allaun 8d25a7b367 cert(p28): official-object certificate — proof analyses the official matrix, not a surrogate ... Reconstructs the Problem 2.8 data directly from the challenge statement (R, u=2n+3, w, the 4x4 M(n), both integer seed rows) and verifies by exact rational arithmetic that the manuscript's specialisation reproduces it: M_N(x_0) == official M(N), all 16 entries, at N = 0,1,2,3,5,8,17,40 A_0 = A*C - (5/4)H_0 == official first seed row A_1 = S*C == official second seed row (14R-567)/9 == 236337691420383 (the deformed coefficient restores) 18 assertions, three with explicit negative controls. fractions.Fraction throughout; no floating point, no CAS. Closes the one gap no existing certificate covered: the other four verify statements about the deformed family, none verified that the family is the official object. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01WY6SfRYvm8zFKMX9GcjS8u		2026-07-31 04:09:39 -05:00
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ramanujan_28/submission	cert(p28): official-object certificate — proof analyses the official matrix, not a surrogate	2026-07-31 04:09:39 -05:00