canonical_realized_closed_scale_admissible_orbit_bridge
plain-language theorem explainer
Given a closed observable framework and a realized closed-scale hierarchy model, the three bridge fields (admissible orbit, admissible-orbit normal form, and closed-scale normal-form equivalence) assemble into one package. Anyone citing the T5→T6 self-similarity route or the minimal closed-scale orbit bridge needs this packing. The proof is a pure structure constructor wiring three named lemmas.
Claim. For any closed observable framework $F$ and any realized closed-scale hierarchy model $H$ on $F$, the triple consisting of (i) the admissible-orbit reflection of $H$'s base state, (ii) the $\varphi$-uniform normal-form reflection of that admissible orbit, and (iii) the closed-scale normal-form equivalence of $H$, forms a single bridge package equating closed-scale realization with admissible-orbit normal form.
background
The module UnifiedForcingChain aims to force the full T-1 through T8 ladder from the Recognition Composition Law plus normalization and calibration. The local stretch here sits between T5 (unique cost $J$, equivalently the shifted $H(x)=J(x)+1=\frac12(x+x^{-1})$ satisfying d'Alembert) and T6 ($\varphi$ as the self-similar fixed point of the discrete ledger).
A closed observable framework supplies a state space, a transition, and a positive ratio observable with nontrivial range and no external input (finite description, conserved charge). A realized closed-scale model is a hierarchy realization of that framework whose scales form a geometric ladder closed under the first nontrivial composition step; minimality of such hierarchies is recorded by MinimalHierarchy (Fibonacci-type closure).
The structure being inhabited packages three views of the same data: admissible-orbit reflection of the base state, the $\varphi$-uniform normal form of that orbit, and the closed-scale normal-form equivalence. Doc-comment: "Closed-scale realization, admissible-orbit reflection, and $\varphi$-uniform normal form are the same bridge package."
proof idea
Term-mode structure constructor, not a tactic script. The admissible field is filled by admissibleOrbitReflection_of_realizedClosedScale F H, which extracts admissible-orbit data from the realized closed-scale model. The admissible_reflection field applies canonical_admissible_orbit_normal_form_reflection to that same admissible orbit, producing the $\varphi$-uniform normal-form reflection. The closed_scale_equivalence field is the already-proved canonical_realized_closed_scale_normal_form_equivalence F H. No new algebra is done here; the theorem only packages the three prior lemmas into the bridge Prop.
why it matters
This packing is the hinge that lets closed-scale realization feed the $\varphi$-forcing route. Downstream, canonical_minimal_closed_scale_orbit_bridge lifts minimal closed-scale orbit data into the same normal-form path, and t5_to_t6_bridge_holds cites the realized-closed-scale normal-form equivalence as one of the legs of the T5→T6 self-similarity bridge ("The T5-to-T6 self-similarity bridge is theorem-backed").
In the forcing chain this is the concrete link from unique $J$ (T5) into self-similarity that pins $\varphi$ (T6). Without a single Prop that identifies closed-scale realization with admissible-orbit normal form, the later hierarchy-dynamics bridges would have to reassemble those fields ad hoc. The declaration closes that interface inside the Complete Inevitability Chain rather than leaving a compatibility gap.
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