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allaun
a247dcb1b6
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.
76 lines
No EOL
2.2 KiB
JSON
76 lines
No EOL
2.2 KiB
JSON
{
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"schema": "taylor_green_betti_v1",
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"description": "Betti number analysis of Taylor-Green vortex with voids",
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"grid": "32x32x32",
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"percentile": 75.0,
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"scenarios": [
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{
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"scenario": "Uniform flow",
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"betti_0": 0,
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"betti_1": 0,
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"betti_2": 0,
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"interpretation": "\u03b2\u2082=0 \u2014 no voids in scar support",
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"scar_density_mean": 0.0,
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"scar_density_max": 0.0,
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"scar_support_fraction": 0.0
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},
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{
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"scenario": "Uniform+void",
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"betti_0": 1,
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"betti_1": 48,
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"betti_2": 1,
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"interpretation": "\u03b2\u2082=1 \u2014 indicating voids in scar support",
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"scar_density_mean": 0.12874603271484375,
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"scar_density_max": 14.0625,
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"scar_support_fraction": 0.015625
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},
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{
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"scenario": "TG smooth",
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"betti_0": 27,
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"betti_1": 12,
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"betti_2": 0,
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"interpretation": "\u03b2\u2082=0 \u2014 no voids in scar support",
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"scar_density_mean": 0.02859044560667393,
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"scar_density_max": 0.0761204674887134,
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"scar_support_fraction": 0.249298095703125
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},
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{
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"scenario": "TG+void r=5",
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"betti_0": 27,
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"betti_1": 51,
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"betti_2": 1,
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"interpretation": "\u03b2\u2082=1 \u2014 indicating voids in scar support",
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"scar_density_mean": 0.030014362461367294,
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"scar_density_max": 0.3295700132353654,
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"scar_support_fraction": 0.249053955078125
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},
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{
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"scenario": "TG+void r=6",
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"betti_0": 27,
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"betti_1": 64,
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"betti_2": 6,
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"interpretation": "\u03b2\u2082=6 \u2014 indicating voids in scar support",
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"scar_density_mean": 0.029546712701779096,
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"scar_density_max": 0.2998060621711367,
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"scar_support_fraction": 0.249298095703125
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},
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{
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"scenario": "Noise",
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"betti_0": 1920,
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"betti_1": 382,
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"betti_2": 77,
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"interpretation": "\u03b2\u2082=77 \u2014 indicating voids in scar support",
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"scar_density_mean": 1.7812399225491227,
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"scar_density_max": 12.489202293401028,
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"scar_support_fraction": 0.25
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}
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],
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"summary": {
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"Uniform flow": 0,
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"Uniform+void": 1,
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"TG smooth": 0,
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"TG+void r=5": 1,
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"TG+void r=6": 6,
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"Noise": 77
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}
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} |