canonicalMinimalHierarchy
plain-language theorem explainer
Packages the golden-ratio geometric scale ladder, already known to be closed under the first ledger composition step, as the canonical minimal hierarchy. Anyone proving uniqueness or scale agreement for minimal hierarchies cites this object as the reference instance. The body is a two-field structure instance: scales from the canonical φ sequence, closure from the matching closedness theorem.
Claim. The canonical minimal hierarchy is the geometric scale sequence with ratio $\varphi$ (the golden ratio), equipped with the proof that it is closed under the first non-trivial composition step of the discrete ledger.
background
In the Unified Forcing Chain, T0–T8 are derived as inevitabilities from the Recognition Composition Law plus normalization and calibration. T6 forces $\varphi$ as the self-similar fixed point of the discrete ledger; the hierarchy layer records what a minimal discrete scale ladder must look like once that fixed point is in hand.
A minimal hierarchy (from HierarchyMinimality) is a geometric scale sequence together with a minimal-closure witness: the ladder is closed under the first non-trivial composition step, which is exactly the Fibonacci relation. The canonical $\varphi$ scale sequence is the geometric ladder with ratio $\varphi>1$, and a companion theorem shows it satisfies that closure via $\varphi^2=\varphi+1$.
This definition simply names that pair as the reference minimal hierarchy against which every other minimal hierarchy is later compared.
proof idea
Pure structure assembly, not a tactic proof. The scales field is set to canonicalPhiScaleSequence (ratio $\varphi$, positivity and $\neq 1$ from the $\varphi$-forcing lemmas). The minimalClosure field is filled by canonicalPhiScaleSequence_closed, which unfolds geometric closedness and ledger composition and discharges the identity with $\varphi^2=\varphi+1$. No further reasoning occurs at this site.
why it matters
Gives the reference object for the canonicality story around T6. Downstream, minimalHierarchy_scale_eq_canonical proves every minimal hierarchy has the same scale values as this one (via the ratio-$\varphi$ lemma), and MinimalHierarchyCanonicality is the certificate structure whose fields are "ratio equals $\varphi$" and "scales agree with the canonical hierarchy." Without a named canonical instance, those uniqueness statements have nothing to compare against. In the forcing chain this is the concrete ladder that realizes the self-similar fixed point forced at T6, feeding the eight-tick and $D=3$ steps that sit above it.
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