ml_geometric
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.
claimThe 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 in Recognition Science
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.
scope and limits
- Does not derive φ from the forcing chain or Recognition Composition Law.
- Does not incorporate explicit stellar-assembly or nucleosynthesis equations.
- Does not specify units, numerical bounds, or conversion to solar values.
- Does not address redshift or distance-dependent observability corrections.
formal statement (Lean)
115noncomputable def ml_geometric : ℝ := φ
proof body
Definition body.
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