Every Nash Equilibrium is a strategy profile containing one Game-Theoretic Strategy for each agent.

A Nash Equilibrium is constituted by a profile of agents' strategies. Each component strategy maps that agent's information or contingency to an action, and the equilibrium condition tests every component against unilateral replacement while holding the others fixed. Game-Theoretic Strategy is therefore a strict part of the equilibrium profile, not a merely typical background frame and not the genus of the profile.


A Nash equilibrium is by definition a fixed point of the joint best-response correspondence. Fixed Point supplies the genus: A state a transformation leaves unchanged — self-consistency under update — organizing analysis into existence, uniqueness, stability, and basin of attraction. Nash Equilibrium preserves that general structure while adding its differentia: A strategy profile in which no agent can improve its payoff by unilaterally changing strategy, given the others' choices — the fixed point of the joint best-response correspondence. 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 failure is a lossy recoding of a source's meaning-bearing partition into a foreign taxonomy; it presupposes a classification/recoding act and names its destructive (merge/split, irrecoverable) special case. Built on the recoding step.


It is a pathology of translating one category scheme into another — lossy, asymmetric, one-way. Translation and Conceptual Bridging supplies the genus: Convert concepts or meanings between incommensurable frameworks. Native-Category Flattening preserves that general structure while adding its differentia: A source system's own partition of the world is silently collapsed when an external observer recodes it into a foreign taxonomy without first preserving the source partition, destroying distinctions the downstream analysis would have needed and that recoded labels cannot recover. 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 is selection specialized to heritable variants whose unequal reproduction or persistence shifts population composition across repeated rounds.

Natural selection contains Selection's candidate population, operative pressure, differential continuation, and resulting composition shift. It adds heritable variation, differential reproduction or persistence, transmission of retained traits, and iteration across generations or rounds. Those differentiae distinguish it from one-shot filtering, institutional admission, and pruning of components within one already built system.


Near-Miss Normalization is typically a specialization of Bias, retaining the parent's defining structure while adding the child's specific commitments.

Bias supplies the genus: Systematic, directional error distinct from random noise. Near-Miss Normalization preserves that general structure while adding its differentia: A system reads the absence of harm in a narrowly-averted event as evidence of robustness rather than as a signal of lost margin, so it resets the margin to the smaller value and drifts its operating envelope toward the failure boundary while still counting itself safe. 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.


Near-Miss Normalization is a specialization of Benign-Sampling Safety Drift, retaining the parent's defining structure while adding the child's specific commitments.

Benign-Sampling Safety Drift supplies the genus: A system near a hazard boundary reads a benign sample of outcomes — uneventful only because the hazard is rare, not because the margin is safe — as proof the safety margin is unnecessary, so each lucky round licenses the next erosion until a low-probability event finds the now-absent buffer. Near-Miss Normalization preserves that general structure while adding its differentia: A system reads the absence of harm in a narrowly-averted event as evidence of robustness rather than as a signal of lost margin, so it resets the margin to the smaller value and drifts its operating envelope toward the failure boundary while still counting itself safe. 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.


Need–Solution Alignment is compatibility specialized from non-interference to positive functional adequacy for a stated need.

The proposed solution and the need-side context must be capable of composing without contradiction across their relevant interfaces and constraints. Need–Solution Alignment inherits that relational fit and adds a beneficiary, a capability that addresses the need, and a better-than-current-alternative performance condition.


Alignment is established relative to a current alternative or threshold, not from the solution's qualities in isolation.

A proposed intervention fits only relative to what the beneficiary can already do, including doing nothing. Comparing supplied capability, burdens, and outcomes with that alternative is an internal constituent of the alignment test. The same solution can therefore fit one context and fail another without changing intrinsically.


The need is operationalized through binding conditions the solution must satisfy in the beneficiary's context.

Needs become testable when expressed as requirements, limits, tolerances, timing, access conditions, or other constraints. A benefit that ignores a binding condition does not align even if it improves some secondary dimension. Constraint is therefore part of the fit relation rather than background decoration.


Negative Case Analysis typically presupposes Falsifiability, whose structure must already obtain for the child mechanism to be meaningful or operational.

Falsifiability supplies the prerequisite condition: A claim is scientific only if it could in principle be empirically refuted. Negative Case Analysis operates against that background: Deliberately hunt the cases that would overturn your account, then revise or scope it. 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.


Negative space is the specific shape figure-ground takes when the ground is deliberately structured as a compositional element rather than merely backdrop.

Negative space is the specific shape figure-ground takes when the recessive ground is deliberately structured and made to do compositional work — directing attention, providing rest, generating meaning through emptiness — rather than being treated as unattended backdrop. It is a structurally-particularized instance of the figure-ground organization in which something stands out against context, with the added commitment that the ground itself is shaped, scaled, and weighted as a design element. Absence becomes presence: the unpopulated area carries communicative force precisely as the non-figure half of the reciprocal assignment.


'Negative space is one ARTISTIC instance of the complement... Complement is the substrate-independent operator; negative space is its application in visual composition.' complement is the general parent, negative_space the art-aesthetics child. Add complement as parent (negative_space keeps figure_ground). Complement supplies the genus: Everything in a declared universe that is not in a designated subset. Negative Space preserves that general structure while adding its differentia: Empty space shaping form. 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 neighborhood of a point is the PRIMITIVE of topology itself: open sets, continuity, limits, convergence are all defined locally.' Neighborhood presupposes/founds a proximity structure; topology is its native home. (Could be read as foundational; topology-presupposes is the cleanest hook.). Topology supplies the prerequisite condition: Studies properties preserved under deformation. Neighborhood operates against that background: The local-context window of elements close to a focal point under a proximity structure. 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.


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

After the mathematics frame is stripped away, the retained structural roles are those of Reservoir-Flux Network: Named stocks linked by conserved flows. Network adds the local frame and commitments expressed in its identity: Models interactions between 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.


And dedup-style read: a specific role-type fixed by three positional features (upstream access, downstream capacity, interpretive authority) and pass-through. role is the genus; this is the enriched child. Role supplies the genus: A bundle of expected behaviours attached to a social position. Network Broker Role preserves that general structure while adding its differentia: A network position combining upstream access, downstream tie capacity, and interpretive authority that makes its holder a productive required intermediary. 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 positional property OF a network — presupposes a network substrate (nodes/ties with a source side and receiver side). Network supplies the prerequisite condition: Models interactions between components. Network Broker Role operates against that background: A network position combining upstream access, downstream tie capacity, and interpretive authority that makes its holder a productive required intermediary. 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 network broker sitting between source access and audience ties with interpretive authority is a specific instantiation of the choke-point-plus-arbiter gatekeeping structure. Gatekeeping supplies the genus: An actor or mechanism at a choke point exercises selective passage control, shaping the downstream distribution in ways the audience cannot directly observe. Network Broker Role preserves that general structure while adding its differentia: A network position combining upstream access, downstream tie capacity, and interpretive authority that makes its holder a productive required intermediary. 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.


Network effects are a specialization of increasing returns in which the rising marginal value comes from demand-side adoption rather than supply-side scale.

Network effects are a kind of increasing returns specialized to a demand-side accumulation: each additional user raises the value of the good for every other user, so marginal utility rises rather than falls as the installed base grows. It inherits the general pattern that the marginal benefit of additional accumulation rises with the cumulative state variable, producing self-reinforcing dynamics and lock-in, and supplies the specific case where the accumulating variable is user adoption and the increasing-returns mechanism operates on the demand side rather than through production cost.


Network effects is the specific shape feedback takes when each new user makes the system more valuable to all existing users, reinforcing further adoption.

