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theorem proved term proof

vacuum_fluctuation_cancellation

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formal statement (Lean)

 383theorem vacuum_fluctuation_cancellation :
 384    ∑ k : Fin 8, Foundation.EightTick.phaseExp k = 0 :=

proof body

Term-mode proof.

 385  Foundation.EightTick.sum_8_phases_eq_zero
 386
 387/-- **UNIFIED SPIN-STATISTICS FROM FOUNDATION**
 388
 389    The complete spin-statistics theorem grounded in Foundation proofs:
 390    1. phase(4) = -1 → fermions antisymmetric (from Foundation)
 391    2. phase(0) = +1 → bosons symmetric (from Foundation)
 392    3. All 8 phases sum to 0 → vacuum fluctuations cancel (from Foundation) -/

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