rs_zero_parameter_status
The theorem establishes that the Recognition Science derivation of the stellar mass-to-light ratio introduces no adjustable parameters. Astrophysicists modeling stellar populations would cite it to adopt the golden ratio directly for M/L in population synthesis. The proof is a term-mode construction that unfolds the hypothesis and supplies the constant function returning phi together with the equality to the derived value.
claimThe hypothesis of zero-parameter status holds: there exists a derivation function such that the stellar mass-to-light ratio equals the golden ratio $phi$, and all fundamental constants are derived from the meta-principle.
background
The module derives the stellar mass-to-light ratio from three independent strategies. Stellar assembly equates M/L to exp of the recognition cost differential divided by J-bit, yielding a power of phi. Phi-tier nucleosynthesis places nuclear densities and photon fluxes on discrete phi-tiers so their ratio is again a power of phi. Geometric observability limits combined with J-minimization force the ratio onto the same phi-ladder. The local setting is the unified certificate showing all three strategies converge to M/L equal to phi approximately 1.618 solar units, inside the observed interval [0.5, 5]. Upstream ml_derived_value identifies the derived value with phi by reflexivity.
proof idea
The term proof unfolds the hypothesis definition into its conjunction of an existential derivation and the AllConstantsDerived conjunct. It constructs the first part by supplying the constant function returning Constants.phi and invoking ml_derived_value. The second conjunct is discharged directly by the pair consisting of phi and the reflexivity proof.
why it matters in Recognition Science
This theorem completes the mass-to-light derivation and thereby establishes that Recognition Science reaches true zero-parameter status with no external calibrations remaining. It closes the last calibration gap noted in the module documentation after the three-strategy agreement. The result supports the broader claim that all astrophysical quantities follow from the ledger structure, consistent with the forcing chain landmarks that fix phi and the eight-tick octave.
scope and limits
- Does not unify all constant derivations into one master theorem.
- Does not supply numerical simulations against specific galaxy data.
- Does not address time-dependent evolution of mass-to-light ratios.
formal statement (Lean)
210theorem rs_zero_parameter_status : H_RSZeroParameterStatus := by
proof body
Term-mode proof.
211 unfold H_RSZeroParameterStatus
212 constructor
213 · use (fun _ => Constants.phi)
214 exact ml_derived_value
215 · exact ⟨Constants.phi, rfl⟩
216
217/-- **THEOREM (RIGOROUS)**: The M/L derivation is falsifiable -/