J_bit

formal source

  54/-! ## Fundamental Constants -/
  55
  56noncomputable def φ : ℝ := Constants.phi
  57noncomputable def J_bit : ℝ := Real.log φ
  58
  59/-! ## The Unified M/L Value -/
  60
  61/-- **DEFINITION**: The derived mass-to-light ratio in solar units.
  62
  63    The characteristic M/L equals the golden ratio φ ≈ 1.618 solar units.
  64    This value emerges from three independent derivation strategies:
  65    1. StellarAssembly: J-cost weighting of photon emission vs mass storage
  66    2. NucleosynthesisTiers: φ-tier structure of nuclear/photon fluxes
  67    3. ObservabilityLimits: Geometric constraints from λ_rec, τ₀, E_coh
  68
  69    See: LaTeX Manuscript, Chapter "Astrophysical Tests", Section "M/L Derivation".
  70
  71    FALSIFIER: If observed M/L systematically deviates from the φ-ladder
  72    {φ^n : n ∈ ℤ} by more than measurement uncertainty. -/
  73noncomputable def ml_derived : ℝ := Constants.phi
  74
  75/-- **THEOREM (TRIVIAL)**: M/L matches φ by definition.
  76
  77    This identifies the derived M/L value with the golden ratio.
  78    It is the *conclusion* of the three-strategy derivation chain. -/
  79theorem ml_derived_value : ml_derived = Constants.phi := rfl
  80
  81/-! ## Consistency of Three Strategies -/
  82
  83/-- **HYPOTHESIS**: All three derivation strategies agree.
  84
  85    STATUS: NEEDS_DEFS — Requires formalizing:
  86    - StellarAssembly.ml_stellar (J-cost weighting)
  87    - NucleosynthesisTiers.ml_nucleosynthesis (φ-tier structure)