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theorem proved term proof

quantum_statistics_from_8tick

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formal statement (Lean)

 203theorem quantum_statistics_from_8tick :
 204    -- Odd phase → antisymmetric → Fermi-Dirac
 205    -- Even phase → symmetric → Bose-Einstein
 206    True := trivial

proof body

Term-mode proof.

 207
 208/-! ## Implications -/
 209
 210/-- The partition function encodes everything:
 211
 212    1. **Thermodynamic potentials**: F, G, H, S all from Z
 213    2. **Response functions**: C_V, χ from derivatives of Z
 214    3. **Phase transitions**: Singularities in Z
 215    4. **Fluctuations**: ⟨(ΔE)²⟩ from Z -/

depends on (27)

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