Six corrections found while reading the registry systematically. Sources are linked for each; every quote below I grepped out of the source text myself rather than taking from a summary. The first three affect recorded values or attribution; the last three are presentation. Happy to open PRs for any subset — just say which.
1. 10c (Spencer discrepancy) records a value the source has since withdrawn
The upper-bound table lists $3\sqrt{3/2} \approx 3.674235$ citing Pesenti–Vladu, arXiv:2211.05509. That paper's v2 (14 Apr 2026) carries an erratum. Its arXiv Comments field reads verbatim:
Updated to include an erratum: the constant in Theorem 4.5 is corrected from 3.7 to 4.1. We thank Haotian Jiang and Nikhil Bansal for identifying the error
and v2's Theorem 4.5 states $\lVert Ax\rVert_\infty \leqslant 4.1\sqrt{n} + O(1)$. Since $3\sqrt{3/2}$ prints as 3.7, the registry holds the pre-erratum constant. The README row 3.674235 (3.65*) would become 4.1 (3.65*), with an erratum row in the entry.
2. 9a (Shannon capacity of $C_7$) is behind four papers
The entry records $367^{1/5} \approx 3.2578$ [PS2018] and was last edited 2026-06-14, just before a cascade:
| bound |
source |
| $> 3.258020$ |
Itty, Rosin, Carstensen, Reichman, arXiv:2607.21517 (23 Jul 2026) |
| $\geq 3.2587891539086910161967650155\ldots$ |
Gao, arXiv:2607.27869 (30 Jul 2026) |
| $\geq 3.258805369885\ldots$ |
Buys, Polak, Zuiddam, arXiv:2607.29681 (31 Jul 2026) — formalised in Lean |
| $\geq 3.25883262\ldots$ |
Tandon, arXiv:2608.30273 (31 Aug 2026) |
3. 4b (Furstenberg–Sárközy) may misattribute its record
The entry credits $\tfrac12(1 + \log 12/\log 205) \approx 0.733412$ to [Lew2015], and cites Beigel–Gasarch only for the trivial $\tfrac12$. But the abstract of Beigel–Gasarch, arXiv:0804.4892 (2008), reads verbatim:
Ruzsa has shown that sdf(n) = \Omega(n^{0.5(1+ \log_{65} 7)}) = \Omega(n^{0.733077...}) We improve on the lower bound by showing sdf(n) = \Omega(n^{0.5(1+ \log_{205} 12)})
— the same modulus 205 and the same set size 12, seven years earlier. (The .7443... in their abstract is a typo; the value is 0.733415, and their own title says 0.7334.) Lewko's distinct contribution may well be the exhaustive verification — he reports checking every modulus below 533 by brute force and extending to 733 — rather than the construction. Settling this needs both full texts, which I have not read, so I am flagging rather than asserting.
Incidentally, I can confirm the certificate reproduces: $r_2(65) = 7$ and $r_2(205) = 12$ are both optimal by exhaustive branch-and-bound, and $|B| = 12$ at $m = 205$ is provably maximal (4.6 s).
4. 45a (Romanoff) prints a certificate for a superseded bound
The section is headed "Certificate for the 0.490249407811155 upper-density bound" (Griego), but the current record row is Yoo's 0.490180063290061, which has no printed certificate. A reader who follows the printed object recomputes the second-best value.
5. 3b asterisk inconsistency
The README marks the record 1.77898 (1.77898884*) — asterisked, i.e. minimally verified under the README's own convention — while the entry's own lower-bound table lists 1.77898884 with no asterisk, and neither does the README's "Recent progress" line. 3a does carry asterisks inside its own table, so one of the two is wrong.
6. 47a bound table is ordered so the record row is not the record
Its lower-bound table lists Aldaz's 1.6211915 first and Melas's weaker 1.5675208 last, so the "last row is the record" convention that the other entries follow selects the weaker bound. The README has it right. Cosmetic for a human reader, but it defeats reading the entries mechanically.
Six corrections found while reading the registry systematically. Sources are linked for each; every quote below I grepped out of the source text myself rather than taking from a summary. The first three affect recorded values or attribution; the last three are presentation. Happy to open PRs for any subset — just say which.
1.
10c(Spencer discrepancy) records a value the source has since withdrawnThe upper-bound table lists$3\sqrt{3/2} \approx 3.674235$ citing Pesenti–Vladu, arXiv:2211.05509. That paper's v2 (14 Apr 2026) carries an erratum. Its arXiv Comments field reads verbatim:
and v2's Theorem 4.5 states$\lVert Ax\rVert_\infty \leqslant 4.1\sqrt{n} + O(1)$ . Since $3\sqrt{3/2}$ prints as 3.7, the registry holds the pre-erratum constant. The README row
3.674235 (3.65*)would become4.1 (3.65*), with an erratum row in the entry.2.$C_7$ ) is behind four papers
9a(Shannon capacity ofThe entry records$367^{1/5} \approx 3.2578$ [PS2018] and was last edited 2026-06-14, just before a cascade:
3.
4b(Furstenberg–Sárközy) may misattribute its recordThe entry credits$\tfrac12(1 + \log 12/\log 205) \approx 0.733412$ to [Lew2015], and cites Beigel–Gasarch only for the trivial $\tfrac12$ . But the abstract of Beigel–Gasarch, arXiv:0804.4892 (2008), reads verbatim:
— the same modulus 205 and the same set size 12, seven years earlier. (The
.7443...in their abstract is a typo; the value is 0.733415, and their own title says 0.7334.) Lewko's distinct contribution may well be the exhaustive verification — he reports checking every modulus below 533 by brute force and extending to 733 — rather than the construction. Settling this needs both full texts, which I have not read, so I am flagging rather than asserting.Incidentally, I can confirm the certificate reproduces:$r_2(65) = 7$ and $r_2(205) = 12$ are both optimal by exhaustive branch-and-bound, and $|B| = 12$ at $m = 205$ is provably maximal (4.6 s).
4.
45a(Romanoff) prints a certificate for a superseded boundThe section is headed "Certificate for the 0.490249407811155 upper-density bound" (Griego), but the current record row is Yoo's 0.490180063290061, which has no printed certificate. A reader who follows the printed object recomputes the second-best value.
5.
3basterisk inconsistencyThe README marks the record
1.77898 (1.77898884*)— asterisked, i.e. minimally verified under the README's own convention — while the entry's own lower-bound table lists1.77898884with no asterisk, and neither does the README's "Recent progress" line.3adoes carry asterisks inside its own table, so one of the two is wrong.6.
47abound table is ordered so the record row is not the recordIts lower-bound table lists Aldaz's 1.6211915 first and Melas's weaker 1.5675208 last, so the "last row is the record" convention that the other entries follow selects the weaker bound. The README has it right. Cosmetic for a human reader, but it defeats reading the entries mechanically.