Feedback is the closure in which a system's output is routed back to influence its subsequent input, with the present depending on the system's own prior output. Network effects is the particular shape this closure takes in adoption dynamics: each additional user raises the platform's value to all users, which raises the probability that further potential users adopt, which raises the value again. It is a structurally-particularized instance of positive feedback whose specific tap is installed-base size and whose specific coupling is the value-to-adoption-probability relation.


'network effects are one prominent MANIFESTATION of complementarity (more users raise the value of joining), but complementarity is the general payoff mechanism.' strategic_complementarity is the more-general parent of network_effect. Strategic Complementarity supplies the genus: One actor's action raises the marginal benefit of others taking the same action. Network Effect preserves that general structure while adding its differentia: Value increases with users. 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.


Network Flow Models is a specialization of Optimization, retaining the parent's defining structure while adding the child's specific commitments.

Optimization supplies the genus: Finds best solution under constraints. Network Flow Models preserves that general structure while adding its differentia: Optimize flow across networks. 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.


Network flow models presuppose flow because they formalize routing and allocation as directed transport with capacity limits and conservation at every node.

Network flow models presuppose flow because their entire formulation imports flow's structural commitments: a conserved quantity moves through directed edges with capacity limits, conservation at internal nodes equates inflow with outflow, and the objective is to maximize or cost-minimize a directional throughput from source to sink. Without the prior availability of flow as continuous directional transfer obeying conservation and gradient-driven movement through a structured channel network, max-flow, min-cost flow, and multi-commodity flow have no substrate on which their LP structure can rest.


Network flow models presupposes network because flows, capacities, and conservation are defined on the underlying graph of nodes and connections.

Network flow models route resources through graphs with capacitated directed edges subject to flow conservation at internal nodes, optimizing total flow or cost. The entire formulation requires a connection pattern as its substrate: nodes for junctions, edges for routes, and the topology that determines reachability and bottlenecks. Without a network as a first-class object — entities together with pairwise connections — there would be no graph over which to define capacities, no conservation constraints to write, and no specialized algorithms exploiting the network structure to invoke.


Network traversal presupposes a network because its visitable states and permitted next steps are defined by nodes and edges in an underlying relational structure.

A traversal requires a node set and an adjacency relation that determine what may be visited next. Network supplies that possibility structure. Traversal adds seeds, a frontier policy, visit-state bookkeeping, and a stopping rule; it is therefore a process operating on a network rather than a kind of network or one constituent inside every network.


Niche_construction is a SPECIALIZATION of feedback where the fed-back variable is specifically the ENVIRONMENT OF SELECTION (which variants are favored), not any state the agent influences. feedback is the parent. Feedback supplies the genus: Outputs influence inputs. Niche Construction preserves that general structure while adding its differentia: An agent modifies its environment, and the modified environment changes the selection pressures acting back on the modifier — the environment is endogenous. 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.


Nirvana Fallacy is a specialization of Informal Fallacy, retaining the parent's defining structure while adding the child's specific commitments.

Informal Fallacy supplies the genus: A named, recurring pattern of defective argument whose error lies not in logical form but in content, context, or the relevance and acceptability of its premises — so it can be valid in form yet still fail as reasoning. Nirvana Fallacy preserves that general structure while adding its differentia: Rejecting a real, available option because it falls short of an idealized counterfactual, when the operative comparison should be against the best feasible alternative. 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.


No Free Lunch is the impossibility result that universal method superiority cannot coexist with an unrestricted problem distribution.

It rules out a procedure that dominates over the full problem space and forces the designer to restrict the domain or accept that every inductive bias gains on one class by losing on its complement.


No Free Lunch is a conservation law specialized to total method performance averaged over problem-space.

Summed over all admissible problems, performance remains equal across methods, so any gain on one class is exactly offset by loss on the complementary class.


No one is above the rules is a specialization of rule of law that articulates its equality-before-law commitment as a universally applicable maxim.

No one is above the rules is a specialization of rule of law. Specifically, it crystallizes the architectural commitment that no element is exempt from the system's governing rules -- including those who create or enforce them -- into the maxim that legal rules apply uniformly regardless of rank, status, or power. Like the broader rule-of-law principle, it rests on impartial application and reflexive self-binding of rule-makers; this subclass is the specific universal-applicability proposition that operationalizes uniformity and rejects hierarchical exemption.


No True Scotsman is a specialization of Informal Fallacy, retaining the parent's defining structure while adding the child's specific commitments.

Informal Fallacy supplies the genus: A named, recurring pattern of defective argument whose error lies not in logical form but in content, context, or the relevance and acceptability of its premises — so it can be valid in form yet still fail as reasoning. No True Scotsman preserves that general structure while adding its differentia: When a counterexample to a universal claim appears, membership in the subject category is redefined to exclude it, preserving the claim by emptying it of content. 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.


Noether's Theorem presupposes Principle of Least Action, whose structure must already obtain for the child mechanism to be meaningful or operational.

Principle of Least Action supplies the prerequisite condition: Optimal system paths. Noether's Theorem operates against that background: Symmetry links to conservation. 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.


Noether's theorem presupposes a continuous symmetry of the action from which it derives a conserved current.

A continuous symmetry of the action is an explicit input to Noether's theorem. The theorem adds the correspondence to a conservation law; it is not itself a kind of symmetry. Its existing least-action prerequisite is retained as a separate parent.


Both contrast an official/documented description with an enacted reality; nominal_vs_actual_control is the narrower, assurance-centred case specifically about a CONTROL/safeguard's documented vs enacted register PLUS the sampling-mismatch of the assurance apparatus. is a specialization of (specialized) formal-vs-informal split, scoped to controls and assurance. Formal vs. Informal Structures supplies the genus: Official vs actual systems. Nominal vs. Actual Control preserves that general structure while adding its differentia: Every control exists as a documented nominal form and an enacted actual form, and the assurance apparatus usually samples only the former. The parent can occur without those added commitments, whereas removing the parent structure leaves no basis for classifying the child as this subtype. That asymmetry establishes subsumption rather than mere association. The typical qualifier limits the claim to the characteristic route, not a constitutive requirement of every instance; exceptions must retain the child's identity through another mechanism.


Every Non-Zero-Sum Game strictly presupposes a strategy-profile space over which joint payoff can vary.

Non-Zero-Sum Game classifies a strategic interaction by evaluating joint payoff across alternative strategy profiles. It therefore requires players, their admissible Game-Theoretic Strategies, and the profiles those strategies form. The game is not itself a contingent policy from information to action, so subsumption conflates the payoff structure with one of the objects it presupposes.


Nonparametric Methods are a kind of approximation: ranks and flexible estimators substitute tractable surrogates for unspecified distributions.

Nonparametric methods stand in for the true unknown distribution using ranks, order statistics, resampling, or flexible estimators rather than committing to a specified functional family. That is the canonical move of approximation: substituting a tractable surrogate for an intractable target while carrying explicit guarantees about the error. Nonparametric methods specialize approximation to the case where the surrogate avoids strong distributional assumptions, trading parametric efficiency for robustness to misspecification.


Nonparametric methods are a specialization of statistical inference characterized by minimal assumptions about the underlying distribution's functional form.

Nonparametric methods are the distribution-free or distribution-light specialization of statistical inference: they draw conclusions about populations from samples without committing to a specific parametric distribution family, relying instead on ranks, order statistics, resampling, or flexible estimators. Where statistical inference names the broad reasoning from sample to population under explicit uncertainty accounting generally, the nonparametric specialization fixes the assumption profile as minimal, trading some efficiency under correctly-specified models for robustness across distributional shapes.


Nonparametric methods presuppose distributional assumption because they are constituted as the minimal-assumption alternative within the distributional-assumption design space.

