C_4b: two 2026 lower bounds (Krachun 0.752796; Jones 0.753742) - #187
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C_4b: two 2026 lower bounds (Krachun 0.752796; Jones 0.753742)#187JD-Jones-ASES wants to merge 1 commit into
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Two rows appended to the lower-bound table with the data needed to recompute each value; README cell and Recent progress updated; references [Kra2026] and [Jon2026] added; AI-use noted in the contribution notes.
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Two rows appended to the lower-bound table of
constants/4b.md, the README cell and "Recent progress" updated, references added. Markdown only.Row 1 — Krachun (arXiv:2608.01325, 2 Aug 2026), 0.752796… — ten Paley chains glued by CRT; the first bound past 3/4. The page listed nothing after Lewko 2015, so this row is added for the record and because the second row builds on it.
Row 2 — Jones (23 Aug 2026), 0.753741541837329405… — Krachun's gluing over an eleven-block pool: his nine chains (the chain at 23 dropped because 23 | 299) plus two certificates on the square-free composite moduli 235 and 299, lifted by one new lemma. The Comments column lists both certificates in full (17 and 19 residues, heights 11 and 12) and the closed form, so the value can be recomputed without downloading anything; I recomputed both rows' constants from that data before submitting (including the two longest-path heights).
Supporting material lives outside this repository, per the contributing guidelines:
0.7537 < alphaInfby kernel-checked integer comparison; standard axioms only): https://github.com/JD-Jones-ASES/fs-formal (commit 4e79656).The recorded value is the limit of the closed form; the construction is finite and explicit at every stage. If the maintainers prefer the unverified marker for a bound whose write-up is a repository note rather than a paper, please add the asterisk; the formalization is offered as the verification.
AI-use disclosure. The result itself is AI-generated with a human managing the workflow (see the repository's DISCLOSURE.md). This pull request's text was drafted with Claude (Anthropic); the references and the recomputation were checked by the contributor, and the contribution note on the page says so.