E.24:4.0 - Constructive Foundation And Math-Lens Boundary

If a reader asks where an FPF ontic gets constructive grounding, follow its exact identity or grounding assertion and defining or constraining ClaimGraph. E.24 records a locator for that rule and only the relations needed by dependent use; it does not turn declarations, descriptions, publication objects, views, or representations into grounding participants. Their exact predicates, assertions, and rule-content locators remain in E.24:4.3a.

For structural identity claims, the constructive chain is E.14 -> B.3.5 -> C.13: Working-Model relation first, declared validationMode, tv:groundedBy, and a reconstructible Γ_m.sum, Γ_m.set, or Γ_m.slice trace. The Γ_m trace is the reconstructible grounding object cited through tv:groundedBy under B.3.5. If a graph, tuple, or another mathematical expression represents that trace, the expression is a separate C.29 representation. Neither the trace nor its representation becomes the public relation vocabulary, and this structural grounding apparatus is not required for non-structural ontics.

For a non-structural ontic, use the exact identity, grounding, or recognition assertion and defining ClaimGraph located by its direct subject-pattern reference. Open E.24.UK only for U-kind admission, C.2.1 only for an episteme’s identity, E.24.PUB only for current availability, and the other rows of E.24:4.3a only when their selection question is true.

A.14, B.2, and A.15.1 carry BORO- and CCO-compatible identity and occurrence discipline. They support the constructive foundation; they do not create a separate durable-kind ontology.

Before a dependent pattern relies on the ontic, classify each current object with E.24:4.3a. The selection question—not a shared label or visual container—decides whether the object is a world-side participant, relation occurrence, reusable declaration, claim-bearing episteme, publication object, view or representation, source expression, or durable ontology unit.

An encountered card illustrates the rule. Its claims, reusable layout, diagram elements, and carrier are separately governed only when their own identity and direct relation are established; the word card identifies none of them and does not make the collection an ontic.

When several current pattern descriptions already contain rule content for the same project concern, select an ontic only if one exact identity rule and minimal relation set must be reused across their dependent uses. Keep every otherwise current object in its E.24:4.3a row; shared topic or proximity cannot fuse their kinds. At the ontology layer, state reliance on exact relation rules without inventing an occurrence whose participants are the kind, pattern, or ontic.

Build the decision evidence in this order; do not select a disposition first and then backfill reasons:

1. Current case and stable decision subject. State the working expression or source claim, one independently identified pre-judgment candidate entity, proposal episteme, or source-construct entity with its direct identity governor, and the named receiving use. Use that fixed object as the decision episteme’s EntityOfConcern. Record source-use status and provenance here when current; they do not settle the ontology disposition.
2. Existing-governor reuse and non-duplication. Name the current direct patterns checked by value. State which current claim they already close, or the exact coordination they fail to supply. Reject a new umbrella when it would merely rename those governed objects or copy their rules.
3. Identity, constitution, or recognition. State the exact rule supplied by the subject’s subject pattern and what would reidentify the subject across the receiving use. Do not replace several required facts with an invented universal relation.
4. Typed connectivity and dependent use. Use E.24:4.3a to classify only the objects that the dependent use consumes. Name each needed direct relation, its exact predicate and definition source, any identity-bearing relation selected by its occurrence-identity rule, each declaration actually reused, and each dependent assertion’s exact reliance basis. Omit every neighboring map row whose selection question is false.
5. Disposition, branch result, and boundary—fill last. Keep the decision EntityOfConcern from step 1. From steps 1–4, record exactly one branch payload: the closing assertions and direct patterns; the bounded episteme, its declared use, and stop; the selected ontology-unit individual and subject pattern; or the unresolved reason and missing evidence. Add an explanatory overread only when it passes F.19:4’s full independent-ground, plausible-reader, contribution, and smallest-clear-correction test.

A relation-participant meaning belongs in one selected direct relation only when that relation’s predicate depends on an actual participant having that meaning and the exact defining ClaimGraph states the admitted kind of that participant. When typed reuse is needed, a compatible RelationSignature declares that admitted kind as the SlotSpec’s ValueKind. Another entity remains under its own direct relation when that relation already expresses the needed use. Reuse pressure can justify a RelationSignature; it cannot turn a neighboring relation, record field, or mathematical operand into a participant or SlotKind of another relation.

Optional-in-use status belongs to a declaration or description. It does not mean that a world-side relation occurrence has an unfilled participant. A missing designation leaves the assertion incomplete or the participant unknown to the current user. It does not show that the participant is absent, and it does not make the direct predicate obtain or cease.

Not every ontic needs every map row. Open one only when its selection question changes the named receiving use; otherwise omit it and keep the object under its subject pattern.

Keep annotation proportional. E.24 calls for recovery only where wording can change ontic identity, a direct relation, participant meaning, a reusable SlotSpec declaration, a description claim, admissible use, or the reliance basis of a dependent pattern. If readable domain prose already preserves those objects, do not replace it with declaration syntax merely to show that an ontic exists.

This differs from pure ontology engineering because FPF patterns are written for action: they may define or constrain a kind or predicate, state an admission test, frame a judgement, or give practical guidance. That does not make every pattern episteme a U.MethodDescription or every subject a U.Method. An engineer-manager uses the applicable claims and guidance to decide what can be done, claimed, relied on, repaired, compared, or stopped. If the current claim says that an E.24 episteme describes an ontic-introduction Method, apply A.3.1 and A.3.2 to identify that Method and show that the episteme substantively describes how it is done. The accepted ontic-introduction decision supplies the object discipline for those practical choices; the pattern text itself performs no action.

Precision restoration uses the same discipline without turning it into lexical style. First recover the source-side entities, direct relations, assertions, descriptions, and defining or constraining ClaimGraph sources compressed by the wording. Then repair toward a current FPF ontic only when one accepted ontic-introduction decision states how those objects are coordinated. If no such ontic exists, state the exact subject assertions, cite their pattern-description locators, keep only the needed claims in a bounded local episteme under C.2.1, or open an E.24 ontic-introduction decision.

When a source expression opens the ontic-introduction question, preserve its source-to-use path independently of the ontology disposition. Name the exact expression and its source episteme; name the source publication occurrence when availability through that occurrence matters; recover the entities, relations, and claims actually carried forward; and set the source-use status to quote-only, reduced use, or one selected stronger use with the smallest condition that licenses it. Keep that trace beside a durable-ontic, bounded-episteme, or direct-use disposition whenever both are current. If no governed payload has been selected, mark the ontology disposition unresolved and retain source-only inquiry material rather than treating provenance as an ontology answer. When a stronger-use condition occurs, reopen the source expression through C.2.P or the direct source-use pattern instead of treating the repaired noun as a substitute for the source relation.

When an E.10.ARCH wording-use restoration row opened the case, retain its four coordinates inside that source-to-use trace: semanticAreaBaseConcept is the source cue, semanticArea is the selected Part-F row or bounded row-set, semanticAreaSenseFamily prevents theme-level overgeneralization, and ontologicalNeighborhood is the applicability neighborhood used to recover the subject kind, relations, and subject patterns. These are coordinates of the wording repair under E.8 and E.10.ARCH. They are not components or identity criteria of U.Ontic; a subject discovered directly through engineering work does not need them.

The defining ClaimGraph located at E.24 states the admission conditions for U.Ontic, and E.24 gives practical guidance for the decision. The ontology unit, its identity rule, selected direct relations, declarations, claim-bearing epistemes, publication occurrences and forms, carriers, views, and representations remain distinct. Self-use does not establish a U.MethodDescription; apply A.3.1 and A.3.2 only when a separate Method and MethodDescription claim matters.