E.18:5.1 - S1 - Selected Structure (conceptual)

Define a typed, editioned transformation-flow structure TransformationFlowStructure := (Loci, Transfer, tau_L, tau_Transfer, Gamma_time, CrossingRefs, TransportRegistryRefs) with:

• Loci: structure positions or bindings to independently defined or constrained FPF values (open world). Common specialisations include but are not limited to one first-principles P2W example: an independently identified actual bounded U.Transformation, U.Signature(profile=FormalSubstrate), U.PrincipleFrame, U.Mechanism, U.ContextNormalization (UNM), a selector relation that satisfies the current selector and comparator definitions or tests, one exact A.15.2 U.WorkPlan optionally carrying declaration-local A.15.3 planned-filling rows, one exact Work individual admitted under U.Work, and current evaluation or currentness relations. This list is illustrative, not exhaustive, and none of its entries is mandatory for general P2W. A structure position may be expressed by a morphism, graph vertex, tuple position, or category-theoretic object under a mathematical lens when that lens is current, but E.18 does not make every position a U.Morphism, graph vertex, or U.Transformation. Selection into the same structure, path adjacency, shared work, or a common affected referent supplies neither the A.3.4 actuality basis nor the facts, predicate, and identity rule needed for a transformation-composition claim.
• Transfer relation: a single relation kind U.Transfer (typed) carrying carrier refs and token refs inside one selected TFS. Raw transfer preserves CtxState. Every actual change to a locality, plane, edition, or design/run binding is represented by one GateCrossing at an OperationalGate(profile) and has one local per-binding account that separates from/to values, establishing facts or claims, applicable declarations or rules, and current applications. An A.6.4 arrow r, an affirmative bounded-use assertion q, and a current-case judgement of satisfies, with unchanged CtxState, follow the limited StructuralReinterpretation route in CC-E18-06-EX instead of becoming a crossing. Transport conversions cite the exact registry entry, conversion rule, and applicable policy. E.18 defines neither a generic semantic Bridge nor a generic penalty policy.
• Scopes: Gamma_time (budgets, horizons), PublicationScope for faces (E.17), and slice ids for refresh (G.11).

CtxState (PS‑projection; closed slots): CtxState = ⟨L, P, E⃗, D⟩ is the projection of E.17 Publication Scope. Slot definitions and changed-binding account boundary (normative):

• L := Locus — one exact U.ContextSlice value identified under A.2.6; any scope-membership or translated-scope claim remains with A.2.6 and its current F.9/C.2.1/A.10-or-B.3 premises when semantic translation is actually required.
• P := ReferencePlane — a ref-only binding to the exact plane and units declaration used by the current case. E.18 supplies no generic plane conversion. Cite the current declaration and applicable conversion rule by value. Return missing-governor only when no current conversion predicate or rule can state the attempted crossing; return missing-information when the needed declaration or case values are unavailable; when the rule and facts are current, state its positive, negative, or inapplicable result rather than a generic blocker.
• E⃗ := Edition vector — a partial map edition_key ↦ EditionId whose members cite each versioned value, its exact edition, and the registry or declaration that assigns that edition; G.11 defines the edition-bump and refresh records, while E.17 defines publication of the refs.
• D := DesignRunTag — design(T^D) or run(T^R) only as consumed by the exact A.21 gate and, at work entry, the A.15.5 readiness claim; the tag does not identify or create Work. Invariants. Raw U.Transfer preserves CtxState (⟨L,P,E⃗,D⟩): it does not write or update any CtxState slot; any CtxState write or update, including a design-to-run tag change for a pre-run work-entry claim, occurs at OperationalGate(profile). The gate changes the claim or decision state, not the ontic identity of a Work occurrence or any independently obtaining relation involving it. Extension discipline. A conforming use registers any extra slot beyond ⟨L,P,E⃗,D⟩ in the E.17 publication discipline and the E.18 LEX “CtxState Extension Registry” with slot‑id, intent, partial‑order rule (neutral or absorbing), and SquareLaw compatibility; unregistered extensions are non‑conformant. Data-shape location. E.18 names the structure and valuation obligations for PathId, PathSliceId, Gamma pins, and lineage: flow is a valuation over U.Transfer, raw transfer preserves CtxState, and E.18 carries the path or slice evidence. Add A.20 only for a current internal-constraint claim, G.6 for evidence-provenance path visibility, and G.11 for refresh wiring. These are the current structure loci for path and slice currentness.

