adaptive capacity because the variety requirement is unsatisfiable in changing environments without the reorganization reserve that adaptive capacity supplies.

Requisite Variety presupposes Adaptive Capacity: matching disturbance variety draws on the regulator's reserve of internal states and response options.


Requisite variety states that only variety can absorb variety, formally V(R) >= V(D) / V(E), so any regulator failing the inequality cannot hold essential variables within bounds. The inequality functions as a binding restriction on admissible regulator designs: configurations below the threshold are not feasible candidates regardless of other merit. That is the defining structure of a constraint, here specialized to cybernetic regulation and the variety budget it demands.

Requisite Variety is a kind of constraint: it imposes a binding lower bound on the regulator's variety relative to disturbance variety.


Requisite variety presupposes diversity because its core inequality, V(R) at least V(D)/V(E), requires that a regulator's available states be functionally distinct from one another so that each can absorb a different disturbance type. Diversity supplies the general notion of meaningful variation across elements where the variation has functional consequences; requisite variety is the cybernetic theorem that, without sufficient functional diversity in the controller's repertoire relative to the environment's disturbance repertoire, essential variables cannot be held within tolerance.

Requisite variety presupposes diversity because a regulator can only absorb disturbance variety if its response repertoire contains functionally distinct types.


RDF is a systematic, directional inferential error (false-positive inflation) produced by an un-audited comparison budget — a specialized inferential bias arising at the analysis/reporting stage, distinct from random noise. is-a bias in the inference pipeline.


The reserve is one named component of economy of force — the hedge against decisive-point misidentification. 'reserve is one component of economy of force, not the prime.'. After the engineering_design frame is stripped away, the retained structural roles are those of Economy Of Force: Deliberate minimum-sufficient under-resourcing of non-decisive efforts so that mass can be concentrated at the decisive point. Reserve adds the local frame and commitments expressed in its identity: Deliberately maintained surplus held beyond expected need so the system can absorb variation, uncertainty, or shock without failing. 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.


After the engineering_design frame is stripped away, the retained structural roles are those of Mobilization: Latent capacity is activated, channeled into directed action, and then sustained or returned to rest. Reserve adds the local frame and commitments expressed in its identity: Deliberately maintained surplus held beyond expected need so the system can absorb variation, uncertainty, or shock without failing. 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.

Reserve is the framed or domain-specific realization of Mobilization; removing the local frame leaves the parent's structural relation intact.


Without conservation closure, changes in named stocks need not equal internal inflows minus outflows plus explicit boundary exchange, and the structure is only a stock-and-flow graph. Conservation Laws supplies the invariant bookkeeping constraint; Reservoir-Flux Network adds multiple named reservoirs, directed fluxes, rate laws, and a boundary over which that constraint makes mass-balance reasoning auditable.

A Reservoir-Flux Network presupposes a conservation law that closes internal transfers over its declared boundary.


Remove the model-relative residuals and there is no leftover series on which to test trend, autocorrelation, heteroscedasticity, or other structure. Residual Analysis is the method that studies a collection of Prediction Errors against a noise specification; the individual error signals are constituents of that method.

Prediction errors are the observed-minus-predicted objects that residual analysis collects and examines for remaining structure.


Resilience is a specialization of adaptive capacity. Adaptive capacity is the reserve of latent resources, flexibilities, and slack determining how effectively a system can reorganize itself when disturbances exceed first-tier regulation. Resilience specializes this by focusing on the function-preserving aspect: absorbing disturbances and continuing to function, either by returning to prior state, remaining within a regime, or reorganizing while maintaining essential function. The general reorganization-reserve principle of adaptive capacity supplies the substrate; resilience names the particular outcome — sustained essential function under disturbance.

Resilience is a specialization of adaptive capacity focused on absorbing disturbances and continuing essential function.


Resilience is a specialization of homeostasis: it is the closed-loop self-regulation capacity to hold key variables (or regimes) within acceptable bounds against perturbations. It inherits homeostasis's sensor–comparator–actuator structure but generalizes the response repertoire beyond simple setpoint restoration to include regime maintenance under wider perturbations and adaptive reorganization. The engineering, ecological, and adaptive senses of resilience are progressively richer specifications of homeostatic regulation under increasingly demanding disturbance regimes.

