MPForcesLedger

formal source

  83This is a PHYSICAL HYPOTHESIS, not a mathematical theorem.
  84It captures the claim that recognition pairing forces conservation.
  85-/
  86class MPForcesLedger (X : Type*) where
  87  /-- Recognition structure exists. -/
  88  recognition : RecognitionStructure X
  89  /-- Charge assignment exists. -/
  90  charge : X → ℤ
  91  /-- Non-trivial transactions balance. -/
  92  balanced : ∀ (txn : List X), txn.length > 1 → (txn.map charge).sum = 0
  93
  94/-- The trivial model satisfies MPForcesLedger (with zero charge). -/
  95instance : MPForcesLedger Unit := {
  96  recognition := { recognizes := fun _ _ => True, has_self_recognition := ⟨(), trivial⟩ },
  97  charge := fun _ => 0,
  98  balanced := fun _ _ => by simp
  99}
 100
 101/-! ## Self-Similarity Principle -/
 102
 103/-- Self-similarity: a scaling transformation.
 104
 105The claim is that recognition structures are invariant under rescaling
 106by a specific factor.
 107-/
 108structure SelfSimilarity (X : Type*) where
 109  /-- The scaling factor. -/
 110  factor : ℝ
 111  /-- Positive factor. -/
 112  factor_pos : 0 < factor
 113  /-- The scaling map. -/
 114  scale : X → X
 115
 116/-- The golden ratio φ = (1 + √5) / 2. -/