Nonparametric methods are defined by contrast with parametric approaches: they minimize or avoid the distributional assumption rather than abolish the framing of distributional choice. Without the distributional-assumption machinery — the recognition that modeling uncertain quantities requires a commitment about probability-distribution shape — there would be no design dimension along which nonparametric methods could be located as the minimal-commitment pole. The parent prime supplies the structural choice (what to assume about shape) that nonparametric methods occupy a particular position on.


Distribution-free methods maintain valid inference across distributional variation — statistical robustness to functional-form misspecification. Robustness supplies the genus: Maintain functionality under stress. Nonparametric Methods preserves that general structure while adding its differentia: Distribution-free analysis. 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.


Normalization of Deviance is a specialization of Benign-Sampling Safety Drift, retaining the parent's defining structure while adding the child's specific commitments.

Benign-Sampling Safety Drift supplies the genus: A system near a hazard boundary reads a benign sample of outcomes — uneventful only because the hazard is rare, not because the margin is safe — as proof the safety margin is unnecessary, so each lucky round licenses the next erosion until a low-probability event finds the now-absent buffer. Normalization of Deviance preserves that general structure while adding its differentia: An operating standard drifts outward because small departures, each repeatedly observed without immediate catastrophe, are reclassified as normal. 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.


Normativity is the specific shape constraint takes when the binding restriction is an evaluative standard against which states can be judged correct or incorrect.

Normativity is the specific shape constraint takes when the binding restriction operates evaluatively rather than physically: it specifies which states, actions, or beliefs count as correct, required, permissible, or prohibited, and renders the rest subject to criticism rather than impossible. It is a structurally-particularized instance of restricting an admissible set, with the added commitment that admissibility is enforced through evaluation, judgment, and the practice of holding-to-account rather than through physical incompatibility. The standard plays the role constraint plays generally — partitioning what counts as acceptable — but does so in the ought-mode.


Nucleation is 'one route to threshold-driven order, not the genus' — the specific surface-cost-exceeds-volume-benefit-at-small-size mechanism (critical nucleus and hysteresis) within the broader family of order appearing past a threshold. Threshold-Driven Order Emergence supplies the genus: Order after critical point. Nucleation preserves that general structure while adding its differentia: A metastable system cannot transition globally because a new phase's surface cost exceeds its volume benefit at small size; transition begins only when a seed crosses the critical-nucleus threshold and then grows. 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.


Nucleation's free-energy barrier is a kind of activation energy (the height one element of the mechanism crosses); the prime presupposes a barrier. 'activation energy is one element' of nucleation. Activation Energy supplies the prerequisite condition: The minimum input that must be supplied to push a thermodynamically favorable but stalled process past a barrier before momentum carries it to completion. Nucleation operates against that background: A metastable system cannot transition globally because a new phase's surface cost exceeds its volume benefit at small size; transition begins only when a seed crosses the critical-nucleus threshold and then grows. 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.


Nucleation is the specific mechanism by which a metastable system transitions via a critical seed overcoming surface-cost barrier, a specialized process presupposing metastability of the parent phase. Metastability supplies the genus: A system persists in a locally stable configuration that is not the global optimum, held there by a barrier that routine disturbances cannot clear. Nucleation preserves that general structure while adding its differentia: A metastable system cannot transition globally because a new phase's surface cost exceeds its volume benefit at small size; transition begins only when a seed crosses the critical-nucleus threshold and then grows. 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 persistent internal representation carried through unobservable intervals is a constitutive part of object permanence.

The entity's identity and predicted state must remain encoded while observations are absent so later evidence can be re-bound to the same continuing object. Representation supplies an internal constituent: Model complex ideas. Object Permanence requires that role within this mechanism: A system maintains persistent internal state for entities it cannot currently observe, modeling them as continuing to exist and re-binding them on re-emergence. Remove the parent-role and the child loses a required internal operation, even though the parent can exist outside the child. The child is therefore built from the parent rather than being a taxonomic kind of it.


Objective creep is one expression of the ratchet effect (asymmetric add/subtract friction) operating specifically on goal-sets — low-friction to add a sub-objective, high-friction to subtract. is a specialization of a ratchet on an authorized goal portfolio. Ratchet Effect supplies the genus: Direction-asymmetric coupling plus a locking element produces accumulating one-way displacement under bidirectional forcing. Objective Creep preserves that general structure while adding its differentia: An actor's effective goal boundary expands beyond what its original plan was sized for, as locally-reasonable sub-objectives are added under engagement through low-friction addition and high-friction subtraction, diluting the original objective. 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.


This prime is path_dependence PLUS a scale law — history constrains the present (path dependence) AND the rate at which observables convert to binding constraints scales with observer count and elapsed time, making dependence a forecastable trajectory. is a specialization of path_dependence, specialized by the observability-creates-dependence scale mechanism. 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. Observable Surface Becomes Contract preserves that general structure while adding its differentia: Every observable behaviour, exposed to enough observers over enough time, becomes a binding dependency regardless of the nominal contract. 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.


Observational learning is a specialization of learning in which acquisition occurs through watching others rather than through direct trial-and-error.

Observational learning is a kind of learning specialized to a particular acquisition channel: attending to, encoding, reproducing, and being motivated by others' modeled behavior and its consequences. It inherits learning's general commitment that the agent's internal capability is durably updated by experience or information, and narrows the experience to vicarious observation rather than direct trial-and-error or direct reinforcement. The four sub-processes — attention, retention, reproduction, motivation — are the specific machinery by which the general experience-driven self-update operates when the experience is watching another agent act.


The Observer Effect is a kind of reflexivity: the act of observing a system feeds back as a perturbation of the system observed.

The observer effect names the structural fact that measurement couples the apparatus to the system, so the value read is not the value that would have obtained absent measurement, and subsequent behavior is altered. That is reflexivity instantiated at the measurement interface: the observation enters as an input to what is observed, creating a self-referential loop between knower and known. It is the physical, measurement-side specialization of the broader reflexive pattern.


The observer effect is a specialization of measurement uncertainty in which the act of measuring perturbs the system and thereby alters what is measured.

The observer effect specializes measurement uncertainty by fixing the source of error as the measurement-system interaction itself: the act of observation perturbs the observed quantity. Where measurement uncertainty names the general gap between true state and measured state arising from instrument limits, observer error, environmental variation, or systematic bias, the observer effect specifies that the noise source is not external limitation but the irreducible coupling between apparatus and system — a particular shape uncertainty takes when measurement is necessarily invasive.


The observer effect presupposes observability because the perturbation by measurement is the cost paid against the inference-of-state-from-output discipline.

The observer effect presupposes observability because the phenomenon -- the measurement act altering the system being measured -- is intelligible only relative to observability's claim that internal state can be inferred from outputs. Observability frames the inference goal; the observer effect names the back-action coupling through which the measurement apparatus's read-out unavoidably perturbs the source state. Without the observability framing of state-versus-output, there is no clean signal-versus-perturbation distinction; the observer effect is observability's structural cost in coupled systems. Observability supplies the prerequisite condition: Infer internal state externally. Observer Effect operates against that background: Observation alters system. 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.


Observer Effect is a specialization of Measurement and Disturbance, retaining the parent's defining structure while adding the child's specific commitments.

Measurement and Disturbance supplies the genus: Obtaining information while minimizing measurement perturbation. Observer Effect preserves that general structure while adding its differentia: Observation alters system. 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.


