H_ThreeStrategiesAgree
The definition asserts that the mass-to-light ratios from stellar assembly, nucleosynthesis tiers, and geometric observability all coincide with the derived value. Researchers closing the astrophysical calibration loop in Recognition Science would cite it to confirm convergence on the golden ratio. It is realized as the direct conjunction of the three strategy-specific equalities.
claimThe proposition that the stellar-assembly mass-to-light ratio equals the nucleosynthesis-derived ratio, which equals the geometric-observability ratio, which equals the derived mass-to-light ratio.
background
The Mass-to-Light module derives the stellar mass-to-light ratio from Recognition Science without external calibration. StellarAssembly.ml_stellar obtains it via J-cost weighting of photon emission versus mass storage. NucleosynthesisTiers.ml_nucleosynthesis places nuclear densities and photon fluxes on discrete phi-tiers. ObservabilityLimits.ml_geometric enforces constraints from recognition wavelength, coherence time, and energy. The upstream ml_derived identifies the common outcome with Constants.phi.
proof idea
The definition is the conjunction of three equalities between the strategy-specific functions and ml_derived. Each upstream definition evaluates to Constants.phi, so the conjunction holds once those definitions are supplied.
why it matters in Recognition Science
This definition supplies the hypothesis discharged by the theorem three_strategies_agree. It completes the mass-to-light derivation and supports the claim of true zero-parameter status, with all astrophysical inputs now obtained from the ledger and phi-ladder structure.
scope and limits
- Does not prove the individual derivations inside each strategy module.
- Does not compute numerical values for specific stellar populations.
- Does not incorporate observational error bars on measured M/L ratios.
Lean usage
theorem three_strategies_agree : H_ThreeStrategiesAgree := by unfold H_ThreeStrategiesAgree; refine ⟨?_, ?_, ?_⟩formal statement (Lean)
94def H_ThreeStrategiesAgree : Prop :=
proof body
Definition body.
95 StellarAssembly.ml_stellar = NucleosynthesisTiers.ml_nucleosynthesis ∧
96 NucleosynthesisTiers.ml_nucleosynthesis = ObservabilityLimits.ml_geometric ∧
97 ObservabilityLimits.ml_geometric = ml_derived
98
99/-- **THEOREM (PROVED): Consistency of M/L Strategies**
100 The thermodynamic, scaling, and architectural derivations agree. -/