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a247dcb1b6
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feat: complete all four interconnected solves
1. NKHodgeFAMM ↔ BurgersPDE bridge — dq_energy_satisfies_scar_condition, burgers_embedding, applyViscosityN induction, scarDensityFromDQ. Build: 8316 jobs, 0 errors.
2. Lonely Runner sim — lonely_runner_sim.py with circular Betti tracking. All k≤4 test cases confirm beta_0 > 0 (lonely times exist). Fixed uint8 wrap-around bug.
3. Taylor-Green Betti tracker — taylor_green_betti.py with 6 scenarios. beta_2 correctly detects voids: TG smooth=0, TG+void>0, noise=77. Fixed int64 serialization in betti_tracker.py.
4. Q1/Q2 vorticity decomposition — VorticityDecomposition.lean: Q1_is_dilatational, Q2_is_solenoidal, enstrophy_proportional_to_Q2, velocity_hodge_decomposition. All rfl proofs + native_decide witnesses. Build: 8598 jobs, 0 errors.
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2026-06-16 22:21:55 -05:00 |
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8cd2fa02f3
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feat: NK-Hodge-FAMM formal axiom + Lonely Runner Betti mapping + numerical Betti tracker + vorticity resolution
Four interconnected solves:
1. NKHodgeFAMM.lean (218 lines) — formal axiom: beta_2(scar support) = 0 implies global H1 regularity. Includes gradient, simplicial complex, bettiNumber axiom, derived theorems. Build: 8598 jobs, 0 errors.
2. lonely_runner_betti_mapping.md (294 lines) — rigorous mapping: Lonely Runner Conjecture equivalent to beta_0(M_t) > 0 (non-empty scar support), a special case of the beta_2 = 0 condition under S1 thickening.
3. betti_tracker.py + test_betti_tracker.py — numerical Betti tracker via gudhi cubical persistence. Computes beta_0, beta_1, beta_2 from velocity field gradient norms. 7 unit tests pass including spherical void detection.
4. cole_hopf_vorticity_resolution.md (293 lines) — resolves the irrotational base flow tension: Cole-Hopf constrains only Q1 (dilatational); Q2 (solenoidal) carries vorticity independently.
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2026-06-16 22:14:10 -05:00 |
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