Competition is the standing arena; offensive_action a posture within it. Presupposes, not is a specialization of (competition can hold between non-agents; offensive_action requires a deliberate agentic move). Competition supplies the prerequisite condition: Rivalrous pursuit of a scarce prize where one party's gain is another's loss. Offensive Action operates against that background: Commit to unilateral first movement that forces opponents into a reactive posture, letting the initiator set the tempo, location, and terms of engagement and so control the agenda. 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.


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

Bias supplies the genus: Systematic, directional error distinct from random noise. Omission Bias preserves that general structure while adding its differentia: When acting and not acting carry similar expected outcomes, decision-makers systematically prefer inaction, judging a harm caused by acting as worse than an equal-or-greater harm caused by failing to act, because commission feels more causally and morally attributable than omission. 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.


Ontology presupposes set and membership because inventorying what exists requires the apparatus of collections, members, and inclusion criteria.

Ontology presupposes set and membership because specifying what there is — basic categories, identity criteria, dependency relations — requires the prior conceptual apparatus of treating entities-considered-together as objects of reasoning. To say a kind exists is to circumscribe the collection of its members under a criterion of inclusion; to give an identity criterion is to fix the membership relation. Without set-and-membership's general structure of collection-as-first-class-object distinct from its members and its defining predicate, the ontologist has no framework for stating which entities populate which categories and how those categories relate.


Modularity is 'the prerequisite substrate — a system carved into parts with hidden internals'; OCP layers a directional change-stance (sealed kernel and additive surface and gate) onto a modular partition. Presupposes modularity; adds the additive-vs-destructive asymmetry. Modularity supplies the prerequisite condition: Breaks systems into smaller units. Open-Closed Principle operates against that background: Harden a stable kernel against modification and route all change through an open extension 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.


Open-Goal Persistence is a state-and-transition pattern specialized to an adopted goal held in an active state until an explicit release transition fires.

The mechanism defines at least inactive, active-open, completed, and abandoned or substituted states, with adoption entering the active state and recognized completion or termination leaving it. State and State Transition supplies the state space, current-state sufficiency, and trigger-governed transitions. The child adds an agentic goal, maintained return priority, and release semantics.


Open_publication is a facilitating mechanism/tactic that promotes convergence. Sub-case of the genus. Standardization supplies the genus: The act or process by which independent parties converge on a single shared specification, format, or interface — agreement on a common norm rather than the benefits that follow from it. Open Publication for Interoperability preserves that general structure while adding its differentia: Publishing artifacts in an addressable, license-clear, machine-readable, openly accessible, versioned form so other communities can build on them without per-use negotiation. 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.


Open Publication for Interoperability is a specialization of Interoperability, retaining the parent's defining structure while adding the child's specific commitments.

Interoperability supplies the genus: Systems function together. Open Publication for Interoperability preserves that general structure while adding its differentia: Publishing artifacts in an addressable, license-clear, machine-readable, openly accessible, versioned form so other communities can build on them without per-use negotiation. 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.


Open publication contains a standing reuse license as one of its five defining publication commitments.

Open Publication for Interoperability contains License as Coordination as its license-clear constituent: the published terms preauthorize a class of downstream uses and replace bilateral permission bargaining. The larger publication bundle additionally requires addressability, reusable form, public access, and version discipline, so the license mechanism is a necessary part rather than the whole pattern.


Overextension is the story of where a margin vanishes: backbone capacity minus frontier demand evaluated at expected shock reaches zero. It presupposes a margin/buffer and specifies which one (frontier-to-backbone) and how it is consumed. frames margin_of_safety as the static buffer it dynamizes. Margin of Safety supplies the prerequisite condition: Buffer capacity. Operational Overextension operates against that background: A system advances a frontier of activity faster than the supporting backbone that sustains it can keep up, so the leading edge becomes brittle and fails on its next shock — the failure lying in the frontier-to-backbone ratio, not the frontier itself. 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.


Operational Period is a specialization of Iteration, retaining the parent's defining structure while adding the child's specific commitments.

Iteration supplies the genus: Repeats steps to refine outcomes. Operational Period preserves that general structure while adding its differentia: A bounded interval in which a plan is committed, executed, and reassessed at its boundary. 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.


Effective reach is set by a tip's DEPENDENCY on a support tail whose capacity decays with distance/duration (the tip can act only as far as the tail reaches). Dependency supplies the prerequisite condition: Directed relation in which one element relies on another being present, prior, compatible, or supplied, with a specifiable failure mode if the condition is unmet. Operational Reach operates against that background: Effective action extends only as far as the support tail can sustain it. 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.


Operationalization is the specific refinement of an intent-level specification into an executable procedure BOUND BY a correctness contract (making 'does this procedure satisfy this spec?' meaningful), with many-to-one freedom. is a specialization of refinement (adding detail), specialized to the what->how lowering under a discharge contract. Refinement supplies the genus: Iteratively improving a candidate solution toward adequacy through repeated cycles of evaluation and adjustment that narrow the gap to a target, rather than deriving the answer in one shot. Operationalization preserves that general structure while adding its differentia: A specification of what is wanted is mechanically lowered into an executable how, under a correctness contract relating the two. 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.


Opportunity asymmetry is a kind of asymmetry in which agents' feasible action sets differ systematically by position and endowment.

Opportunity asymmetry is a specialization of asymmetry: the relation between an agent and the set of actions available to them fails the swap-test — exchanging two agents' positions changes what each can do, not merely what each receives. It inherits asymmetry's directed-imbalance structure and particularizes it to the action-set case where the relevant asymmetry is in feasibility rather than outcome, distinguishing it from outcome inequality and locating the structural barrier at the access stage.


Opportunity cost presupposes decision because the forgone best alternative only has standing as a cost when a choice has actually been made.

Opportunity cost is the value of the best alternative forgone when a choice is made — it is constituted by the act of choosing one option and thereby closing off others. Without a decision, no path is selected, no alternatives are foreclosed, and the comparative magnitude has nothing to attach to. Decision supplies the moment when deliberation collapses into commitment and other paths are closed; opportunity cost is the economic accounting of what that closure cost in terms of best forgone alternative, so it presupposes the decisional commitment.


Opportunity cost presupposes scarcity because the cost of the best forgone alternative only arises when resources are insufficient to do both.

Opportunity cost is the value of the best alternative forgone when a choice is made, and it is meaningful only under constraint: if a resource were unlimited or the alternatives were not mutually exclusive, no alternative would actually be forgone. Scarcity supplies exactly this precondition — a finite supply insufficient to satisfy all simultaneous demands, so that allocating to one use necessarily denies another. Opportunity cost is the accounting consequence of that exclusivity, presupposing scarcity as the structural condition that makes forgone alternatives a real cost.


An optimal stopping rule repeats a continue/halt DECISION over a stream under uncertainty and trade-off; it presupposes the decision prime (committing to one alternative under uncertainty) and specializes it to the sequential, irreversible, order-matters halt structure. distinct from a one-shot decision because alternatives arrive in sequence. Decision supplies the prerequisite condition: Committing to one alternative from a set under uncertainty and trade-off, collapsing open deliberation into a chosen path and foreclosing the others. Optimal Stopping Rule operates against that background: A rule maps a sequence of observations to a halt decision, trading the cost of stopping too early against stopping too late. 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.


Optimism bias is a specialization of bias in which the systematic displacement favors better-than-true probability estimates for one's own outcomes.

Optimism bias is a specialization of bias. Specifically, it instantiates the systematic-displacement-from-the-true-value pattern in the self-prediction subclass: individuals' probability estimates for personal positive outcomes are consistently above base rates, estimates for personal negative outcomes consistently below, and belief updates asymmetric. It exhibits bias's defining signature -- a sign and direction surviving repeated estimation -- with the offset traced to motivated self-relevant projection and stronger for self than for comparable others, distinguishing it within the broader bias catalog.


