`PhysicsState`

definition

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module: IndisputableMonolith.Foundation.PhysicsLogicRealization
domain: Foundation
line: 19 · github
papers citing: none yet

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IndisputableMonolith.Foundation.PhysicsLogicRealization on GitHub at line 19.

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formal source

  16namespace PhysicsLogicRealization
  17
  18/-- Minimal recognition-state skeleton indexed by identity ticks. -/
  19structure PhysicsState where
  20  tick : ArithmeticFromLogic.LogicNat
  21  deriving DecidableEq
  22
  23/-- Equality cost on physics states. -/
  24def physicsCost (x y : PhysicsState) : Nat :=
  25  if x = y then 0 else 1
  26
  27@[simp] theorem physicsCost_self (x : PhysicsState) : physicsCost x x = 0 := by
  28  simp [physicsCost]
  29
  30theorem physicsCost_symm (x y : PhysicsState) : physicsCost x y = physicsCost y x := by
  31  by_cases h : x = y
  32  · subst h
  33    simp [physicsCost]
  34  · have h' : y ≠ x := by intro hyx; exact h hyx.symm
  35    simp [physicsCost, h, h']
  36
  37/-- Identity-tick successor. -/
  38def tickStep (x : PhysicsState) : PhysicsState :=
  39  ⟨ArithmeticFromLogic.LogicNat.succ x.tick⟩
  40
  41/-- Interpret the free arithmetic orbit as identity-tick states. -/
  42def physicsInterpret (n : ArithmeticFromLogic.LogicNat) : PhysicsState :=
  43  ⟨n⟩
  44
  45/-- Physics realization skeleton. -/
  46def physicsRealization : LogicRealization where
  47  Carrier := PhysicsState
  48  Cost := Nat
  49  zeroCost := inferInstance

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