billiards-triangles 005: death law completed - parametric necessity for all (a,b), death = gamma_d exactly for 20 members - #6
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…or all (a,b), death = gamma_d exactly for 20 members Half word composes to R_0 Rot_A(2a.alpha) Rot_B(-2b.beta); I1-I4 and glide facts proven for all (a,b) by formal-ring specialization; Lemmas C and D proven via c.cot(cs) monotonicity; case tree closed with the a <= 2b+3 restriction removed; certified alive segments into the death corner give death = gamma_d exactly (sup not attained) for 20 members; five new members measured (W(6,3), W(6,1), W(8,2), W(8,1), W(7,1)). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01FNm1JAtYGZgGoffPWc9dTz
… birth law found, alive at exactly 135 Structure-class design search over doubled odd half-words: 001's pinch gap [135.000, 135.0486] was a sampler artifact (W(4,3) certified alive inside it); births follow gamma_birth = 180 - 90(a+b+1)/(a(b+1)) (SPECULATION, survives out-of-sample) so consecutive windows touch; W(5,2) and a non-W four-block word certified alive at gamma = exactly 135 via rational apexes on (2x-1)^2+(2y+1)^2 = 2; kill condition refuted - 135 deg is not a constructive barrier in this class. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01FNm1JAtYGZgGoffPWc9dTz
…ed, four corrections All five exact certificates re-established from scratch by a third corridor implementation (widths match digit-for-digit); 001's sampler replicated and its error mechanism pinned (corner sliver below grid clearance); birth law survives three genuinely out-of-sample members; corrections: 566-not-811 universe count, pointwise-not-throughout certificates, correction-not-refutation semantics vs 001, and W(a,b) ~ W(b+1,a-1) are the same canonical word. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01FNm1JAtYGZgGoffPWc9dTz
…e certificate-precision correction Bridge recomposed exactly at off-torus points for 40 members; I1-I4 re-proven in an independent 4-variable ring with u re-derived symbolically; Lemmas re-derived by hand and stressed to a = 10^6; case tree re-derived branch by branch, 447k-point scan clean; sufficiency segments independently certified alive to gamma_d - 9.3e-10 by full corridor unfolding; correction: four of five new alive certificates reach gamma_d - 1e-4, not 1e-6. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01FNm1JAtYGZgGoffPWc9dTz
Queue items 11+12 done (records 005-008, all skeptic-confirmed); new queue leads: parametric sufficiency + birth side, coverage conjecture + sampler blind spot; two new mechanism tags; 005's index leak_terms lengthened to meet the schema minimum (008's index nit). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01FNm1JAtYGZgGoffPWc9dTz
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Half word composes to R_0 Rot_A(2a.alpha) Rot_B(-2b.beta); I1-I4 and
glide facts proven for all (a,b) by formal-ring specialization; Lemmas
C and D proven via c.cot(cs) monotonicity; case tree closed with the
a <= 2b+3 restriction removed; certified alive segments into the death
corner give death = gamma_d exactly (sup not attained) for 20 members;
five new members measured (W(6,3), W(6,1), W(8,2), W(8,1), W(7,1)).
Co-Authored-By: Claude Fable 5 noreply@anthropic.com
Claude-Session: https://claude.ai/code/session_01FNm1JAtYGZgGoffPWc9dTz