ml_derived_value
plain-language theorem explainer
The characteristic stellar mass-to-light ratio derived from Recognition Science equals the golden ratio φ. Researchers closing the astrophysical calibration chain cite this to confirm that no external parameters remain. The proof is a one-line reflexivity step that follows immediately from the definition of ml_derived.
Claim. The derived stellar mass-to-light ratio satisfies $M/L = φ$, where $φ = (1 + √5)/2$ is the golden ratio in solar units.
background
The MassToLight module unifies three independent derivations of the stellar mass-to-light ratio. StellarAssembly weights photon emission versus mass storage by J-cost minimization, yielding M/L = exp(Δδ / J_bit) = φ^n. NucleosynthesisTiers places nuclear densities and photon fluxes on discrete φ-tiers so that M/L = φ^{Δn}. ObservabilityLimits combines recognition wavelength, coherence time, and energy constraints with J-minimization to force M/L onto the φ-ladder. The upstream definition ml_derived sets this value to Constants.phi, and the theorem identifies the result explicitly as the conclusion of the chain.
proof idea
The proof is a one-line term-mode reflexivity that matches the left-hand side ml_derived directly to its defining expression Constants.phi.
why it matters
This theorem concludes the three-strategy derivation chain and supplies the key equality used by ml_derivation_complete, rs_zero_parameter_status, and ml_in_observed_range. It realizes the framework goal of deriving the astrophysical calibration M/L from the ledger structure, consistent with J-uniqueness and the phi fixed-point steps. The module notes that full agreement among the three strategies remains a hypothesis pending complete formalization of the component lemmas.
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