ml_stellar_value
Stellar mass-to-light ratio equals the golden ratio φ under the Recognition Science derivation from cost differentials in stellar collapse. Researchers comparing M/L across assembly, nucleosynthesis, and geometric strategies cite this result to establish consistency. The proof is a one-line wrapper that unfolds ml_stellar as φ to the power of the characteristic tier scaffold (fixed at 1) and simplifies the exponent.
claimIn the Recognition Science model the stellar mass-to-light ratio satisfies $M/L = φ$, where $φ$ is the golden ratio fixed by the J-cost function and the eight-tick cycle.
background
The module derives M/L from the recognition cost differential between photon emission (cost J(r_emit)) and mass storage (cost J(r_store)) during stellar collapse. The convex cost is given by J(x) = ½(x + 1/x) - 1; the characteristic tier scaffold is the integer tier from the 5:3 partition of the eight-tick cycle and is set to 1. ml_stellar is therefore defined as φ raised to this tier, placing the ratio on the φ-ladder at n = 1.
proof idea
The proof is a one-line wrapper. It unfolds the definitions of ml_stellar and characteristic_tier_scaffold, then applies simp only [zpow_one] to reduce φ^1 to φ.
why it matters in Recognition Science
This supplies the stellar-assembly value M/L = φ used in MassToLight.three_strategies_agree to show the thermodynamic, scaling, and architectural derivations coincide. It likewise feeds NucleosynthesisTiers.strategies_agree and ObservabilityLimits.agrees_with_stellar_assembly. The result instantiates the module's main claim that stellar M/L lies on the φ-ladder with n ∈ [0,3] and aligns with T6 (φ as self-similar fixed point) and T7 (eight-tick octave).
scope and limits
- Does not derive the tier scaffold from ledger axioms without the 5:3 partition assumption.
- Does not compute M/L for specific stellar populations or metallicities.
- Does not address time evolution or initial-mass-function dependence.
Lean usage
rw [StellarAssembly.ml_stellar_value]formal statement (Lean)
162theorem ml_stellar_value : ml_stellar = φ := by
proof body
Term-mode proof.
163 unfold ml_stellar characteristic_tier_scaffold
164 simp only [zpow_one]
165
166/-- **CERT(definitional)**: Stellar M/L is a power of φ. -/