Ramanujan Challenge Problem 2.8 Solution & Proof
allaun
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F1 run_checks.sh exited 1 on any machine WITH SageMath. set -euo pipefail made the declared-optional cross-checks fatal, so the script passed without the optional tooling and failed with it. Optional calls are now guarded by run_optional(), failures are counted and reported non-fatally, and the script ends exit 0 with a summary line. F2 false assertion in p28_lattice_hypotheses_certificate.sage. Component 1 read 216 + 108x + 46x; b2 = (1,2,1,0) contributes 216x, so the true value is 216 + 216x + 46x. The load-bearing identity below it (Bcomb == 4x*Crow) was always correct, so no mathematics changes. F3 Sage 10.9 raised 'keys do not match self's parent' at the subs() call: q lives in the fraction field K while .numerator()/.denominator() return elements of the underlying polynomial ring. The substitution key is now coerced into the polynomial parent. This error had been MASKING F2. Verified after the fixes: run_checks.sh exit 0, 48 mandatory PASS (up from 43 -- the previously failing certificate now runs to completion), 0 optional failures falsifiability intact: 64R-44 -> 64R-43 exits 1, and 236337691420383 -> ...384 exits 1 pdflatex x3: 0 errors, 0 warnings, 0 undefined, 17 pages, 0 broken refs Documentation: states plainly that no base is claimed superior to any other -- the non-injectivity holds for every b >= 2, [0,1] and [1] collide in decimal exactly as in octal, and both repairs are stated for general b. Base 8 is only the inherited worked example. Without this a reader could take the radix work for a claim that base 8 beats base 10 or binary, which is not claimed anywhere. Housekeeping: removes three Sage preparser .sage.py outputs that an earlier 'git add -A' in this branch had wrongly committed, and adds a .gitignore for Sage and LaTeX build artifacts. Release zip and PDF rebuilt. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01WY6SfRYvm8zFKMX9GcjS8u |
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