 186/-! ## 8-Tick Phase in Quantum Ledger -/
 187
 188/-- The phase factor for a ledger entry. -/
 189noncomputable def entryPhase (e : LedgerEntry) : ℂ :=
 190  EightTick.phaseExp e.phase
 191
 192/-- The total phase of a ledger (product of entry phases). -/
 193noncomputable def ledgerPhase (L : Ledger) : ℂ :=
 194  (L.entries.map entryPhase).prod
 195
 196/-- An empty ledger has phase 1. -/
 197theorem empty_ledger_phase : ledgerPhase emptyLedger = 1 := by
 198  simp [ledgerPhase, emptyLedger]
 199
 200/-- **8-TICK INTERFERENCE**: When summing over all 8 phase configurations
 201    with equal amplitudes, the sum is zero.
 202
 203    This is the quantum version of vacuum fluctuation cancellation. -/
 204theorem eight_tick_interference :
 205    (∑ k : Fin 8, EightTick.phaseExp k) = 0 :=
 206  EightTick.sum_8_phases_eq_zero
 207
 208/-! ## Summary Theorem -/
 209
 210/-- **QUANTUM LEDGER FUNDAMENTALS**
 211
 212    The quantum ledger formalization establishes:
 213    1. Ledger entries have well-defined J-cost
 214    2. Ledger balance is conserved under updates
 215    3. Quantum states are superpositions over ledgers
 216    4. Born rule connects to J-cost minimization
 217    5. 8-tick phases enable interference -/
 218theorem quantum_ledger_fundamentals :
 219    -- Entry costs are non-negative

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