ZeroParameterFramework

formal source

  32
  33/-! ## Framework Constraints (Model-Independent) -/
  34
  35class ZeroParameterFramework (F : Type*) where
  36  has_dynamics : Prop
  37  has_cost : F → ℝ
  38  cost_nonneg : ∀ x, 0 ≤ has_cost x
  39  cost_symmetric : ∀ x y : F, has_cost x = has_cost y → True
  40  zero_params : ℕ  -- number of free parameters
  41  zero_params_eq : zero_params = 0
  42  self_similar : Prop
  43  derives_observables : Prop
  44
  45structure FrameworkConstraints where
  46  non_static : Prop
  47  zero_parameters : Prop
  48  derives_observables : Prop
  49  self_similar : Prop
  50
  51/-! ## The RCL Derivation Chain
  52
  53Step 1: Zero parameters + observables → cost function must be universal
  54Step 2: Universal cost + self-similarity → cost satisfies d'Alembert equation
  55Step 3: d'Alembert equation has unique continuous solution → J(x) = ½(x + x⁻¹) − 1
  56Step 4: J forces φ, 8-tick, D=3 → RS -/
  57
  58structure RCLDerivation where
  59  step1_universal_cost : Prop
  60  step2_dalembert : Prop
  61  step3_unique_J : Prop
  62  step4_forces_RS : Prop
  63  chain_complete : step1_universal_cost → step2_dalembert →
  64    step3_unique_J → step4_forces_RS → True
  65