Resilience is a kind of homeostasis that maintains essential function under disturbance, either by returning to setpoint or reorganizing within a regime.


Resilience is a specialization of robustness in which the maintained function is achieved through absorption-and-recovery dynamics: returning to the prior state, remaining within a regime, or reorganizing to preserve essential function. It inherits the general robustness commitment of sustained adequate function across a wide envelope of perturbations and conditions, and specializes by emphasizing the time-extended response to disturbance: absorbing the hit, then returning, persisting, or transforming. Robustness names the static envelope; resilience names the dynamic trajectory back into it after a disturbance.

Resilience is a specialization of robustness in which the maintained function is reached by absorbing disturbance and recovering or adapting rather than only by graceful degradation.


Resistance to change is the specific shape equilibrium takes in human and organizational systems when the balanced quantities are driving forces (toward change) and restraining forces (toward the status quo), and the balance is preserved against perturbations that propose alteration. It is a structurally-particularized instance of a balance condition holding against transformations, with the added commitment that the restraining forces are not mere inertia but active, often legitimate, psychological and social commitments — habits, identities, relationships, mental models — whose weight must be specifically weakened or counterbalanced for the equilibrium to shift.

Resistance to change is the specific shape equilibrium takes when driving forces toward alteration balance against restraining forces preserving the status quo.


Resistance to change is the specific shape homeostasis takes when the regulated variables are organizational routines, identities, processes, and mental models, and the corrective mechanism is the array of psychological and social forces that push back when those variables drift from their established settings. It is a structurally-particularized instance of closed-loop self-regulation maintaining a setpoint against disturbance, with the added commitment that the regulation is performed not by a dedicated physiological loop but by distributed human responses — habit, identity defense, coalition formation — that collectively sense deviation from how-we-do-things-here and act to restore it.

Resistance to change is the specific shape homeostasis takes when human and organizational systems regulate against alterations to their established state.


Resistance to change is the tendency of human and organizational systems to defend their existing structures, processes, and identities against alteration, requiring active effort to overcome the forces reinforcing the current state. This is a particular case of the general inertia pattern: a system's default behavior is continuation of its current trajectory, with departure requiring force proportional to the change desired. Inertia supplies the structural commitment — trajectory-persistence-against-net-zero-force — that organizational resistance instantiates with human, social, and structural restraining forces as its specific mass.

Resistance to change presupposes inertia because organizational and social resistance manifests the general structural pattern of trajectory-persistence requiring force to alter.


Scale supplies the level of granularity at which a system observes, records, or acts. Resolution Matching specializes it by introducing a second, task-required scale and classifying the relation as under-resolution, sufficient fit, or costly over-resolution.

Resolution Matching is scale specialized to the fit between a resolver's discrimination scale and the smallest distinction a task must preserve.


Resonance is a specialization of amplification in which the gain mechanism is the cumulative storage of energy in a system driven near one of its natural frequencies. It inherits the general amplification commitment that an input controls a much larger output drawing on a separate energy source, and specializes by making the response frequency-dependent, peaked at the natural frequencies, and limited by damping. The amplifying "power supply" is the system's own oscillatory storage, and gain can become arbitrarily large as damping vanishes.

Resonance is a specialization of amplification in which the gain is frequency-selective and powered by stored oscillatory energy at a matched natural frequency.


Resonance is the disproportionate amplification that occurs when driving forces match a system's natural frequencies, with the buildup arising because the system's prior oscillatory output returns in phase to constructively amplify subsequent input. That accumulation requires Feedback — output rerouted back to influence subsequent input — as the underlying structural arrangement. Without the loop, energy cannot accumulate selectively at the natural frequency, so resonance presupposes feedback as the substrate on which frequency-selective amplification rides.

Resonance presupposes Feedback: amplitude builds because energy returned through the system's own dynamics constructively reinforces the input.


Resonance is a specialization of temporal synchronization and phase alignment in which the phase relationship at issue is between an external driver and a system's natural frequency. It inherits the general phase-alignment commitment that aligned phases produce constructive coherence and amplification while misaligned phases cancel, and specializes by fixing one party to a system with a frequency-peaked response function and showing that energy accumulates efficiently exactly when the driving phase tracks the natural-frequency phase, with amplitude limited only by damping.