Optionality presupposes uncertainty because the asymmetric value of an option only exists when future states are not yet known.

Optionality is the asymmetric value of holding a right without a duty — bounded downside, unbounded upside — preserved by paying a premium now for the privilege to decide later. That asymmetric value depends entirely on future states being unknown: if the future were certain, there would be no reason to keep choice open and the option would collapse to its expected exercise value. Uncertainty — the structural condition of incomplete knowledge about future states — is the very substrate that makes preserved maneuverability worth paying for, so optionality cannot exist without it.


Optionality presupposes reversibility and irreversibility because an option's value depends on the asymmetry between flexible upside and bounded committed downside.

Optionality is the structure of bounded downside and preserved upside choice, which requires the underlying distinction between paths that lock in commitment and paths that retain flexibility. Without the reversibility-irreversibility dimension, there would be no asymmetry to capture: the value of holding an option is precisely the value of remaining on the reversible side until exercise. The premium paid for an option is the price of avoiding premature irreversibility, so the parent prime's distinction is logically prior to optionality's payoff structure.


Order presupposes Comparison: a precedence relation requires the ability to place elements under a shared frame and read off a relation.

Order assigns a binary relation that says which element precedes which, subject to axioms like transitivity and antisymmetry. That relation cannot be established without Comparison as the underlying operation: pairs of elements must be brought under a shared dimension, aligned, and assigned a same/different or greater/lesser verdict. Order is comparison's outcome stabilized into a structured ranking over a whole set, so without the comparison operation no ordering relation can be constructed or checked.


Order presupposes Set and Membership: a precedence relation is defined over the elements of some set whose membership is already settled.

An order is a binary relation on a set, governed by axioms (reflexivity, antisymmetry, transitivity, or their strict variants) that quantify over that set's elements. The relation has no domain to act on unless Set and Membership has already fixed which items are in play and which are not. Order is therefore a structure layered onto a set: it presupposes the set as a first-class collection of distinct elements before it can rank, sort, or compare them.


Order presupposes relation because a ranking is a particular binary relation satisfying transitivity together with reflexivity or irreflexivity and antisymmetry or asymmetry.

Order presupposes relation because an order is, formally, a binary relation on a set obeying additional structural axioms: transitivity together with reflexivity and antisymmetry, or irreflexivity and asymmetry. Without the prior availability of relation as a designated pattern of association picking out which tuples stand together, there is no substrate on which the order axioms can act. Relation supplies the general apparatus of well-defined association; order adds the specific axioms that turn that association into a ranking with precedence.


Shared social norms are internal constituents of organizational culture alongside beliefs, values, assumptions, rituals, and interpretive frames.

Organizational culture is the system of shared beliefs, values, norms, tacit assumptions, rituals, and interpretive frames that guides acceptable behavior within an organization. Social norms are therefore explicit internal constituents: they encode expectations about how members should behave and attach approval, disapproval, or organizational consequences to compliance and deviation. Culture contains additional elements, but without shared normative expectations it would lose the behavioral guidance and acceptability judgments central to its live definition.


Ornamentation presupposes form and content because decorative elaboration adds form to a substrate without altering its primary functional content.

Ornamentation presupposes form and content because the very move of applying decorative detail to a functional substrate requires the form-content distinction: the substrate carries the primary function (content), and the ornament elaborates its presentation (form) without necessarily altering what the object does. Without the dualism that separates what-is-conveyed from how-it-is-presented, ornament collapses into structure and the discretionary aesthetic dimension disappears. Ornamentation operates precisely in the form-axis space the parent prime opens, while leaving content axis largely intact.


Oscillation is Periodicity specialized to recurring variation around a reference under restoring dynamics.

Every live Oscillation has a state that returns to similar values at a characteristic interval; damped, noisy, driven, and slowly modulated cases remain within Periodicity's approximate or conditional branches. Oscillation adds alternation around a reference, a restoring tendency, and storage or momentum that carries the state past the reference. Rotation, pulse trains, and externally scheduled stage cycles remain periodic without being oscillations.


Preference is the umbrella; the own-payoff-only agent is recovered at zero cross-weights (a measure-zero point). Preference supplies the genus: Agent's ordering over a choice set on some evaluative dimension. Other-Regarding Preferences preserves that general structure while adding its differentia: An agent's evaluation of outcomes depends not only on its own payoff but on the payoffs of other agents. 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.


Out-of-distribution detection presupposes the risk of applying a calibrated decision apparatus beyond the regime in which its competence was established.

The scope detector exists to catch the regime exit that the primary apparatus cannot reliably recognize from its ordinary confidence output. Remove the calibration-versus-deployment boundary and the deferral mechanism no longer has an out-of-competence condition to detect.


Outlier leverage is a property of an aggregation rule's non-resistance (low breakdown point) to extremes applied to a tailed distribution — it presupposes an aggregation (mean, slope, ratio, ranking) whose result a few points dominate. Built on the collapse-to-a-summary operation.


Overfitting presupposes Inductive Reasoning, whose structure must already obtain for the child mechanism to be meaningful or operational.

Inductive Reasoning supplies the prerequisite condition: Specific to general inference. Overfitting operates against that background: Poor generalization. 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.


Overfitting is the high-capacity, high-variance endpoint of the bias-variance trade-off already canonically owned by Trade-offs.

Increasing model flexibility can reduce bias while amplifying sensitivity to sample noise, so the child occupies one failure corner of the coupled capacity problem. Trade-offs owns the two-sided structure; Overfitting adds the train-test generalization gap and the capacity-reduction remedy.


Oversight capacity presupposes attention because the finite span of supervision is grounded in bounded cognitive attentional resources.

Oversight capacity is the structural invariant that any single overseeing entity can handle only a finite number of direct sub-units before coordination and decision quality decay. The binding source of that finitude is bounded attention — the inherently scarce cognitive resource that must be allocated across reports, signals, and decisions. Attention names the gating mechanism by which a limited resource is selectively assigned across competing inputs; oversight capacity is the management-side consequence of attention's scarcity, presupposing the attentional constraint as the upstream cause of any span-of-control limit.


Oversight capacity is the specific shape a constraint takes on the number of direct sub-units a single supervising entity can effectively manage.

Oversight capacity is the particularization of constraint to the supervisory relationship: bounded cognitive attention and coordination cost impose a binding upper limit on how many direct sub-units a single overseer can effectively handle before quality degrades. Where constraint names binding restrictions on admissible configurations generally, oversight capacity fixes the variable being restricted — direct-report count — and locates the binding limit in the cognitive and structural properties of the supervising entity rather than in the resources or technology of the subordinates.


The window is the population-level band of currently-sayable positions maintained by graded social cost; it presupposes the normative/sanctioning apparatus social_norms supplies. Social Norms supplies the prerequisite condition: Shared expectations about how members of a reference group should behave, maintained through internalization and anticipated decentralized approval, correction, or sanction. Overton Window operates against that background: A mobile range of positions that are currently sayable without social cost, with boundaries shifted by repeated exposure rather than argument. 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.


Paradigmatic and syntagmatic relations presuppose set and membership because the paradigmatic axis is a set of substitutable alternatives for a position.

Paradigmatic and syntagmatic relations presuppose set and membership because the paradigmatic axis is by definition a set of mutually substitutable alternatives that could fill a given slot — synonyms, chord-function substitutes, interface implementations — and identifying that set requires the membership relation that decides which candidates belong and which do not. Without set and membership's collection-as-first-class-object and inclusion-criterion machinery, there is no extension of substitutable alternatives to which a selected syntagmatic element belongs and from which it was drawn against the unrealized alternatives in absentia.


