canonical_minimal_closed_scale_orbit_bridge
plain-language theorem explainer
Any minimal closed-scale orbit in a closed observable framework carries a full bridge into the φ-uniform normal-form package: realized closed-scale equivalence, admissible orbit reflection, and the closed-scale/admissible link. Hierarchy and T5–T6 authors cite it when routing orbit data into the self-similarity forcing path. The proof is a short term assembly of four canonical constructors from the orbit.
Claim. Let $F$ be a closed observable framework and let $O$ be a minimal closed-scale orbit in $F$ (positive amplitude, base state, and a minimal geometric hierarchy realized by the ratio observables along the orbit). Then $O$ determines a bridge certificate: the induced realized closed-scale model is equivalent to the $\varphi$-uniform normal form; the orbit yields an admissible orbit reflection in normal form; and the realized closed-scale and admissible-orbit sides are linked by the canonical bridge.
background
The module UnifiedForcingChain aims at a complete inevitability chain T-1 through T8 from the Recognition Composition Law plus normalization and calibration. T5 pins the unique cost $J$; T6 forces $\varphi$ as the self-similar fixed point of the discrete ledger hierarchy.
A closed observable framework supplies a state space $S$, dynamics $T$, and positive ratio observables $r$ with nontriviality and closure (no external input, finite description). A minimal closed-scale orbit packages a base state, positive amplitude, and a MinimalHierarchy so that $r(T^k(\mathrm{base})) = \mathrm{amplitude}\cdot\mathrm{scale}(k)$ for every $k$. Growth and closedness are derived from hierarchy minimality rather than listed as separate fields.
The bridge structure bundles four certificates: realized closed-scale normal-form equivalence, admissible orbit data, admissible normal-form reflection, and the closed-scale/admissible link. That package is the φ-uniform route used later when self-similarity forces $\varphi$.
proof idea
Term-mode structure construction, not a tactic script. From the minimal orbit $O$ one builds the realized closed-scale model via realizedClosedScaleModel_of_minimalOrbit, then feeds it to canonical_realized_closed_scale_normal_form_equivalence for the first field. Admissible data come from admissibleOrbitReflection_of_minimalClosedScaleOrbit; that reflection is passed to canonical_admissible_orbit_normal_form_reflection. The last field applies canonical_realized_closed_scale_admissible_orbit_bridge to the same realized model. No new arithmetic: pure wiring of existing canonical maps.
why it matters
This sits on the T5→T6 self-similarity bridge inside the forcing chain. Downstream, t5_to_t6_bridge_holds consumes realized-closed-scale normal-form equivalence among other hierarchy bridges to certify that unique $J$ plus internal hierarchy forces $\varphi$. The sibling canonical_minimal_orbit_realization_bridge routes fixed-data realizations into the same minimal-orbit path, so this theorem is the orbit-side half of that pair.
In framework terms it is the concrete link from geometric hierarchy data (closed scales on an orbit) into the φ-uniform normal form that T6 needs. Without it, minimal orbits would not automatically inherit the admissible and normal-form certificates required by the self-similarity step. It does not itself prove uniqueness of $J$ or pin $\varphi$; it only packages orbit data for those later theorems.
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