Ramanujan Challenge Problem 2.8 Solution & Proof

allaun b2ed813203 docs(p28): the encoder approach -- method, evidence, and honest limits ... Documents the compact-form method: re-express opaque exact data in a structurally-chosen fixed basis and read the coordinates, treating a successful short exact encoding as a receipt of provenance rather than as compression. Concrete instance, verified exactly: the challenge's eight large seed integers decode in the Pascal basis to the Chudnovsky constants A=13591409, B=545140134, S=426880, which in turn satisfy A = den(s2)-num(s2), B = 6*den(s2), A/B = (1-s2)/6 for the CM invariant s2 = 77265280/90856689. Chain: opaque integers -> Pascal coordinates -> Chudnovsky constants -> CM invariant -> modular origin. States the limits plainly: - NOT a compressor. Measured 3.54x (588 -> 166 bits); unremarkable, and any compression claim should be rejected. Consistent with the finding elsewhere in this programme that char-poly encoding adds overhead vs an entropy-coded baseline. - Falsifiable, not numerology: basis fixed in advance, encoding exact with no tolerance, and the recovered coordinates were pinned beforehand by an unrelated classical formula. - Distinctiveness assessed fairly: this is a disciplined exact-arithmetic variant of established inverse-symbolic practice (PSLQ, ISC), unusual mainly in targeting structured integer arrays and in carrying the encoding into the proof. 'Unique' would overclaim. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01WY6SfRYvm8zFKMX9GcjS8u		2026-07-31 04:22:13 -05:00
docs/proofs	feat(p28): harden exact proof equations	2026-07-31 15:33:21 +07:00
experiments/ramanujan_28/submission	docs(p28): the encoder approach -- method, evidence, and honest limits	2026-07-31 04:22:13 -05:00