FPF Reference

E.18::5.1 - S1 - Graph object (conceptual)

Preface node heading:e-18-5-1-s1-graph-object-conceptual:46183

Content

Define a typed, editioned, directed multigraph TransductionGraph := (V, E, τ_V, τ_E, Γ_time, Bridge, CL, TransportRegistry^Φ) with:

  • Vertices V: instances of U.Morphism (open world). Common specialisations include but are not limited to the assignment’s set: U.FormalSubstrate, U.PrincipleFrame, U.Mechanism, U.ContextNormalization (UNM), U.SelectionAndTuning, U.WorkPlanning, U.Work, U.EvaluatingAndRefreshing. This list is illustrative, not exhaustive—the graph does not depend on this particular set.
  • Edges E: a single edge kind U.Transfer (typed) carrying artifacts/tokens; all plane/Context/edition changes occur only at nodes via OperationalGate(profile) with Bridge + CL annotations; penalties → R only. Transport conversions pin Φ‑policies and editions.
  • Scopes: Γ_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 (normative): • L := Locus — an element of a partially ordered ContextSlice poset; addresses where claims apply (disciplinary / organizational / holonic slice). • P := ReferencePlane — the reference plane/units registry id; no plane/unit declarations or translations occur in CV; crossings remain gated (A.21). • E⃗ := Edition vector — a partial map edition_key ↦ EditionId over named families {CG‑Spec, ComparatorSet, UNM.TransportRegistryΦ} and optional {DescriptorMapRef, DistanceDefRef, CharacteristicSpaceRef} when cited. • D := DesignRunTag — design(T^D) or run(T^R), used by LaunchGate and acceptance/telemetry duties. Invariants. Raw U.Transfer preserves CtxState (⟨L,P,E⃗,D⟩): it does not write/update any CtxState slot; any CtxState write/update (or entry to U.WorkEnactment) occurs at OperationalGate(profile). Extension discipline. Any extra slot beyond ⟨L,P,E⃗,D⟩ SHALL be registered in the E.17/LEX “CtxState Extension Registry” with slot‑id, intent, partial‑order law (neutral/absorbing), and SquareLaw compatibility; unregistered extensions are non‑conformant. Data‑shape location. Concrete record shapes for PathId/PathSliceId, Γ‑pins, and lineage remain in A.22 FlowSpec; E.TGA fixes that flow = valuation and that CtxState is preserved across raw transfers.

  • Kinds: U.Transduction(kind∈{Signature, Mechanism, Work, Check, StructuralReinterpretation}).
    Exact identification (no TGA‑local taxonomy):
    — Signature ≡ A.6.0 U.Signature (universal, law‑governed declaration).
    — Mechanism ≡ A.6.1 U.Mechanism (law‑governed application over a SubjectKind/BaseType).
    — Work ≡ A.15 U.WorkEnactment (world‑contact; FinalizeLaunchValues only here).
    — Check ≡ OperationalGate(profile) (universal gate; A.* patternisation pending; CC‑TGA catalog applies).
    — StructuralReinterpretation ≡ a species of A.6.4 U.EpistemicRetargeting used as a graph node in E.TGA. All retargeting semantics (slot‑level discipline, DescribedEntitySlot/GroundingHolonSlot behaviour, invariants, Bridges, witnesses) come from C.2.1 and A.6.2–A.6.5; E.TGA does not introduce a TGA‑local variant of retargeting.
    OperationalGate ≔ U.Transduction(kind=Check) with DecisionLog aggregation.
    The only extra discipline E.TGA adds for StructuralReinterpretation is graph‑local: CtxState and GateCrossing behaviour are governed by CC‑TGA‑06‑EX and CC‑TGA‑11 (projection‑preserving w.r.t. ⟨L,P,E⃗,D⟩, PathSlice‑local, and “no plane/unit change without a gate”).

MVPK integration (import). Every vertex with an external surface is published via MVPK faces (PlainView, TechCard, AssuranceLane, InteropCard) under a declared PublicationScope (E.17). E.TGA reuses MVPK’s publication laws (pins, lawful‑order discipline, “no new numeric claims / no I/O re‑listing”) and only adds graph‑level constraints in S3 and CC‑TGA‑09/10; it does not define a second, local publication semantics.

GateCrossing (normative) Definition. A GateCrossing is the typed transition at a node that writes/updates any of: (i) U.BoundedContext (Context), (ii) ReferencePlane, (iii) any member of the Edition vector E⃗ (e.g., CG‑Spec, ComparatorSet, UNM.TransportRegistryΦ, DescriptorMapRef, DistanceDefRef, CharacteristicSpaceRef), (iv) DesignRunTag (T^D↔T^R), or (v) Kind/describedEntity (only under StructuralReinterpretation subject to CC‑TGA‑06‑EX). Invariants. Raw U.Transfer preserves CtxState; a GateCrossing occurs at exactly one OperationalGate(profile) (SquareLaw applies). Required pins (minimum). BridgeCard + UTS row; CL for scope bridges; CL^plane for plane crossings; CL^k with bridgeChannel=Kind for kind transitions; PublicationScopeId; PathSliceId; Γ‑pins on compare/launch faces. Canonical reference. CrossingRef := ⟨GateId, channel, from, to, UTS.RowId, PathSliceId⟩. Any DecisionLog entry whose rationale depends on a crossing SHALL cite CrossingRef. CrossingBundle (normative) Definition. A CrossingBundle is the published bundle that makes a GateCrossing auditable and replayable (crossing visibility). It includes:

  • the canonical CrossingRef;
  • the matching UTS row (UTS.RowId) for the crossing;
  • the required pins PublicationScopeId and PathSliceId;
  • where a Bridge is involved: the BridgeCard (F.9) and its disclosed fields (BridgeId, bridgeChannel, CL and loss notes; CL^k when bridgeChannel=Kind; ReferencePlane(src,tgt));
  • where planes differ: CL^plane and the active Φ_plane as a PolicyIdRef (policy-id + resolvable refs; F.8:8.1);
  • the active penalty policy identifiers Φ(CL) (and Ψ(CL^k) if used) as PolicyIdRef bundles (policy-id + PolicySpecRef + MintDecisionRef?; F.8:8.1);
  • any additional pins mandated by the active GateProfile / GateChecks (A.21) for this crossing.

Obligation. Every GateCrossing MUST publish its CrossingBundle. Missing or non‑conformant CrossingBundle is a blocking defect for downstream consumption (selectors, acceptance, audits).

Term separation. Transfer denotes the sole edge kind U.Transfer (graph edges). Transport denotes Φ‑governed conversion policies/registries (TransportRegistry^Φ under UNM). Wording “reuse via Transport” refers to registries/policies, not to an additional graph edge.