Billiards: independent skeptic engine for the 015 margin system - #18
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wmsk015.py: own margin implementation validated against 002's blind-era corridor geometry (1200/1200 sign agreements incl. far-from-window triangles), identity checks (AC0 = -N1, BC0 = N4, AB_a = -PB, tau closed form vs exact symbolic tau), fresh 62-member exact ring bijection, adversarial scans of the seven S-lemmas plus every intermediate step of their new proofs (32 inequalities, a <= 40 dense + 20k random members to a = 3000, zero violations), a 453k-point beyond-the-wall T2 scan, and n4leg - the exact certificate leg (ring identity + rational ranges) for the death-segment BC0 row that wmargins_certify.py never evaluates. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01HwxBQP4s5qBEciD4tzk3Tv
…or all (a,b) Skeptic pass on 015 (confirmed with corrections) doing the queue-11 main task in the same record: all seven fan-margin lemmas plus tau re-derived from scratch (drafts never read - not in the repo) and proven for all a >= b >= 1, a >= 2 at k = 1/2. D-AB/B-AB fall to progression-window bounds, D-BA/D-BC to single cosine comparisons, D-AC to an exact product-to-sum pairing with one W(2,2) special case, B-AC/B-BC jointly to one new birth-core inequality, and tau collapses to R = -4 sin(th) sin(a al) sin((b+1) be) - so tau != 0 is automatic at every alive point. T2 confirmed with a one-line simplification; N1 re-proven derivative-free. With 005 + T2 + 013/014: window(W(a,b)) = (gamma_birth, gamma_d) exactly for every member and every obtuse angle has an explicit alive W(a,b) triangle. Corrections to 015, neither load-bearing: the s=0 C-image margin is -N1 (not -N1-N2), and the a <= 14 run never certified the death BC0/N4 row (repaired by n4leg, 104/104 members exact). Remaining: general-(a,b) endpoint bookkeeping (formal ring pass queued) and the skeptic pass on this record's proofs. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01HwxBQP4s5qBEciD4tzk3Tv
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wmsk015.py: own margin implementation validated against 002's blind-era
corridor geometry (1200/1200 sign agreements incl. far-from-window
triangles), identity checks (AC0 = -N1, BC0 = N4, AB_a = -PB, tau closed
form vs exact symbolic tau), fresh 62-member exact ring bijection,
adversarial scans of the seven S-lemmas plus every intermediate step of
their new proofs (32 inequalities, a <= 40 dense + 20k random members to
a = 3000, zero violations), a 453k-point beyond-the-wall T2 scan, and
n4leg - the exact certificate leg (ring identity + rational ranges) for
the death-segment BC0 row that wmargins_certify.py never evaluates.
Co-Authored-By: Claude Fable 5 noreply@anthropic.com
Claude-Session: https://claude.ai/code/session_01HwxBQP4s5qBEciD4tzk3Tv