`H_UniquenessVerified`

definition

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module: IndisputableMonolith.Information
domain: Information
line: 29 · github
papers citing: none yet

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IndisputableMonolith.Information on GitHub at line 29.

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formal source

  26
  27    STATUS: SCAFFOLD — Proof established in `Information.JCostNecessity`.
  28    TODO: Fully unify the uniqueness theorem with the aggregator. -/
  29def H_UniquenessVerified : Prop :=
  30  ∀ (F : ℝ → ℝ), InformationCost F → (∀ x > 0, F x = Cost.Jcost x)
  31
  32-- Legacy axiom eliminated. See CostUniqueness.T5_uniqueness_complete.
  33
  34/-- **HYPOTHESIS**: Thermodynamic Bound.
  35    Recognition cost satisfies the Landauer bound for information erasure.
  36
  37    STATUS: SCAFFOLD — Bound derived in `Information.Thermodynamics`.
  38    TODO: Complete the Taylor expansion proof in `Thermodynamics.lean`. -/
  39def H_ThermodynamicsVerified : Prop :=
  40  ∀ (s : Thermodynamics.LedgerState), ∀ b ∈ s.active_bonds,
  41    let m := s.bond_multipliers b
  42    let u := Real.log m
  43    Cost.Jcost m ≥ u^2 / 2
  44
  45-- Legacy axiom eliminated. See Foundation.ConstantDerivations.
  46
  47end Information
  48end IndisputableMonolith

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