diff --git a/constants/59a.md b/constants/59a.md index 4981408..0254747 100644 --- a/constants/59a.md +++ b/constants/59a.md @@ -43,10 +43,10 @@ The exact value of $K_d$ is unknown for every $d>1$; in particular, the exact va The best established range currently is $$ -0.3006\ \le\ K_2\ <\ 0.3177. +0.3006\ \le\ K_2\ <\ 0.3174541. $$ -[Kne2025-lb-K2-0-3006] [BPWW2026-ub-K2-0-3177] +[Kne2025-lb-K2-0-3006] [G2026-ub-K2-0-3174541] ## Known upper bounds @@ -54,6 +54,7 @@ $$ | ----- | --------- | -------- | | $1/3$ | [BK1997] | General upper bound $K_n\le 1/3$ (hence $K_2\le 1/3$). [BK1997-ub-1-3] | | $0.3177$ | [BPWW2026] | Explicit construction giving $K_2<0.3177$ (Theorem 6.4). [BPWW2026-ub-K2-0-3177] | +| $0.3174541$ | [G2026] | Degree-$(250,250)$ polynomial from a rational-inner Fejer averaging certificate. Exact integer verification gives $B\_{3174541/10000000}(p)>1$. [G2026-ub-K2-0-3174541] | ## Known lower bounds @@ -118,6 +119,11 @@ $$ **loc:** arXiv v1 PDF p.18, Theorem 6.4 **quote:** “Theorem 6.4. $K_2<0.3177$.” +- **[G2026]** Griego, Sebastian. Rational-inner Fejer averaging certificate for the bidisc Bohr radius bound $K\_2<0.3174541$, [submitted to this repository](https://github.com/teorth/optimizationproblems/pull/75) (2026). + - **[G2026-ub-K2-0-3174541]** + **loc:** pull request certificate and exact verifier + **quote:** “The exact integer verifier proves $B\_{3174541/10000000}(p)>1+1/7307638490$ and the rational-inner Fejer averaging certificate proves $\lvert p\rvert\le 1$ on the bidisc.” + ## Contribution notes -Prepared with assistance from ChatGPT 5.2 Pro. +Prepared initially with assistance from ChatGPT 5.2 Pro and updated with assistance from ChatGPT 5.5 Pro.