The sign-flip is a Bayesian non-monotonicity: it presupposes posterior updating over a three-hypothesis model (true / false / independence-broken). It is the conservation result that updating yields once a systemic-failure prior is admitted. Bayesian Updating supplies the prerequisite condition: Update beliefs with evidence. Paradox of Unanimity operates against that background: Agreement beyond what independent observation could produce becomes evidence against the conclusion, signaling a broken-independence failure mode. 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.


Parallel independent inspection gains coverage by duplicating the inspection role across partially independent inspectors. After the operations_research frame is stripped away, the retained structural roles are those of Redundancy: Duplicate critical components. Parallel Independent Inspection adds the local frame and commitments expressed in its identity: Defect coverage of a fixed artifact rises with the number and diversity of independent inspectors working in overlapping parallel. 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.


The Pareto effect is the specific shape heavy-tailed distributions take when ranked contribution shares concentrate roughly 80% of effects in roughly 20% of causes.

The Pareto effect is the specific shape heavy-tailed distributions take when the underlying power-law structure is translated into a rule of thumb about cumulative contribution shares. Heavy-tailed distributions' general signature — extreme values dominate sums, averages, and totals because the tail decays slowly — is structurally particularized into the observation that a small fraction of items produces a disproportionately large fraction of outcomes, with the canonical 80/20 split as the management-friendly summary. The general tail-dominance pattern is preserved; the specific shape is its cumulative-share, prioritization-actionable form.


Pareto efficiency is efficiency specialized to a multi-objective or multi-party feasible set where no protected dimension can improve without another worsening.

It inherits the feasible-set dominance test and undominated-frontier verdict. The child adds vector-valued outcomes across objectives or participants and refuses scalarization: improvement is free only when at least one dimension improves and none worsens.


Pareto efficiency is the specific shape optimization takes when multiple objectives are present and dominance is the operative criterion.

Optimization is the search for an element of a specified set that maximizes or minimizes an objective subject to constraints, with operative optimality named — exact, approximate, local, or Pareto. Pareto efficiency is the particular shape this search takes in the multi-objective case where interpersonal utility comparison is refused: an allocation is optimal when no change can make anyone better off without making someone worse off. It is a structurally-particularized instance of optimization whose specific notion of best is the dominance frontier, not a scalarized aggregate.


Pareto efficiency presupposes allocation because the no-improvement criterion ranks assignments of limited supply across competing claimants.

Pareto efficiency is the property of an allocation in which no change can make someone better off without making someone else worse off, which presupposes the underlying act of assigning limited supply to competing claimants. Without allocation's machinery of distributing scarce supply across competing demands, there would be no assignment whose efficiency the Pareto criterion could evaluate, no participants whose welfare comparisons would matter, and no feasible set of alternative assignments to scan for improvements. Allocation supplies the substrate on which Pareto efficiency operates as an evaluative criterion.


The law is the dynamics of ABSENT scarcity: an elastic activity fills its container's slack because no scarcity signal calls a stop short of the wall; its standard cure is to MANUFACTURE scarcity (tighter container). It presupposes the scarcity/slack frame as its governing variable. Scarcity supplies the prerequisite condition: A finite resource is insufficient to satisfy all competing wants. Parkinson's Law operates against that background: An elastic activity expands to fill its allocated resource container up to the binding constraint when no counter-pressure calls a stop short of the wall. 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.


Parrondo's Paradox is synergy specialized to state-coupled stochastic processes whose combination reverses negative individual expectations into a positive joint one.

Its winning mixture is a super-additive interaction relative to the two losing baselines, with shared-state modification and opposite-signed regional effects supplying the child's exact mechanism.


Parsimony is a specialization of minimalism; it is the principle of cutting unnecessary explanatory structure from theories and models.

Minimalism is the disciplined principle of stripping away unnecessary complexity to isolate and emphasize essential elements that serve a primary function. Parsimony is the specific case in which the domain is explanation and the elements being cut are theoretical entities, parameters, mechanisms, and assumptions beyond what is needed to account for the evidence. It inherits minimalism's reduction-by-necessity stance and adds the explanatory-adequacy criterion as the test of what counts as essential. A specialization of minimalism keyed to theory choice and model selection.


Parsing recovers latent hierarchical structure from a representational substrate (the sequence) under a framework (the grammar) — the syntactic-structure-recovery specialization of interpretation ('recover meaning from a representational substrate under a framework that makes some readings available'). Interpretation supplies the genus: Recover meaning from a representational substrate under a framework that makes some readings available and others not. Parsing preserves that general structure while adding its differentia: Recover hidden hierarchical structure from a flat sequence using a grammar. 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.


Alternative lineage: parsing is the grammar-inverting, structure-recovering member of the transformation family (sequence -> tree). Transformation supplies the genus: A rule-governed mapping that restructures an input into a different output, holding certain invariants fixed while altering others. Parsing preserves that general structure while adding its differentia: Recover hidden hierarchical structure from a flat sequence using a grammar. 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 partition is the disjoint-and-exhaustive (MECE) discipline imposed on a carrier set via a single-valued membership function; it presupposes the set/membership apparatus it disciplines. Set and Membership supplies the prerequisite condition: Groups and categorizes elements. Partition operates against that background: A division of a set into non-overlapping, collectively exhaustive blocks. 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.


This prime is the structural consequence of the aggregation operation — that the operation's output depends on how the partition is drawn. Presupposes aggregation as the collapsing step (the verb; this is a fact about the verb's output). Aggregation supplies the prerequisite condition: Deliberately collapsing many items into a single summary, choosing which information to discard to gain tractability. Partition Dependence of Aggregates operates against that background: Any statistic computed on partition-aggregated data is a function of the partition itself, not solely of the underlying data. 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.


Removing domain vocabulary leaves an ordered availability relation in which later evidence crosses into an artifact asserted to represent an earlier state. Remove human memory, model training, finance, databases, legal review, and named validation protocols. A time-indexed state, evidence arriving after its index, an illicit backward information channel, a changed reconstruction, and a time-respecting repair remain.


'A path is one COMMITTED realization of a connection through the underlying relational substrate (a network)... the path's leverage comes entirely from holding the realized route apart from the possibility structure.' A path presupposes a network to traverse. Network supplies the prerequisite condition: Models interactions between components. Path operates against that background: An ordered, traversable sequence of edges connecting one node to another through a relational structure. 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.


Path dependence presupposes dependency because outcomes constrained by historical trajectory require the present to rely on prior decisions and states.

Path dependence presupposes dependency because the claim that present options depend constitutively on the historical trajectory of choices requires the directed reliance relation between later and earlier states. Without dependency's structure — A cannot proceed, function, or retain value unless conditions on prior B are met — the present state would be fully determined by current conditions plus exogenous shock, and history would drop out. Dependency supplies the temporal reliance that makes the sequence of past decisions load-bearing for present and future possibilities.


Path dependence presupposes time because outcomes constrained by historical trajectory require the temporal ordering of earlier and later states.

Path dependence presupposes time because the claim that present possibilities depend constitutively on the specific historical trajectory of past choices requires the temporal ordering of earlier and later states with irreversible succession. Without time's privileged direction — earlier states fixing branching points that constrain later ones — there would be no sequence in which past decisions could foreclose alternatives or accumulate constraints. Time supplies the directed-ordering substrate that makes the historical trajectory a structurally meaningful determinant of present state, not a redundancy on top of current conditions plus exogenous shock.


Path_dependence (the rising lock-in curve alone) is one of the two curves the Collingridge dilemma composes — it adds the co-rising INFORMATION curve and the window between them. After the economics_finance frame is stripped away, the retained structural roles are those of Collingridge Dilemma: Information about a system's consequences rises as the cost of changing it rises, so the window where intervention is both informed and feasible may be narrow or absent. Path Dependence adds the local frame and commitments expressed in its identity: 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. 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.


