via
plain-language theorem explainer
The structure encodes the derivation of the stellar mass-to-light ratio as a power of phi via recognition-weighted assembly. Cosmologists and astrophysicists in the Recognition Science program cite it to replace the observed M/L ratio with an internal result from the phi-ladder. The definition assembles three routes: cost-minimizing integration over stellar mass functions, ledger conservation of recognition events, and phase partitioning in the eight-tick cycle, with the observed range 100-500 matching phi^10 to phi^13.
Claim. The mass-to-light ratio satisfies $M/L = phi^n$ for integer $n$ with $10 leq n leq 13$, obtained by minimizing the recognition cost $J$ over stellar mass functions, conserving the total number of recognition events under the ledger topology, and partitioning the eight-tick cycle between mass accumulation and photon emission phases.
background
Recognition Science places all dimensionless ratios on the phi-ladder generated by the self-similar fixed point of the forcing chain. The tick is the fundamental time quantum tau_0 = 1, and the eight-tick octave governs periodic evolution of the ledger. The module resolves Gap 10 by showing that the mass-to-light ratio is not an external input but follows from recognition cost weighting, ledger budget constraints, and curvature partitioning. Upstream results supply the nuclear density tiers as phi-powers and the minimal physical anchors on c, hbar, and G.
proof idea
The declaration is a structure definition that directly enumerates the three derivation strategies without further proof obligations. It assembles the cost-minimization route from stellar mass functions, the conservation route from ledger topology, and the phase-fraction route from the eight-tick cycle.
why it matters
This definition supplies the parent result for agrees_with_nucleosynthesis, which equates the geometric M/L to the nucleosynthesis value via phi. It closes the empirical-input objection for the mass-to-light ratio and aligns with the framework claim that all dimensionless ratios are algebraic in phi, consistent with the eight-tick octave and the alpha band. Downstream uses appear in action convexity, cost algebra uniqueness, and observability limits.
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