`RecognitionStructure`

definition

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module: IndisputableMonolith.RRF.Foundation.MetaPrinciple
domain: RRF
line: 61 · github
papers citing: none yet

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IndisputableMonolith.RRF.Foundation.MetaPrinciple on GitHub at line 61.

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formal source

  58
  59This captures the minimal structure needed for "things to be recognized."
  60-/
  61structure RecognitionStructure (X : Type*) where
  62  /-- The recognition relation: R x y means "x recognizes y". -/
  63  recognizes : X → X → Prop
  64  /-- At least one thing can recognize itself (closure). -/
  65  has_self_recognition : ∃ x, recognizes x x
  66
  67/-- Any recognition structure implies nonemptiness. -/
  68theorem recognition_structure_nonempty {X : Type*}
  69    (R : RecognitionStructure X) : Nonempty X :=
  70  MetaPrinciple X ⟨R.recognizes, R.has_self_recognition⟩
  71
  72/-! ## From Recognition to Ledger -/
  73
  74/-- A minimal ledger: balanced debits and credits. -/
  75structure MinimalLedger (X : Type*) where
  76  /-- The charge of an element. -/
  77  charge : X → ℤ
  78  /-- Conservation: sum of charges is zero in any valid transaction. -/
  79  conserved : ∀ (txn : List X), (txn.map charge).sum = 0
  80
  81/-- Hypothesis class: MP forces ledger structure.
  82
  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. -/

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