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Update C_22b upper bound to 7.2012719* (optimal unequal double helix) - #267

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YouhuaLi:C22b_tight_alternating
Oct 26, 2026
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YouhuaLi:C22b_tight_alternating

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Adds a computer-assisted upper bound $C_{22b} \le 7.2012719$*: an optimal coaxial double helix with unequal radii (all thickness constraints, including curvature) gives an explicit $C^{1,1}$ conformation of $T(2,n)$ with certified thickness ≥ 1 and $L \le 7.2012719,n + 19.649$ for odd $n \ge 59$. Verification by interval arithmetic (~40 s, one core); code, parameters and log at a pinned commit of https://github.com/YouhuaLi/tight-alternating-knot-constant. Asterisked as self-archived and computer-assisted. Also notes the paper's finding that the conformation behind the 7.31 bound [Kim2024] violates the curvature constraint. README cell and Recent progress updated.

▎ 🤖 Generated with Claude Code

Computer-assisted bound Rop(T(2,n)) <= 7.2012719 n + 19.649 for odd
n >= 59, from an optimal coaxial double helix with unequal radii under
all thickness constraints, with thickness certified by interval
arithmetic. Asterisked: the verification code is self-archived.

Also records the paper's observation that the conformation behind the
7.31 bound of Kim-Oh-Huh (2024) violates the curvature constraint.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
@teorth
teorth merged commit d9d102d into teorth:main Oct 26, 2026
teorth added a commit that referenced this pull request Oct 26, 2026
My resolver script had been cleared from the scratchpad between sessions,
so the merge was committed with the markers still in README.md. Both
changelog entries were present and correct underneath; only the three
marker lines needed deleting.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
teorth added a commit that referenced this pull request Oct 26, 2026
I committed three of them to README.md an hour ago resolving #267, and
the checker passed clean over the result. Conflict markers are the one
defect here that is unambiguous and trivially detectable, so they should
be an error.

Self-tested: planting a marker in a page makes the run report E4 and
exit non-zero; removing it returns the run to clean.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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2 participants