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Improve C42 and C51 bounds with verification certificates - #184

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AndreRoehrig:improve-c42-c51-bounds
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Improve C42 and C51 bounds with verification certificates#184
AndreRoehrig wants to merge 1 commit into
teorth:mainfrom
AndreRoehrig:improve-c42-c51-bounds

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This PR adds two proposed computer-assisted improvements:

  • C42: upper bound 0.688983, improving 0.6906538.
  • C51: lower bound 0.5850788196744, improving the prior paper’s 0.585078819653.

Historical bound rows are preserved. Both README table entries and “Recent progress” are updated, with references pinned to the supporting package’s commit.

Proofs, exact inputs, and Python verification](https://github.com/AndreRoehrig/optimization-constants-certificates/tree/ed6387399cf6de02eaa4cf10c43787633496619a)

Both certificates pass at 100 and 200 decimal places, and the additional mathematical audit passes. The C42 construction is asymptotic; no explicit finite threshold N is supplied. Both new bounds retain the verification-status asterisk.

This work was developed with AI assistance (gpt-6-astra max in codex). I, André Röhrig, reviewed the mathematical arguments, references, and supporting verification material.

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