three_strategies_agree
plain-language theorem explainer
The theorem establishes that the stellar mass-to-light ratio derived via recognition cost weighting in stellar assembly equals the value from phi-tier nucleosynthesis and also equals the value from geometric observability limits, with all three coinciding on the golden ratio phi. Researchers closing the astrophysical calibration loop in Recognition Science would cite this result to confirm internal consistency. The proof is a term-mode construction that unfolds the target conjunction and rewrites each leg using the equality lemmas supplied by 1
Claim. Let $M/L_1$, $M/L_2$, $M/L_3$, and $M/L$ denote the mass-to-light ratios obtained from stellar assembly via J-cost weighting, from nucleosynthesis via phi-tier differences, from geometric observability constraints, and from the overall derivation, respectively. Then $M/L_1 = M/L_2 = M/L_3 = M/L = phi$, where $phi$ is the golden ratio.
background
The Mass-to-Light module derives the stellar mass-to-light ratio in three independent ways. Stellar assembly equates the ratio to phi^n via recognition cost differentials between photon emission and mass storage. Nucleosynthesis tiers equate it to phi to the power of the difference in nuclear and photon tiers. Geometric observability limits force the ratio onto the phi-ladder using constraints from recognition wavelength, coherence time, and energy. The hypothesis H_ThreeStrategiesAgree asserts that these three quantities coincide with the derived value, which is defined as the golden ratio phi. Upstream, ml_derived_value identifies the derived value with phi by reflexivity, while the strategy modules supply the individual equalities to phi.
proof idea
The proof unfolds the conjunction hypothesis into its three conjuncts. It then constructs each equality separately by rewriting with the strategy-specific theorems (stellar assembly equality, nucleosynthesis equality to phi, geometric equality to phi, and the derived-value reflexivity) and applying simplification to equate the phi symbols across modules.
why it matters
This theorem supplies the consistency proof required by ml_derivation_complete, which assembles the full M/L derivation certificate depending on ml_derived_value and three_strategies_agree. It also supports ml_in_observed_range. In the framework it realizes the module's main result that all astrophysical calibrations are derived from the ledger structure, achieving true zero-parameter status together with the derived constants c, hbar, G, and alpha inverse. It closes the loop on phi-ladder derivations originating from the self-similar fixed point.
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