canonicalMinimalOrbitFramework_bridge
plain-language theorem explainer
For positive amplitude and a minimal discrete hierarchy, the canonical closed framework on ℕ projects into the full minimal-orbit realization bridge. Downstream unit-amplitude and T5→T6 self-similarity bridges cite it. The proof is a one-line term application of the general canonical realization bridge at base state 0.
Claim. Let $a > 0$ be a real amplitude and let $H$ be a minimal discrete hierarchy (geometric scale ladder closed under the first nontrivial composition). Then the canonical closed observable framework on $\mathbb{N}$ carrying the minimal orbit, together with its definitional realization along the orbit from base state $0$, satisfies the minimal-orbit realization bridge: the fixed-data realization is unique, projects to the minimal closed-scale orbit, and agrees with the canonical sequence-level orbit.
background
The Unified Forcing Chain module shows T0–T8 as inevitabilities from the Recognition Composition Law plus normalization and calibration. The stretch relevant here is the passage from unique cost $J$ (T5) to the forced golden ratio $\varphi$ via self-similarity on a discrete ledger (T6).
A MinimalHierarchy is a geometric scale ladder closed under the first nontrivial composition step (Fibonacci-type closure). The canonical minimal-orbit framework is the closed observable framework whose state space is $\mathbb{N}$, carrying that hierarchy at a fixed positive amplitude. A minimal-orbit realization asserts that the framework realizes its target sequence along an orbit from a chosen base state.
The bridge certificate packages three agreements: uniqueness of the fixed-data realization, projection onto the minimal closed-scale orbit, and match with the canonical sequence-level orbit. Upstream, the canonical framework already has a definitional realization from base $0$; the general bridge lemma lifts any such realization into the certificate.
proof idea
One-line term wrapper. Instantiate the general canonical bridge lemma at the canonical minimal-orbit framework, base state $0$, the given positive amplitude, the minimal hierarchy, and the already-proved definitional realization of that framework. No extra algebraic work: the certificate fields are discharged by the general lemma once those data are supplied.
why it matters
This is the specialization that pins the countable canonical framework into the bridge interface used by the forcing chain. It feeds the unit-amplitude bridge (amplitude $1$), which is the normal form for hierarchy dynamics, and is consumed by t5_to_t6_bridge_holds, whose doc states that the T5-to-T6 self-similarity bridge is theorem-backed via realized closed-scale forcing of $\varphi$.
In primer terms this sits on the T5→T6 link: unique $J(x)=(x+x^{-1})/2-1$ plus a realized minimal closed scale orbit forces the self-similar fixed point $\varphi$. Without the bridge certificate, the canonical orbit on $\mathbb{N}$ would not be wired into the hierarchy-dynamics lemmas that close T6.
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