[carlostoledo1891]

#216 applied the CONTRIBUTING rule that 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 the same replay for the one asterisked bound #221 added, decided from the certificate bytes the registry cites, with no code shared with the claimant. Markdown only.

bound	bytes replayed	result
$C_{3c} \geq 1.674894211307116$ [J2026]	Zenodo 10.5281/zenodo.23289305 (its latest version), certificate.json, sha256 8b6612ef9134… (md5 277fbedab582…, as Zenodo lists it): two laws on 51 and 47 points, counts 39041372760532870645 : 60958627239467129355, base 55	ratio enclosed as 1.67489421130711622876434373706…

How. As the certificate states the construction: every form ($x$, $y$, $x+y$, $x+2y$, $x-y$) is at most 27 = (55−1)/2 in absolute value on both supports (checked; the maximum is 27), so each $L(X,Y)$ is a balanced base-55 expansion, the digit map is injective, and $H(L(X,Y)) = a,H_A(L) + b,H_B(L)$ exactly. Per-law pushforwards are exact rationals, every $-p \ln p$ is an outward-rounded interval, and the integer counts are multiplied in before the quotient. Two implementations do this, sharing no code with each other or with the certificate's checkers (python-flint and PARI/GP, not run): JavaScript over BigInt with dyadic intervals at 128 bits, and the Python standard library alone (decimal at 120 digits). Their enclosures agree to 30 digits. The Python one carries three red controls that must fire: the smallest 30-digit claim above the ratio is refuted; base 53, where (53−1)/2 < 27, is refused for injectivity; a weight one unit off is refused.

Re-derive from https://github.com/carlostoledo1891/cert-machine at 9925150:

python3 tools/verify_twolaw.py          # standard library only, < 1 s; the three red controls must fire
python3 -I tools/run-optq-ledger.py     # both implementations (~3 min; the queue's other rows dominate)

Write-up: https://carlostoledo.co/reports/optconst-queue.html (§3).

What changes:

• The README cell for 3c shows 1.674894211307116 without the asterisk (the page row had none).
• The "(unverified)" Recent-progress line is updated, and one line is added in the form Remove the asterisk from C3b, C3c and C71: certificates independently replayed #216's replay was recorded.
• The page row gets a one-sentence replay note, a [T2026b] reference and a contribution note.
• One restoration on the same page: the L2026 row's note "Independently replayed [T2026]: …", merged in ad40c53 (Remove the asterisk from C3b, C3c and C71: certificates independently replayed #216), was reverted 36 seconds later by the C_3c: improved lower bound 1.674894211307116 from two independent digit laws #221 merge, whose branch predated Remove the asterisk from C3b, C3c and C71: certificates independently replayed #216, which left the [T2026] reference with nothing citing it. The row is put back byte for byte as ad40c53 had it.

The first implementation's result was posted on #221 on 15 Oct (#221 (comment)); the second was added so that this replay meets the same two-implementation standard as #216.

AI-assisted: prepared with Claude (Anthropic) in a certified-arithmetic setting: the replay code, the records and this pull request. Every number above is read from the pinned record at the commit cited, and was re-checked against the upstream files and the Zenodo deposit before sending.