Replace the withdrawn Pesenti–Vladu 3.7 bound on C₁₀c with 4.1

README.md

@@ -33,7 +33,7 @@ Bounds for which the level of available verification is currently at minimal lev
 | [9](https://teorth.github.io/optimizationproblems/constants/9a.html) | Shannon capacity of the 7-cycle | 3.2578 | 3.3177 |
 | [10a](https://teorth.github.io/optimizationproblems/constants/10a.html) | The real Grothendieck constant | $\frac{6\pi}{11}\approx 1.71360$ | $\frac{\pi}{2\log(1+\sqrt{2})} - 10^{-4} \approx 1.78211$ |
 | [10b](https://teorth.github.io/optimizationproblems/constants/10b.html) | The complex Grothendieck constant | 1.338 | 1.40491 |
-| [10c](https://teorth.github.io/optimizationproblems/constants/10c.html) | Spencer discrepancy constant (“six standard deviations suffice”) | 1.697749 | 3.674235 (3.65*) |
+| [10c](https://teorth.github.io/optimizationproblems/constants/10c.html) | Spencer discrepancy constant (“six standard deviations suffice”) | 1.697749 | 4.1 (3.65*) |
 | [11a](https://teorth.github.io/optimizationproblems/constants/11a.html) | $L^1$ Poincaré constant on the Hamming cube | $\sqrt{\pi/2} \approx 1.2533$ | $\pi/2 - 0.00013 \approx 1.5707$ |
 | [11b](https://teorth.github.io/optimizationproblems/constants/11b.html) | Critical exponent for isoperimetric inequality on the Hamming cube | 0.5 | 0.5 |
 | [12](https://teorth.github.io/optimizationproblems/constants/12a.html) | The Beardwood–Halton–Hammersley constant | 0.6277 | 0.90304 |
@@ -159,6 +159,8 @@ Bounds for which the level of available verification is currently at minimal lev
 - [43](https://teorth.github.io/optimizationproblems/constants/43a.html) **improved lower bound (unverified):** $C_{43} \geq 0.860*$ (exact $43/50$; certificate-layer result conditional on the lemma set of [KHSHGW2026](https://arxiv.org/abs/2601.22365)) by [J. Savva](https://doi.org/10.5281/zenodo.22223485), 1 Sep 2026.
 - [88a](https://teorth.github.io/optimizationproblems/constants/88a.html) **improved upper bound:** $C_{88a} \leq 186$ via $\mathrm{DHL}[40,2]$, by [OpenAI](https://cdn.openai.com/pdf/51126fac-1b68-4128-9666-c908bcc16033/short_gaps.pdf), 30 Aug 2026, with a Lean 4 formalization conditional on three declared axioms.
 
+- [10c](https://teorth.github.io/optimizationproblems/constants/10c.html) **upper bound correction:** $C_{10c}\le 4.1$ by [Pesenti–Vladu](https://arxiv.org/abs/2211.05509) v2 (14 Apr 2026), replacing the withdrawn $3\sqrt{3/2}$ constant in Theorem 4.5.
+
 ## Maintainers
 
 This site is maintained by Damek Davis, Paata Ivanisvili and Terence Tao.

constants/10c.md

@@ -36,7 +36,8 @@ $$
 | $5.32$ | [Spe1985] | Usually reported as $6$. The celebrated “six standard deviations suffice” theorem of Spencer; also applies to rectangular matrices or set systems. |
 | $5.199$ | [Bel2013] | Re-optimizes Spencer’s method. |
 | $3.65$ (unpublished) | Schmidt [Bel2013] | Some of the computations are given only as a personal communication. |
-| $3\sqrt{3/2}\approx 3.674235$ | [PV2022] | Also gives an algorithmic version. |
+| $3\sqrt{3/2}\approx 3.674235$ | [PV2022] | Withdrawn. arXiv v2 (14 Apr 2026) comments: “the constant in Theorem 4.5 is corrected from 3.7 to 4.1”. |
+| $4.1$ | [PV2022] | v2 Theorem 4.5: $\lVert Ax\rVert_\infty\leqslant 4.1\sqrt{n}+O(1)$. Algorithmic. |
 
 ## Known lower bounds
 
@@ -360,3 +361,5 @@ The centres $T_i$ were found by a greedy set-cover search for a small radius-$5$
 ## Contribution notes
 
 ChatGPT Pro was used to generate an initial version of this page.
+
+The v2 erratum on Theorem 4.5 was checked against the arXiv comments field of [2211.05509](https://arxiv.org/abs/2211.05509) and against the statement of Theorem 4.5 in the v2 html. AI assistance was used to draft the wording.