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0a: static Fisher–Rao on Δ₃ proven constant-curvature 1/4, ∇R≡0 (symbolic). 0b: rossbyDriftFromChirality drift-flip metric has signature (2,1), drift direction time-like at 3 exact rational points. 0c: drift-flipped metric is PROPER — not locally symmetric (108 nonzero ∇R components at centroid, exact), not semisymmetric, not Deszcz- pseudosymmetric (inconsistent L ratios at two points). 0d: obstruction is carried by the drift direction. Refutes the semi-symmetry hypothesis for the drift-FLIP geometrization at m=4; Randers/torsion geometrizations and the m=8 Sidon-block case remain open (Δ₇ run pending). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
22 lines
1.3 KiB
Text
22 lines
1.3 KiB
Text
Δ_3: m=4 outcomes, chirality weights w=[1, -1, 1/2, 0], β_reduced=[7/8, -9/8, 3/8]
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[0a] static Fisher–Rao baseline
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R = 1/4 (g∧g) (constant curvature 1/4, symbolic): True
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⇒ ∇R ≡ 0 (constant-curvature ⇒ locally symmetric): True
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⇒ signature (m−1, 0) positive-definite, holonomy SO(m−1)
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[0b] drift-flipped metric g' = g − 2 β♭⊗β♭ / g(β,β)
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centroid: signature (2, 1), g'(β,β) = -35/4 (<0 ⇒ β time-like)
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offcenter1: signature (2, 1), g'(β,β) = -8389/208 (<0 ⇒ β time-like)
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offcenter2: signature (2, 1), g'(β,β) = -14801/640 (<0 ⇒ β time-like)
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[0c] discriminator on g'
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∇R' at centroid: 108 nonzero components ⇒ NOT locally symmetric
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e.g. (∇R')_(0, 0, 1, 0, 1) = 1987584/1500625
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L candidates at centroid: {1271/16100, -15059/9100, -19/140, 3569/11900, 2221/9100}
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L candidates at offcenter1: {-8590214568267575/3241881668558884, 16772053384459/155461617600556, 75435268381579/218698066038316, 774808063467871/5447322057141628, 269928732683725/1252646089142068, 4602893418717781/9220566956885332}
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[verdict] baseline: LOCALLY SYMMETRIC (∇R=0). drift-perturbed: ∇R ≠ 0; PROPER (neither semi- nor pseudo-symmetric at sample points) — R·R ≠ L·Q(g,R)
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[0d] obstruction vs drift direction (centroid)
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Σ (β^a ∇_a R')² at centroid = 69439107209066496/2251875390625 (drift direction carries obstruction)
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