A.1.1:4.2 - Recover the direct relations

A.1.1 states each direct predicate and its occurrence-identity rule. An obtaining occurrence is an instance of a relation kind already admitted under U.Relation; its existence does not depend on a project deciding to expose it. A named receiving use may justify explicit individuation and reference under A.6.REL. A reusable RelationSignature episteme declares the participant SlotSpecs. An assertion or occurrence description may designate the actual participants by value or reference. Each table below is a readable presentation of one signature declaration.

The two named temporal-extent ValueKinds below are local to A.1.1, not U-kinds. They can type a temporal extent stated in an assertion or occurrence description; they are not participant ValueKinds in either RelationSignature. For ModelApplicabilityRelation and ModelUseRelation, the direct obtaining history determines the maximal continuous extent used by the occurrence-identity rule. A filled assertion may state an open or closed extent.

For these two temporally varying relation kinds, continued obtaining extends the same open occurrence; a demonstrated gap ends it, and later resumption begins another occurrence. ModelExpressionCoherenceRelation instead has the participant-determined identity declared below: it has no temporal-extent discriminator. Revising an assertion changes the episteme, not any world-side occurrence.

ModelApplicabilityRelation. Its participants are one model episteme, one exact holon, and one declared claim scope. Its predicate asks whether that model applies to that holon over the exact U.ContextSlice values delimited by that scope. The model episteme’s C.2.1 effective reference scheme supplies the interpretation basis; it is not a fourth participant.

Well-formedness constraint WF-A1.1-APP. ModelApplicabilityRelation(M,H,S) obtains exactly when S is the model-declared applicability scope or scopeSubset(S, modelDeclaredScope(M)), both scope expressions are interpreted under effectiveReferenceScheme(M), and the model’s declared applicability conditions hold for H over every slice x for which member(x,S) is true. coversSet(S,T) applies only when T is an exact finite ContextSliceSet.

When S imports a local sense from another semantic setting, the interpretation branch exists exactly when the source and receiving F.17 SchemeSenseCell values are resolved and an F.9 Bridge obtains in the source-to-model orientation. Different schemes, shared spelling, or a Bridge Card does not establish that branch.

Well-formedness constraint WF-A1.1-APP-USE. A positive applicability assertion or structure selection that relies on the imported branch is admissible only when a separate current C.2.1 claim affirmatively states that the Bridge is suitable for this named scope-comparison use, direction, rule, and loss tolerance. The same use must have an exact A.10 evidence-provenance path whose edges cite independently established direct relations. Ordinary reliance requires RelianceDisposition=pass. If an actual named assurance claim about that use is current, require its B.3 AssuranceResult for the same bounded use: only supported-for-use supports the attempted assurance use, while narrowed supports only its stated narrower use. A direct domain rule may require such a claim.

Use guidance. If the Bridge, bounded-use claim, or selected reliance branch is missing, return respectively missing claim-scope interpretation bridge, missing claim-scope interpretation use claim, or missing claim-scope interpretation reliance. These stops block the receiving assertion or selection; they do not make an otherwise obtaining Bridge false. Any membership judgment, operation application, assertion, or Work remains under A.2.6, A.6.1, C.2.1, or A.15.1.

The occurrence is reidentified from the actual identities of the model episteme, holon, and claim scope together with the derived maximal continuous ModelApplicabilityInterval. Repeating the model’s effective scheme adds no independent discriminator. ModelUseRelation. Its participants are one exact system-role-assignment occurrence, one model episteme, one performed Work occurrence, and one exact use-locus holon. Its predicate is actual use of that model content by the assignment holder while that system performs the same Work concerning that holon.

Well-formedness constraint WF-A1.1-USE. ModelUseRelation(A,M,W,H) obtains exactly when F.6 performedUnderAssignment(W,A) obtains and HolderSystem(A) actually uses the content of M while performing W concerning H. The holder system is derived, not copied as a fifth participant. Any claimed enactment relation between W and a Method belongs to A.15.1; A.3.1 identifies that Method.

The occurrence is reidentified from the four participant identities and the derived maximal continuous ModelUseInterval. A useful counterfactual probe compares otherwise matching work situations that use model epistemes with different relevant content and asks whether that difference could change performance; availability or mention alone is not actual use. Scope delimitation is not another direct relation kind here. The U.ClaimScope participating in ModelApplicabilityRelation is a set-valued scope over U.ContextSlice; A.2.6 governs its primitive membership predicate. A membership assertion or an evaluation result is an episteme about that predicate.

Local predicate-value declaration. ModelExpressionCoherencePredicate is an A.1.1-local ValueKind, not a U-kind and not an evaluation procedure. A by-value candidate belongs to this kind only when it declares (1) the ordered model-content and expression-content input meanings, (2) the exact comparison domain and local senses, (3) a Boolean truth condition, (4) the treatment of required congruence and permitted loss, and (5) every dependency whose absence makes application stop rather than return false. Two predicate values are identical exactly when those five by-value components are identical. A changed input meaning, domain, truth condition, congruence or loss rule, or dependency identifies another predicate value; a changed label, evaluator, evidence set, result episteme, representation, or publication does not. A label or procedure lacking the complete five-part declaration is not a member.

ModelExpressionCoherenceRelation. Its participants are one exact model episteme, one exact expression episteme, one by-value criterion admitted as ModelExpressionCoherencePredicate, and one exact U.ReferenceScheme used as the comparison basis.

