theorem
proved
eight_tick_interference
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IndisputableMonolith.Foundation.QuantumLedger on GitHub at line 204.
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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
220 (∀ e : LedgerEntry, 0 ≤ e.cost) ∧
221 -- Empty ledger has zero balance
222 emptyLedger.balance = 0 ∧
223 -- Updates preserve balance
224 (∀ L u, (applyUpdate L u).balance = L.balance) ∧
225 -- 8-tick phases sum to zero
226 (∑ k : Fin 8, EightTick.phaseExp k = 0) :=
227 ⟨entry_cost_nonneg, empty_ledger_balance, ledger_balance_conserved, eight_tick_interference⟩
228
229end QuantumLedger
230end Foundation
231end IndisputableMonolith