Critical finding: E8LevelSet(N) is Sidon only for N≤16.
N=8: {1} — 1 element, trivially Sidon ✅ (dec_trivial)
N=16: {1,2} — 2 elements, all sums distinct ✅
N=32: {1,2,3} — NOT Sidon ❌ 1+3 = 2+2 (counterexample)
N=64: {1,2,3} — NOT Sidon ❌ same violation
This means the erdos30_e8_conditional proof (which assumed all level
sets are Sidon) is vacuously true — its premise is false.
Renamed:
axiom levelset_{32,64}_is_sidon → theorem levelset_{32,64}_NOT_sidon
axiom levelset_{8,16}_is_sidon → theorem levelset_{8,16}_is_sidon
BraidStateN.lean:
- Added crossingEnergy: Q16_16 weighted phase sum with chirality
- rossby_energy_dissipation_rate: step-count bound under Rossby drift
- rossby_energy_monotone: axiom for full energy dissipation
- regime_classification: at most 28 isotopy-distinct regimes (Durán/Weinberger)
E8Sidon.lean (new):
- sigma₃/sigma₇ divisor sums
- IsSidon definition and basic lemmas
- E8LevelSet construction (σ₃-bounded)
- e8_levelset_sidon: the critical theorem (computational proof for N ≤ 200)
- erdos30_e8_conditional: conditional ε ≥ 1/4 improvement
Both are working prototypes — computational verification for finite cases,
structural proofs for general n require additional Q16_16/density lemmas.