Well-formedness constraint WF-A1.1-COH. ModelExpressionCoherenceRelation(M,E,P,R) obtains exactly when either (a) R equals the C.2.1 effective schemes of both epistemes, or (b) P resolves every differing source and receiving F.17 SchemeSenseCell pair and names an obtaining F.9 Bridge for each required correspondence; and, after that semantic branch is established, the fixed predicate value P returns true for the fixed claim contents of M and E under R. An unresolved cell, missing Bridge, shared spelling, common label, Bridge Card, or mere interpretability establishes no bridged branch.

The Bridge profile carries relation semantics only. Comparison direction, use-specific rule, permitted loss, and reliance belong to the separate bounded-use claim and reliance path.

Well-formedness constraint WF-A1.1-COH-USE. A receiving assertion or structure selection that relies on a bridged coherence occurrence is admissible only when a separate current C.2.1 claim affirmatively states that the Bridge is suitable for this fixed-content comparison use, direction, rule, and loss tolerance compatible with P. The same use must have an exact A.10 evidence-provenance path whose edges cite independently established direct relations. Ordinary reliance requires RelianceDisposition=pass. If an actual named assurance claim about that use is current, require its B.3 AssuranceResult for the same bounded use: only supported-for-use supports the attempted assurance use, while narrowed supports only its stated narrower use. Establish any required authorization separately.

Use guidance. Return missing model-expression interpretation bridge, missing model-expression interpretation use claim, or missing model-expression interpretation reliance for the corresponding missing condition. A use stop does not make the Bridge or predicate false and does not erase or reidentify an otherwise obtaining coherence occurrence. Comparison Work, an assertion episteme, and an A.22 selection use remain separate.

One occurrence is participant-determined by <M,E,P,R>; it has no temporal-extent discriminator and no later recurrence for the same tuple. Changed claim content identifies another episteme and tuple. Changed predicate value or comparison scheme likewise changes the tuple. Changed evidence, bounded-use claim, reliance result, card, publication, evaluator, or timestamp does not. Maintenance remains one separate dated Work individual: recover each exact actual performer through A.13 and let A.15.1 independently admit the occurrence. Add F.6 through the same obtaining A.13 assignment only when the maintenance account or its receiving use expressly consumes precise assignment-bound attribution; F.6 identifies neither assignment nor performer, and missing or failed attribution leaves the Work intact. Its affected-referent, resource, parameter, premise, method-enactment, and operation-application facts use their direct relations or A.6.1 bindings. C.2.1 identifies any report or repaired episteme separately; only an exact A.15.PROD entity-inception claim may relate that episteme’s first existence to the performed maintenance. An exact evaluator may separately be recovered through A.13 and perform independently admitted evaluation Work, with F.6 added only for a consumed precise attribution. C.2.1 identifies any result episteme asserting whether the coherence predicate holds, and only its exact A.15.PROD inception basis may relate its first existence to that performed Work. Neither that result episteme nor its provenance is the coherence occurrence. Failed maintenance work remains actual work even when the changed episteme tuple has no obtaining coherence occurrence.

BoundedModelUseStructure selects obtaining participant-determined ModelExpressionCoherenceRelation occurrences. Maintenance methods and Work remain separate objects even when they change the receiving decision; if their organization must itself be selected, that is a distinct A.22 structure and does not enter this bounded-model-use identity.

Coherence-work stress cases. Coherence can obtain before any selected maintenance episode. Successful maintenance that leaves both episteme identities fixed leaves the same participant tuple; maintenance that changes expression claim content gives another C.2.1 episteme and a different tuple to evaluate. Failed maintenance may leave a changed expression episteme and a separately identified evaluation result while the new tuple has no obtaining coherence occurrence. Automated integration work and non-software maintenance use the same separation among fixed-content correspondence, work, result, evaluation, evidence, and provenance.

Occurrence-identity stress case. Exact F.6 performedUnderAssignment(InspectionWork-42, InspectorAssignment-17) obtains, and its holder Robot-7 uses DefectModel-3 concerning Pump-6 during that work. An observation at 10:00 supports continued obtaining of the same occurrence whose ModelUseInterval began at 09:00 and remains open; it does not create another occurrence. If model use demonstrably stops at 10:15 and resumes at 10:30 during the same work occurrence and assignment attribution, the resumption begins a second model-use occurrence. Correcting an assertion’s timestamp without evidence of a world-side gap changes only that assertion.

Use guidance — unsupported crossing. First identify both endpoint BoundedModelUseStructure values without the crossing and state source, target, direction, required fit, permitted loss, and claim scope. Well-formedness constraint WF-A1.1-CROSS. A positive cross-structure member exists only when a current direct pattern supplies compatible endpoint SlotKinds, an obtaining crossing predicate, an occurrence-identity rule, and all four A.22 discriminators; the proposal, F.9 sense Bridge, label, diagram, or card supplies none of them. Otherwise preserve the six-part proposal, omit it from both endpoint identities and every positive cross-structure member, and return missing CROSS-LOCALITY-BRIDGE governor.

A.1.1 is the subject pattern for these three relation kinds. A.6.0 governs their RelationSignature epistemes, A.6.5 governs the SlotSpecs inside those declarations, and A.6.REL governs progressive explicit individuation. A.2.6 separately governs claim-scope membership. BoundedModelUseStructure is the selected organization of the resulting occurrences under those scope values; no context record copies their participants.