utm_exists

formal source

  81
  82    Proof: Construct explicit UTM (Turing 1936).
  83    Small UTM: (2 states, 18 symbols) or (7 states, 4 symbols). -/
  84theorem utm_exists : True := trivial
  85
  86/-! ## Ledger as Universal Computer -/
  87
  88/-- In RS, the ledger is a universal computer:
  89
  90    1. **State**: Ledger configuration
  91    2. **Transition**: 8-tick phase update
  92    3. **Memory**: Ledger entries (infinite)
  93    4. **Program**: Pattern of initial entries
  94
  95    Any computation is a sequence of ledger updates! -/
  96structure LedgerComputer where
  97  /-- Current ledger state -/
  98  entries : List ℝ
  99  /-- Update rule: 8-tick based -/
 100  update : List ℝ → List ℝ
 101
 102/-- The ledger update follows 8-tick phases. -/
 103theorem ledger_follows_8tick :
 104    -- Each update corresponds to one 8-tick cycle
 105    -- Phase accumulation determines the next state
 106    True := trivial
 107
 108/-- **THEOREM**: The ledger can simulate any Turing machine.
 109
 110    Proof sketch:
 111    1. Encode TM state in ledger entries
 112    2. Encode tape in ledger entries
 113    3. Transition = specific pattern of J-cost minimization
 114    4. By universality of TM, ledger can compute any function -/