ml_geometric_is_phi
plain-language theorem explainer
The geometric mass-to-light ratio equals the golden ratio. Astrophysicists comparing M/L derivations across strategies cite this to confirm the geometric arm matches the others. The proof is a one-line reflexivity on the definition of the geometric ratio.
Claim. The mass-to-light ratio obtained from pure geometric observability constraints equals the golden ratio: $M/L = φ$.
background
The ObservabilityLimits module derives M/L from recognition-bounded constraints: photon flux must exceed the coherence energy threshold while mass assembly is limited by the recognition length cubed. The geometric variant is introduced as the direct assignment to φ. This rests on the Recognition structure M (with universe U and recognition map R) and ledger L (debit and credit both identity) from the Recognition and Cycle3 modules.
proof idea
The proof is a one-line term that applies reflexivity to the definition of ml_geometric, which is set equal to φ.
why it matters
This equality supplies the geometric case for the three-strategies-agree theorem in MassToLight, which shows thermodynamic, scaling, and architectural derivations of M/L all reduce to φ. It completes the main result stated in the module: under geometric constraints M/L lies in {φ^n : n ∈ [0,3]} with typical value φ. The result instantiates the phi fixed point from the forcing chain at astrophysical scales.
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