ml_geometric
plain-language theorem explainer
The geometric mass-to-light ratio is defined as the golden ratio φ. Astrophysicists comparing Recognition Science derivations cite it to close the third independent route via observability constraints. The definition is a direct one-line assignment with no further reduction.
Claim. The mass-to-light ratio obtained from geometric observability constraints (recognition length, coherence energy per tick, and J-cost minimization) equals the golden ratio $φ$.
background
This module develops Strategy 3 for the stellar mass-to-light ratio. Observable flux must exceed the recognition threshold $F_θ ≈ E_coh / τ_0$, while mass is assembled inside coherence volumes $V ≈ l_rec^3$. The total J-cost $J_total = J_mass(M) + J_light(L)$ is minimized subject to these bounds, forcing the ratio into the set of φ-powers. The definition supplies the pure-geometry case that must match the stellar-assembly and nucleosynthesis routes.
proof idea
Direct definition that assigns the constant φ to the geometric mass-to-light ratio.
why it matters
The definition supplies the geometric leg required by the hypothesis that all three M/L strategies converge and by the theorem that the derived value equals φ. It realizes the module claim that M/L lies in {φ^n : n ∈ [0,3]} with typical value φ, thereby closing the observability-constrained derivation inside the Recognition Science framework.
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