ml_derived

formal source

  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)
  88    - ObservabilityLimits.ml_geometric (observability constraints)
  89
  90    Each is defined in its respective module but the convergence proof
  91    is not yet complete.
  92
  93    The hypothesis structure makes explicit what needs to be proven. -/
  94def H_ThreeStrategiesAgree : Prop :=
  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. -/
 101theorem three_strategies_agree : H_ThreeStrategiesAgree := by
 102  unfold H_ThreeStrategiesAgree
 103  refine ⟨?_, ?_, ?_⟩