canonical_minimal_hierarchy_canonicality

The Unified Forcing Chain module shows that T0 through T8 are forced from the cost foundation (Recognition Composition Law with normalization and calibration). T5 pins the unique cost $J(x)=(x+x^{-1})/2-1$; T6 forces $\varphi$ as the self-similar fixed point of the discrete ledger.

A minimal hierarchy is a geometric scale sequence closed under the first non-trivial composition step (the Fibonacci-type closure). Canonicality for such an $H$ is the pair of statements that its ratio equals $\varphi$ and that its scale function agrees with a fixed canonical minimal hierarchy at every rung.

Upstream, the shifted cost $H(x)=J(x)+1$ converts RCL into d'Alembert form, and geometric scales of the form $\varphi^k$ appear as the natural discrete ladder once self-similarity is in force.

Term-mode construction of the MinimalHierarchyCanonicality certificate. The ratio_eq field is filled by minimalHierarchy_ratio_eq_phi H; the scale_eq field by minimalHierarchy_scale_eq_canonical H. No further tactics: the theorem is the packaging of those two prior equalities into the Prop structure.

This certificate is consumed by t5_to_t6_bridge_holds, which asserts that the T5-to-T6 self-similarity bridge is theorem-backed: uniqueness of $J$ plus internal hierarchy dynamics and realized closed-scale normal form force $\varphi$. In the forcing chain, T6 is exactly "$\varphi$ forced as the self-similar fixed point"; showing every minimal hierarchy is the canonical $\varphi$-ladder removes free scale choice between unique cost and the discrete self-similar rung structure. It sits inside the Complete Inevitability Chain claim that every level from absolute floor through D=3 is forced, not merely compatible.