• Locus kinds: Transformation, Signature, Mechanism, WorkPlanning, Work, Check, and StructuralReinterpretation are the current minimal structure-positioned locus baseline. Domain-specific species are open-world and non-exhaustive, but each species binds to one of the locus kinds or requires an explicit E.18 update. These are positioned loci in the selected structure, not a local taxonomy of new FPF kinds. Exact identification (no local ontology):

• Transformation ≡ A.3.4 U.Transformation only when the structure locus binds one independently identified actual bounded change with its exact changed referent, extent or ordering boundary, boundary conditions, actual change facts, and continuity or reidentification rule. Desired, intended, planned, modeled, selected, described, evaluated, published, or transferred change content remains under the definition or test for that exact claim; it is not a Transformation binding merely because it occupies the selected structure. Current-resolution identification establishes neither finer parts nor partlessness. A positive transformation-composition, TransformationPartOfRelation, composite-transformation identity, or transformation-holonhood claim stops under D14.16 with the exact A.6.RCD result: TC-MWH missing-governor only when no current predicate, applicability condition, or occurrence rule states the required contribution, compatibility, parthood, or whole-identity claim; TC-MWH factually unsupported when the governor exists and the available case basis is sufficient to apply its positive test but that test fails; and TC-MWH missing-information when a fact needed to decide the test is unavailable. A negative needs its own applicable non-obtaining criterion or complete closure basis and satisfying facts. E.18 retains the independently identified transformations and supplies no provisional contribution, compatibility, parthood, or whole-change architecture; it does not preselect whether a later settlement uses a generic derived relation, subject-specific relations, local compound claims, or non-admission.
• Signature ≡ A.6.0 U.Signature (universal, law-governed declaration).
• Mechanism ≡ A.6.1 U.Mechanism (law-governed application over a SubjectKind and RangedValueKind), with placement and stabilization relations in E.20 when current.
• WorkPlanning ≡ one exact A.15.2 U.WorkPlan when that plan occupies the structure position. Declaration-local A.15.3 SlotFillingsPlanItem rows remain content inside that WorkPlan and do not occupy a locus or identify a relation independently.
• Work ≡ an exact dated Work individual admitted under A.15.1 U.Work. A structure locus may point to that occurrence after it exists; before execution it points only to a U.WorkPlan, A.15.5 readiness relation, or another exact work-entry claim. No second enactment kind is introduced.
• Check ≡ OperationalGate(profile) when a gate/check locus is present. A.20 supplies exact internal-constraint results when those constraints are current; A.21 defines the gate profile, independent check retention, result mapping, aggregate decision, and publication minima when a gate decision is current.
• StructuralReinterpretation is only the E.18 position of an independently identified A.6.4 arrow r, bounded-use assertion q, and current-case judgement; it is not a new retargeting kind. E.18 records r and q, the exact case basis and judgement result needed by this placement, and path-slice locality. q’s ClaimGraph carries the invariant, visible loss, named receiving use, conditions, and affirmative or negative polarity; the judgement separately reports satisfies, fails, or cannot decide. A cannot decide result names the exact missing fact and reopen condition. F.9 is additional only when the same case asserts a semantic relation between two exact F.17 local senses and its predicate obtains; its bounded-use claim, optional CL, evidence, and reliance remain separate. OperationalGate is the E.18 check locus when a gate or check position is present. A.20 supplies an exact internal-constraint result when that claim is current. When a gate decision is current, A.21 supplies the exact profile application, independently identified check-application results, GateDecisionResult, and rationale. A DecisionLog is added only for a current audit, history, replay, or reuse need. E.18 adds only a structure-local placement rule: when r, an affirmative q, and a current-case judgement of satisfies are current and CtxState is unchanged, record their basis and PathSliceId without calling the placement a GateCrossing. If any CtxState binding changes, use a GateCrossing and state the changed binding’s from/to values, establishing basis, and any applicable declaration, rule, and current application. A Bridge, card, UTS row, optional CL, witness publication, gate decision, or permission claim neither identifies r nor supplies q’s polarity or the case judgement.

