[carlostoledo1891]

On #176 you wrote: "If the 13-point certificate does get independently replayed, or formalized, the asterisk comes off — that is the point of it. Closing this, and I would happily take a PR that removes it on those grounds." CONTRIBUTING now states the rule: the marker "is removed when that changes — when the paper is refereed and published, or when the argument is formalized or independently replayed."

This PR offers that replay for three asterisked lower bounds, decided from the certificate bytes the registry cites with no code shared with the claimants. Markdown only.

bound	bytes replayed	result
$C_{3b} \geq 1.77898884$ [MI2026]	Zenodo 10.5281/zenodo.20794135, c3b_pr92/certificate_3b_13pt.json, sha256 2efe99360a1f…, 13 points	ratio enclosed as 1.77898884142069354980…
$C_{3c} \geq 1.6747338950414058$ [L2026]	gist CoolRmal/5368357c @ 62621d2d, certificate_3c_147pt.json, sha256 b3dc9587ba7a…, 147 points	ratio enclosed as 1.67473389504140587006…; the 60-digit bound on the page also holds
$C_{71} > 6.521845710923046575$ [Num2026]	Zenodo 10.5281/zenodo.21497769, fei_c71_n18_artifact.json, sha256 57f5a1ad2bf5…	$I = 261/128$ exactly; $H/(I-1)$ = 6.52184571092304657565…

How. For C3b and C3c, pushforwards are exact rationals and every $-p \ln p$ is an outward-rounded interval. Two implementations do this, sharing no code with each other or with the claimants' checkers: JavaScript over BigInt, and the Python standard library alone. For C71: the integer Walsh–Hadamard transform of all $2^{18}$ entries, the exact influence, and the entropy in outward-rounded intervals. The amplification rule $C \geq H/(I-1)$ is cited, not re-proved.

Re-derive from https://github.com/carlostoledo1891/cert-machine at 422b952 (archived as doi:10.5281/zenodo.23171167):

python3 tools/verify_sumdiff.py           # standard library only, < 1 s; its red control must come back REFUTED
node tools/run-sumdiff-ledger.js --check  # ~1 s
python3 tools/run-fei-ledger.py --check   # ~1.5 s

Write-up: https://carlostoledo.co/reports/optimization-constants.html

What changes:

• The README cells for 3b, 3c and 71 lose the asterisk. For 3c and 71 this also ends the README's disagreement with their pages, whose rows had none.
• The two "(unverified)" Recent-progress lines are updated, and one line is added.
• Each page row gets a one-sentence replay note and a [T2026] reference.

Happy to split this per constant.

Related: the 147-point certificate's own checker compares at 53 bits, so it would also print OK for the false $C_{3c} \geq 1.6747338950414059$ (reported to its author: https://gist.github.com/CoolRmal/5368357cd781d7e5c676c9d68ad24d22#gistcomment-6408607). The bound above is decided without it.

Whether a replay by a third party is enough is yours to judge; if you would rather the marker stay until a formalization, I will close this.

AI-assisted: built with Claude (Anthropic) in a certified-arithmetic setting; the replay code, the records and this pull request were prepared with it, and I have checked every number and reference above against the records and the upstream files.