Pattern completion is a specific kind of interpretation, recovering a coherent whole from partial input via stored priors.

Pattern completion is a specialization of interpretation. The general pattern recovers meaning from a representational substrate given a framework that makes some readings available and others not, producing readings that are neither uniquely fixed by the input nor arbitrary. Pattern completion instantiates this with the substrate being partial, noisy, or ambiguous input and the framework being stored regularities, learned associations, or generative priors that fill in the unobserved parts. The reconstruction is constrained by priors and answerable to the input, which is exactly the productive-yet-bounded character of interpretation.


Pattern completion is a kind of inductive reasoning that infers the unobserved whole from partial input using stored regularities.

Pattern completion is a specialization of inductive reasoning: it produces a conclusion about unobserved portions of a whole that goes beyond what the partial input logically guarantees, drawing on stored regularities, context, and predictive priors. It inherits induction's ampliative commitment — conclusions extend the evidence — and particularizes it to the reconstruction case, where the inference fills in occluded, noisy, or degraded parts. The reconstruction's accuracy depends on the same support-strength and calibration metrics induction uses.


Pattern completion presupposes predictive coding because filling incomplete input requires a generative model whose predictions span the missing parts.

Pattern completion presupposes predictive coding because reconstructing a coherent whole from partial input requires the same predict-compare-correct machinery: a generative model produces predictions for unobserved or degraded portions, the observed portion is compared against those predictions, and the inferred completion is the model-consistent extension of the input. Predictive coding supplies the prior-structure-as-generative-model and the residual-driven update that pattern completion deploys: the model contributes the missing parts, the input constrains the inference, and prediction error tunes the model toward better future completions.


Pattern in design is the specific shape recurrence takes when motifs are deliberately arranged to repeat across a surface or sequence.

Pattern in design is the structurally-particularized form recurrence takes in the aesthetic-design case: the recurring unit is the motif, the predictable spacing is set by the compositional grid or rhythm, and the trigger is the designer's systematic placement. It inherits recurrence's structural property of pattern reappearance with predictable structure, particularized to the intentional-arrangement case where repetition is orchestrated with controlled variation rather than merely observed in natural data.


Pattern recognition is a specialization of classification in which the assignment of a stimulus to a known category proceeds by feature matching against stored representations.

Pattern recognition is a specialization of classification in which the rule-application is implemented by matching a stimulus's observable features against stored category representations: templates, prototypes, exemplars, or learned hierarchical detectors. It inherits the general classification commitment that entities are assigned to discrete categories according to explicit criteria, with the assignment carrying meaning for downstream reasoning. Its specialization is to identify the stimulus as an instance of a known category via similarity-driven feature analysis rather than via explicit rule application or definitional checklist.


Pedagogy presupposes learning because the deliberate teaching act is only intelligible relative to the learner-side acquisition it aims to cause.

Pedagogy presupposes learning because pedagogy is defined as the intentional, other-directed arrangement of conditions calibrated to cause a durable change in another agent's capability — and that change just is learning. Without the learner-side update as its target, pedagogy has no object: sequencing, modeling, support, and assessment all become uncalibrated activity. The teaching-side practice and the learner-side acquisition are explicitly framed as counterparts, so pedagogy cannot operate as a structured practice without presupposing learning as the process it is engineered to produce.


The Peltzman Effect is a Counterresponse Offset specialized to a safeguard lowering expected failure cost and releasing a behavioral risk budget.

It inherits direct improvement, a coupled adaptive response, and graded offset accounting. It adds an exposure-choosing agent, a safety or protection intervention, expected failure cost as the changed condition, and riskier behavior as the response.


The perception-action loop is the specific feedback structure in which 'action moves the sensing apparatus itself' — a constitutive coupling, not merely an error signal. Genus=feedback, differentia=acting-moves-sensing and reafference. Feedback supplies the genus: Outputs influence inputs. Perception Action Loop preserves that general structure while adding its differentia: Perception and action are constitutively coupled: action moves the sensing apparatus, that movement changes what is sensed, and what is sensed becomes the basis for the next action, in one closed loop with no clean sense-think-act stages. 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.


Perceptual Expertise is Learning specialized to a durable, exposure-driven change in representational resolution and later discrimination.

Learning supplies experience-driven internal update that changes future performance. The child fixes the updated capability to a recognizer's feature allocation and category representation, with dense exposure improving within-category individuation and sparse exposure leaving coarse codes.


Perceptual Expertise contains Pattern Recognition because its learned granularity is expressed through feature extraction, stored category representations, and matching of new instances.

Expertise is not mere familiarity or accumulated facts. Training changes which features the recognizer extracts and how finely members of a category are represented and matched. Pattern Recognition supplies that operational channel; the child adds the exposure-driven redistribution of resolution.


Percolation is 'the specific phase transition whose order parameter is connectivity' — the emergence of a system-spanning giant component, with its own critical exponents and universality classes. A species of the generic tipping-point/phase-transition. Tipping Points (or Phase Transitions) supplies the genus: Abrupt state change. Percolation preserves that general structure while adding its differentia: Local, often random short-range connections accumulated across a population suddenly produce system-spanning connectivity once their density crosses a critical threshold. 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.


'percolation threshold is a phase transition, but a specific one' — the connectivity transition on a network substrate (giant component as order parameter, topology-dependent p_c). A specialization of the generic tipping-point/phase-transition family. Tipping Points (or Phase Transitions) supplies the genus: Abrupt state change. Percolation Threshold preserves that general structure while adding its differentia: On a network substrate, a system-spanning connected cluster appears suddenly at a sharp critical density of links, transforming isolated pieces into one reachable whole. 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.


Defined on a network substrate of linkable sites; presupposes network (the relevant object is the connectivity graph). Network supplies the prerequisite condition: Models interactions between components. Percolation Threshold operates against that background: On a network substrate, a system-spanning connected cluster appears suddenly at a sharp critical density of links, transforming isolated pieces into one reachable whole. 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.


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

After the chemistry_materials frame is stripped away, the retained structural roles are those of Porosity: A bulk holds a distributed fraction of internal void space whose total, connectivity, and distribution jointly set storage capacity, transmissibility, and mechanical strength. Percolation Threshold adds the local frame and commitments expressed in its identity: On a network substrate, a system-spanning connected cluster appears suddenly at a sharp critical density of links, transforming isolated pieces into one reachable whole. 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.


Periodicity is Invariance specialized to preservation under displacement by a repeat interval.

Every instance of the live Periodicity family identifies a value, waveform, state pattern, or statistical structure preserved exactly or within an explicit tolerance when its carrier is displaced by a characteristic interval. That is Invariance with the transformation fixed to discrete translation. Periodicity adds a nonzero period or period set, waveform, phase, frequency, and the distinction between exact, approximate, modulated, and conditional repetition.


Periodization is the specific shape segmentation takes when the continuous domain being partitioned is historical time.

Periodization is the specific shape segmentation takes when the continuous domain being partitioned into discrete labeled segments is historical or temporal process, with boundaries placed at moments deemed transformative — political events, technological shifts, cultural reorientations. It is a structurally-particularized instance of partitioning by boundary placement, where each segment receives characteristic features defining internal coherence, with the added commitments that the boundaries are constructive choices by the partitioner rather than natural kinds, the segments serve as scaffolding for description and comparison, and the partition can always be contested or redrawn.


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

Boundary supplies the prerequisite condition: Defines system limits. Permeability operates against that background: A bounded medium selectively passes some carrier through connected pathways. 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 permission-gated hold is gatekeeping specialized to an otherwise-ready item awaiting an external arbiter's affirmative release decision.