MVPK integration (import). Every locus with an external publication face is published via MVPK faces (PlainView, TechCard, AssuranceLane, InteropCard) under a declared PublicationScope (E.17). E.18 reuses MVPK’s source-reference, pin, declared-order, and no-new-claim rules. Input/output non-duplication and functorial publication apply within E.17’s optional morphism profile. E.18 adds the structure-scope constraints in S3 and CC-E18-09 and CC-E18-10; it does not define a second publication semantics.

GateCrossing (normative)

Definition. A GateCrossing is E.18’s structure-local transition from one exact <FlowPositionRef, CtxState> binding to another at one exact OperationalGate(profile). It is selected only when at least one CtxState binding changes. It is not a U.Relation, an F.9 Bridge, a gate decision, a plane conversion, an A.6.4 arrow or use assertion, a penalty, or a publication occurrence.

Per-binding account. For an ordinary local crossing, one sentence or table row is enough: name the changed binding, its from and to values, the facts or claims that establish those values for this case, and any declaration or rule whose application is current. No record is required. When a named downstream use needs replay, the same distinctions may be packaged in this local E.18 block:

ChangedBindingAccount:  # local replay block, not an FPF kind or relation
  changedBindingId
  fromValueRef
  toValueRef
  establishingFactRefs[]?
  establishingClaimEpistemeRefs[]?
  applicableDeclarationRefs[]?
  applicableRuleRefs[]?
  ruleApplicationRefs[]?
  honestStop?

Facts or claims establish the case values. A declaration or rule supplies only the meaning, admissibility condition, or constraint it actually states; ruleApplicationRefs is present only when the current case depends on that rule applying to these values. A gate decision evaluates the crossing under A.21 and does not establish the underlying facts or apply a rule by itself. A permission claim is separate under A.2.8.PER and is cited only when authorization is current. None of those items entails another.

A.20 may supply an exact current constraint-validity result and witness or reason; A.21 supplies the gate profile, retained check results, mapping, aggregate decision, and decision log. Neither supplies a changed locality, plane, edition, tag, retargeting fact, rule application, or permission claim.

Canonical reference. CrossingRef := ⟨TFSRef, GateId, FromPositionRef, ToPositionRef, FromCtxStateRef, ToCtxStateRef, ChangedBindingIds, PathSliceId⟩. A DecisionLog or downstream use that depends on the crossing cites this ref and the required per-binding accounts.

CrossingBundle publication block. Materialize a CrossingBundle only when a named selector, acceptance, audit, replay, or other downstream use relies on durable crossing evidence. The bundle is publication packaging under E.17, not a constituent of the crossing or gate decision. It contains the CrossingRef, ChangedBindingAccountRefs[], GateId, the current profileApplicationRef and GateDecisionResultRef when a gate decision exists, an optional current DecisionLogRef, optional separately current PermissionClaimEpistemeRefs[], PublicationScopeId, PathSliceId, and any current witness refs. When that downstream use also relies on cross-semantic correspondence, add a separate F.9 block: the two exact SchemeSenseCell endpoints, the obtaining Bridge and its exact profile, the C.2.1 claim that says whether the Bridge suits this named structural use in the named direction under its rule and tolerance, and the current A.10 or B.3 reliance branch if reliance is claimed. A Bridge Card remains optional packaging and CL remains optional evidence shorthand; neither makes the structural crossing obtain, makes the gate pass, or grants the use.

A penalty appears only when one exact current policy applies to this crossing and its rule application to the crossing facts supports that penalty. Cite the policy and PolicyIdRef; when the claim also depends on who may issue or enforce it, cite the separately obtaining direct authority relation and its actual participants. E.18 derives no penalty from CL, plane difference, edition difference, or Bridge publication. If the policy, applicability, rule application, or any separately required authority fact is absent, make no penalty claim and infer no default.

Term separation. Transfer denotes the sole relation kind U.Transfer in the selected structure. Transport denotes Phi-governed conversion policies and registries (TransportRegistry^Phi under UNM). Wording “reuse via Transport” refers to registries and policies, not to an additional transfer relation.