phiRatioConfig
plain-language theorem explainer
Packages the integer power φ^n as a one-channel ledger configuration (a single positive ratio entry). Mass and generation-torsion arguments cite it to realize torsion exponents as ground-state configurations. The body is a thin wrapper around the generic ratio-to-configuration constructor, using positivity of φ.
Claim. For each integer $n$, define the one-channel configuration whose sole ledger entry is the positive real $\varphi^n$, where $\varphi$ is the golden-ratio fixed point of the Recognition self-similarity equation.
background
In the Generation Torsion Bridge module, charged-generation torsion ${0,11,17}$ is derived from $D=3$ cube combinatorics (passive edges and faces) and matched to every other torsion representation in the codebase. Configurations are finite tuples of positive real ledger ratios; the one-channel case is a single positive entry.
The upstream constructor takes any $r>0$ and builds a one-channel configuration with that entry. Here the entry is a power of $\varphi$, the self-similar fixed point forced in the T5–T6 segment of the unified forcing chain. Positivity of $\varphi$ supplies the required positivity certificate for every integer exponent.
The local setting upgrades hardcoded torsion numerals to an explicit structural premise (ground / passive-edge / face+edge coupling) with uniqueness, while leaving the coupling rule itself as a premise until it is derived from the Recognition Composition Law.
proof idea
Definitional wrapper only. Apply the one-channel ratio constructor to the real $\varphi^n$, discharging the positivity hypothesis by the standard fact that positive bases raised to integer powers remain positive (using $\varphi>0$). No further algebraic work.
why it matters
Feeds the ground-state compatibility predicate on torsion schedules: a schedule is ground-state compatible when its first-generation exponent, realized as this $\varphi$-power configuration, is a neutral equilibrium of the variational dynamics (equilibrium and vanishing log-charge). That predicate is the bridge from cube-geometric torsion to the mass-sector ground state.
In the broader RS picture, $\varphi$-ladder ratios are the native coordinates for mass rungs and generation structure; packaging $\varphi^n$ as a configuration lets torsion integers act inside the same variational language used for J-cost equilibria. The module still treats the generation-to-cube-feature assignment as a structural premise rather than an RCL consequence; this definition is the concrete carrier that makes that premise checkable.
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