Resonance is a specialization of temporal synchronization and phase alignment in which constructive amplification occurs when driver phase matches a natural frequency.


Resource management is the operational discipline of handling the full lifecycle of finite resources — acquisition, provisioning, monitoring, reclamation — and at its heart sits the moment of assigning supply across competing consumers. Without allocation's machinery of assigning limited supply to competing claims under feasibility constraints, the management discipline would have no central act to coordinate around: scarcity would not translate into a distribution decision, and competing demands could not be served from a common pool.

Resource management presupposes allocation because acquiring, provisioning, and reclaiming finite resources requires assigning supply across competing demands.


Propagation is one of the two processes in the race; this prime is the COMPARISON of propagation against a containing response, with a threshold at the crossover. Presupposes propagation as one term. Propagation supplies the prerequisite condition: The systematic spreading of a signal, effect, or state from a source through a medium or network, where the medium's structure governs how fast it moves, how it attenuates, and which paths it follows. Response-vs-Propagation Race operates against that background: Containment wins or loses by timescale comparison. 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.


Responsibility attribution is the specific shape causality takes when the cause-effect relation is read backward for the purpose of apportioning credit or blame to agents. The causal apparatus -- antecedent, consequent, productive connection, modal robustness -- supplies the input: the counterfactual-dependence test asks whether the outcome would have differed had the agent acted otherwise. Attribution adds normative gates (control, foresight, fault) that select which of the causal contributors bear responsibility, transforming bare causal facts into a directed assignment from effects to morally answerable sources.

Responsibility attribution is the specific shape causality takes when the directed assignment runs from outcome back to agents under normative gating.


The retention dynamic depends on uncertainty about an element's hidden function or the consequences of removing it. Uncertainty supplies the prerequisite condition: Incomplete knowledge. Retention Under Removal Uncertainty operates against that background: A durable system accumulates obsolete-but-not-removable elements because each removal decision faces an asymmetric cost that loses individually and wins only in the integral. 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.


A specific design pattern within maintenance for handling labels that must change (sunset of new use and read-back guarantee and migration signal). A specialization of the general keep-a-system-in-working-order activity, scoped to naming systems. Maintenance supplies the genus: Sustained preventive work that keeps a system's intended function intact against inevitable degradation, acting ahead of failure rather than repairing after it. Retired Term preserves that general structure while adding its differentia: A label withdrawn from new use but kept resolvable for existing references, with its retired status and successor publicly marked. 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.


Reversibility is the PROPERTY (can a change be undone in principle); return_path is the separately-designed INFRASTRUCTURE that makes reversal operationally available. The infrastructure presupposes the property — a system reversible in principle may have no return path in practice. Reversibility and Irreversibility supplies the prerequisite condition: Actions or transitions may or may not be undone or reverted. Return Path operates against that background: Every forward-flow pipeline serving goal-directed users requires a separately-designed backward channel whose optimisation criteria invert the forward channel's. 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.


Is emphatic: 'Revealed preference is an INFERENCE METHOD... RIDING ON the deeper notion preference. The recovered ranking is what one estimation procedure produced under its axioms, not the agent's valuation as such.' It presupposes preference (the latent valuation it recovers). Preference supplies the prerequisite condition: Agent's ordering over a choice set on some evaluative dimension. Revealed Preference operates against that background: Infer latent value from observed choices rather than stated reports. 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.


Abductive reasoning is inference to the best explanation: starting from an observation, the reasoner posits the hypothesis that, if true, would best account for it. Reverse engineering is the particular shape this move takes in engineering and analysis: starting from an assembled product or executing system, the reasoner infers the underlying design intent, component relationships, and architectural choices that best explain the observed form and behavior. It is a structurally-particularized instance of ampliative inference whose target hypothesis is design intent and whose evidence base is observable final form.

Reverse engineering is the specific shape abductive reasoning takes when inferring design intent backward from an observed artifact.


Reverse engineering works backward from an existing artifact or observable system to recover its components, interfaces, operational logic, and design rationale. Decomposition is an internal operation within that larger process: the analyst separates the whole into independently examinable parts and maps their relations before using abductive inference and validation to reconstruct how and why the system works. Decomposition is therefore necessary internal machinery, but it does not exhaust reverse engineering's inference, documentation, or validation commitments.