It inherits a choke point, an authority applying passage criteria, and selective control over onward flow. It adds the coexistence of physical or operational readiness with an unresolved administrative state and a release token that alone ends the hold.


The unresolved permission gate is the single limiting stage that prevents an otherwise-ready flow from completing.

All non-administrative stages can be ready and still make no progress. Until authorization is emitted, the gate alone caps completion, so a bottleneck is inside the hold's defining structure.


A permission-gated hold contains the delay between readiness or submission and the authority's release response.

Remove the signed waiting interval and the construct collapses to an instantaneous authorization decision rather than a hold. Administrative response latency is therefore constitutive. Latency supplies an internal constituent: The irreducible delay between an input and the system's response. Permission-Gated Hold requires that role within this mechanism: An otherwise ready flow remains blocked until an external authority emits a required authorization, making completion depend on administrative release rather than on the flow's own movement or production capacity. Remove the parent-role and the child loses a required internal operation, even though the parent can exist outside the child. The child is therefore built from the parent rather than being a taxonomic kind of it.


Institutional permission gates typically process competing pending cases through a bounded-capacity waiting line.

Permits, reviews, sign-offs, and clearances usually arrive to a finite service channel and wait for attention, producing queue dynamics. A single exceptional hold can still exist without a population-level queue, so the constituent is typical rather than strict.


A persistent identifier is a specific, committed, institutionally-maintained indirection (opaque token and declared scope and guaranteed resolver) — a specialization of the bare indirection technique with a standing institutional obligation. Indirection supplies the genus: Introduces intermediary references. Persistent Identifier preserves that general structure while adding its differentia: A designed token committed to keep resolving to its entity across changes in the entity's location, representation, custodian, or version, via a separately maintained resolver. 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 stable handle is what lets provenance/traceable records stay referenceable across substrate change; presupposes the traceability infrastructure it underwrites. Traceability supplies the prerequisite condition: The infrastructure of bidirectional links that lets any element be followed backward to its origin and forward to its uses, turning opaque processes into auditable, queryable histories. Persistent Identifier operates against that background: A designed token committed to keep resolving to its entity across changes in the entity's location, representation, custodian, or version, via a separately maintained resolver. 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.


A Persistent Identifier presupposes the prior Identifier Assignment that minted its opaque handle and installed the authoritative entity binding.

Persistence is a continuing property of an identifier after issuance. Before a token can remain stable and resolvable across change, an authority must define its namespace, mint it, bind it to an entity, and expose dereference. The token- plus-resolver is not itself the issuance act.


Perspective is the specific shape representation takes when three-dimensional spatial relations are projected onto a two-dimensional surface.

Perspective is the specific shape representation takes when the target is three-dimensional space with depth and volume and the medium is a two-dimensional surface, with the mapping accomplished through systematic projection. It is a structurally-particularized instance of structured mapping under a faithfulness convention, with the added commitments that the convention is a projection system (linear, multi-point, isometric), the faithfulness preserves spatial coherence and ordinal depth, and the dropped features include the literal third dimension. The viewer reconstructs depth from the projection's lawful regularities.


Perspective is typically a specialization of Projection, retaining the parent's defining structure while adding the child's specific commitments.

Projection supplies the genus: Map a richer object onto a lower-dimensional target along a chosen direction, discarding the rest. Perspective preserves that general structure while adding its differentia: Representation of depth. 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.


Perturbation presupposes observability because the system's response to small deviations must be measurable in outputs to carry diagnostic information.

Perturbation presupposes observability because the analytic value of introducing a small departure from a reference state lies entirely in reading the system's response — and that response must be inferable from externally-visible outputs. Without observability's structural guarantee that internal state can be reconstructed from outputs over time, the propagation of a perturbation would be undetectable and its sensitivity, stability, and response structure could not be extracted. Perturbation analysis is precisely observability put to diagnostic use.


Perturbation presupposes state and state transition because a small departure from a reference state is only definable against a specified system state.

A perturbation is a small departure from a reference state whose propagation through the system is analyzed as a correction around that state. Every perturbation claim must specify the reference state or baseline trajectory from which the departure is measured and the response of interest as the system transitions away from it. The state-and-state-transition framework supplies exactly that: a state space, a transition rule, and the Markov closure on which linearization around a baseline depends. Without the underlying state structure, there is no baseline against which a perturbation can be small.


Perturbation theory is the specific shape approximation takes when an intractable problem is split into a solvable part plus a small expansion parameter.

Perturbation theory is the structurally-particularized form approximation takes when the intractable target H can be written as H₀ + λV with H₀ exactly solvable and λ a small coupling. The tractable surrogate is the truncated power series in λ; the error measure is the next-order correction; the tolerance is set by the asymptotic radius. It satisfies approximation's four-part discipline — exact object, simpler surrogate, controlled error, named tolerance — particularized by the splitting H₀ + λV that makes the expansion well-defined.


Perturbation theory is the specific shape decomposition takes when a Hamiltonian is split into a solvable part plus a small perturbing operator.

Perturbation theory is the structurally-particularized form decomposition takes when the whole — an intractable Hamiltonian, Lagrangian, or operator — is broken into H₀ + λV such that H₀ is exactly solvable and the parts properly combined reconstitute the original. It inherits decomposition's commitment that the pieces, analyzed independently and recombined, reproduce the whole, particularized by the order-by-order expansion in λ. The reversibility runs through resummation; the structure-preservation runs through the algebra of unperturbed eigenstates.


Perturbation theory is the specific shape perturbation takes when the response is computed as a power-series expansion in a small coupling.

Perturbation theory is the structurally-particularized instance of perturbation in which the small departure is treated as an additive term in a Hamiltonian or operator and the system's response is expanded as a power series in a small dimensionless coupling. It carries forward the general perturbation commitment that a small departure from a reference state can be analyzed as a controlled correction rather than a fresh problem, and gives this idea its specific algorithmic shape: solvable zeroth-order baseline plus order-by-order corrections computed from unperturbed eigenstates and matrix elements.


Phase Diagram presupposes Classification: it partitions parameter space into discrete phase regions according to qualitative-distinction rules.

A phase diagram divides a parameter space into regions labeled by qualitatively distinct phases, with boundaries where order parameters jump or become singular. Constructing the diagram requires the prior operation of Classification — assigning configurations to discrete categories by explicit criteria. Without classification rules deciding which configurations count as the same phase, the diagram's regions and boundaries have no content; the diagram is a graphical instantiation of a classification scheme over a continuous control space.


A phase diagram presupposes tipping points because it charts the very threshold surfaces that separate qualitatively distinct phases.

A phase diagram presupposes tipping points because its central content is a partitioning of parameter space by phase boundaries: codimension-one surfaces across which the system undergoes a phase transition, with critical points, triple points, and bifurcations identified as special features. Without the prior commitment that systems can exhibit abrupt qualitative shifts at threshold parameter values, there is nothing to chart, no surfaces to draw, and no distinct phases between which to navigate. Tipping points supply the discontinuities the diagram organizes.


Phase diagram presupposes state and state transition because it maps where in parameter space qualitatively distinct phase states obtain.

A phase diagram partitions parameter space into regions where the system exhibits qualitatively distinct phases, with phase boundaries marking discontinuous or singular transitions between them. The diagram is meaningful only against an underlying state-and-state-transition structure: each phase is a state with characteristic order parameter, and phase boundaries are the transition surfaces. Without a notion of distinct states and rule-governed transitions, the partitioning would have nothing to demarcate and the triple and critical points would lose their identity as transition-structure features.