ml_stellar
Stellar mass-to-light ratio is defined as φ raised to the characteristic tier scaffold. Researchers assembling M/L derivations from recognition cost differentials cite this value when verifying consistency across stellar assembly, nucleosynthesis, and geometric strategies. The definition is realized as a direct one-line assignment that pulls the tier integer from the 5:3 partition of the eight-tick cycle.
claimThe stellar mass-to-light ratio in solar units is given by $M/L = φ^k$ where the integer exponent $k=1$ is the characteristic tier fixed by the recognition-weighted collapse model.
background
The module derives M/L from the recognition cost differential between photon emission (cost δ_emit = J(r_emit)) and mass storage (cost δ_store = J(r_store)) during stellar collapse. Equilibrium occurs when the ratio M/L minimizes total ledger cost under the convex cost function J(x) = ½(x + 1/x) - 1. When the differential equals n · J_bit = n · ln φ, the ratio lands on the φ-ladder as M/L = φ^n with n fixed by the eight-tick structure, yielding the interval {φ^n : n ∈ [0,3]} and the typical value φ^1 ≈ 1.618 solar units.
proof idea
This is a direct definition that sets ml_stellar to φ raised to the characteristic tier scaffold. The tier itself is supplied by the upstream constant characteristic_tier_scaffold := 1, which encodes the 5:3 partition of the eight-tick cycle.
why it matters in Recognition Science
The definition supplies the concrete value for Strategy 1 inside the three-strategies agreement hypothesis H_ThreeStrategiesAgree. It is invoked by ml_derivation_complete to establish ml_stellar = ml_derived = φ and by the agreement theorems in NucleosynthesisTiers and ObservabilityLimits. The construction rests on the eight-tick octave (T7) and the self-similar fixed point φ (T6) from the forcing chain.
scope and limits
- Does not derive the tier exponent from first principles inside this module.
- Does not incorporate observational error bars or selection effects.
- Does not address non-stellar contributions such as dark matter to the total M/L.
- Does not extend the result beyond the φ-ladder interval [0,3].
formal statement (Lean)
159noncomputable def ml_stellar : ℝ := φ ^ characteristic_tier_scaffold
proof body
Definition body.
160
161/-- **THEOREM (PROVED)**: Stellar M/L value is φ. -/