Decomposition is an internal operation in reverse engineering, separating an existing system into components and relations before its design logic is reconstructed.


Reversibility horizon requires that the costs of reversing a decision accumulate as a function of the historical trajectory — sunk investments, ecosystem dependencies, downstream commitments — which is precisely the path-dependence mechanism. Without the prior commitment that current options are constrained by the specific sequence of past choices rather than by present conditions alone, there would be no rising reversal cost to define a horizon, and the closing of the window would have no causal substrate.

Reversibility horizon presupposes path dependence because the rising reversal cost over time is the mechanism by which prior decisions lock in future options.


Reversibility horizon is the temporal-threshold particularization of the reversibility-versus-irreversibility dimension: it names the moment in a decision's timeline at which the cost of reversal crosses the cost of committing forward. Where the parent prime treats reversibility as a structural property of actions, the horizon adds the time dimension along which that property degrades, so that an action which was reversible early becomes effectively irreversible later as sunk costs, ecosystem dependencies, and lock-in accumulate.

Reversibility horizon is the specific shape reversibility takes when reversal cost rises over time, converting a reversible decision into an effectively irreversible one.


Revisionism is a kind of interpretation specialized by its stance toward existing consensus readings: the prior interpretation is explicitly held as provisional, and new evidence, perspectives, or theoretical lenses are brought into contact with it to test, partly revise, or replace it. It inherits interpretation's commitment to recovering meaning from a representational substrate within a framework that constrains available readings, and supplies the specific case where the framework itself is held corrigible by design and successor interpretations are themselves offered as further open to revision.

Revisionism is a specialization of interpretation in which an existing interpretive consensus is treated as provisional and tested against new inputs.


Refinement is the iterative process of progressively improving the precision or fitness of a candidate through cycles of evaluation and adjustment, starting from an initial approximation rather than first principles. Revisionism is the particular shape this pattern takes in interpretive disciplines: an existing consensus is treated as the current approximation, new evidence or perspectives are brought to bear, and the consensus is partially revised and offered for further revision. A structurally-particularized instance of refinement whose specific medium is interpretive consensus and whose feedback signal is new evidence or perspective.

Revisionism is the specific shape refinement takes when an interpretive consensus is treated as provisional and incrementally revised against new evidence.


Without a recognized right to issue a binding grant or status, there is no authoritative withdrawal whose reach can be evaluated; raw causal interruption is not revocation.

Revocation Closure presupposes Authority because some recognized issuer must have standing to create and later invalidate the grant.


Revocation Closure claims not merely that all effects may someday end but that every active effect becomes invalid within a declared finite interval; Boundedness supplies that deadline property.

A finite revocation horizon is a strict constituent because eventual withdrawal with no upper time bound does not provide operational closure.


The property fails if even one active manifestation or derivative lies beyond every revocation pathway, so the required target set must be covered by the issuer's invalidation mechanisms.

Complete reachability over the grant's actual live effect set is a strict constituent of Revocation Closure.


Both compute a signed operational residual between a prediction and a realized observation. Reward Prediction Error fixes the predicted quantity to reward, return, or value and fixes the main consumer to a value estimate, policy, or reward-linked association. Generic forecast, sensor, and reconstruction residuals remain instances of Prediction Error without becoming reward errors.

Reward prediction error is prediction error specialized to reward or value predictions and value-policy updating.


Modularity supplies the prerequisite condition: Breaks systems into smaller units. Rhetorical Velocity operates against that background: Compose an artefact in anticipation of how others will cut, remix, and forward its fragments. 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.

Rhetorical Velocity presupposes Modularity, whose structure must already obtain for the child mechanism to be meaningful or operational.


Rhythm is a specialization of recurrence. Specifically, it instantiates the pattern-reappearance-across-time structure with the additional commitment that the repetitions are organized into accented groups laid over a recurring frame, so that each event is heard as strong or weak, on-time or displaced, against the established expectation. Like other recurrences, it has identifiable spacing and triggers; rhythm is the subclass where the repetition becomes a parsing structure for time, with information carried in how stresses confirm or violate the recurrent template.

Rhythm is a specialization of recurrence that organizes repeated events into accented hierarchical patterns generating expectation.