From 3d729de3cbdd5003bd97d86d293936aa3babeccc Mon Sep 17 00:00:00 2001 From: Dank1995 Date: Mon, 7 Sep 2026 19:39:39 +1000 Subject: [PATCH 1/3] Update C21 upper bound to 0.172422 --- constants/21a.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/constants/21a.md b/constants/21a.md index ba6b26b8..f295b5fc 100644 --- a/constants/21a.md +++ b/constants/21a.md @@ -22,7 +22,7 @@ Newman showed in [N1976] that there exists a finite constant $C_{21}$ (the de Br | 0.2 | [PT2021] | | | 0.1965 | [MI2026] | certified record package (Euler-3 mollifier route); same barrier site; see PR | | 0.1875 | [MI2026b] | certified record package (window-tiling assembly route); same barrier site; see PR | - +| 0.172422 | [Z2026] | computer-assisted collision-exclusion descent; paper, theorem certificate, and full replay bundle | ## Known lower bounds | Bound | Reference | Comments | @@ -57,3 +57,4 @@ Newman showed in [N1976] that there exists a finite constant $C_{21}$ (the de Br - [D2020] Dobner, Alexander. "A New Proof of Newman's Conjecture and a Generalization." [arXiv:2005.05142](https://arxiv.org/abs/2005.05142) - [MI2026] Mosaic Intelligence. "A certified unconditional upper bound Λ ≤ 0.1965 for the de Bruijn–Newman constant." 2026. Paper and certificate bundle: https://doi.org/10.5281/zenodo.20724170 - [MI2026b] Mosaic Intelligence. "A certified unconditional upper bound Λ ≤ 0.1875 for the de Bruijn–Newman constant." 2026. Paper and certificate bundle: https://doi.org/10.5281/zenodo.21175533 +- [Z2026] Daniel Martin Kornaus. "A computer-assisted unconditional upper bound $\Lambda < 0.172422$ for the de Bruijn-Newman constant." 2026. Paper, theorem certificate, and full replay bundle: https://zenodo.org/records/22337308 From e28198c7b23fa89b34c86f59bde6c4e9d3f5305a Mon Sep 17 00:00:00 2001 From: Dank1995 Date: Mon, 7 Sep 2026 19:48:24 +1000 Subject: [PATCH 2/3] Update README.md --- README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index c2c630fc..2d224180 100644 --- a/README.md +++ b/README.md @@ -49,7 +49,7 @@ Bounds for which the level of available verification is currently at minimal lev | [20a](https://teorth.github.io/optimizationproblems/constants/20a.html) | Thin shell conjecture constant | 2 | $< \infty$ | | [20b](https://teorth.github.io/optimizationproblems/constants/20b.html) | Isotropic constant of a log-concave probability measure | $1/e$ | $< \infty$ | | [20c](https://teorth.github.io/optimizationproblems/constants/20c.html) | KLS constant for log-concave probability measures | $\sqrt{\pi/2} \approx 1.25331$ | $\infty$ | -| [21](https://teorth.github.io/optimizationproblems/constants/21a.html) | de Bruijn–Newman constant | 0 | 0.2 (0.1875*) | +| [21](https://teorth.github.io/optimizationproblems/constants/21a.html) | de Bruijn–Newman constant | 0 | 0.2 (0.172422*) | | [22a](https://teorth.github.io/optimizationproblems/constants/22a.html) | Tight knot constant | 1.105 | 10.76 (10.02*) | | [22b](https://teorth.github.io/optimizationproblems/constants/22b.html) | Tight alternating knot constant | 0.017 | 7.31 | | [23a](https://teorth.github.io/optimizationproblems/constants/23a.html) | Smallest unsolved instance of the Hadamard conjecture | 668 | $\infty$ | @@ -132,7 +132,7 @@ Bounds for which the level of available verification is currently at minimal lev ## Recent progress - + * [21](https://teorth.github.io/optimizationproblems/constants/21a.html) improved upper bound (unverified): $C_{21} < 0.172422*$ by Daniel Martin Kornaus, 5 Sep 2026; paper, theorem certificate, and full replay bundle: https://zenodo.org/records/22337308 - [51](https://teorth.github.io/optimizationproblems/constants/51a.html) **improved lower bound:** $C_{51} \geq 0.5850724$ by [Y. He and Q. Tang](https://arxiv.org/abs/2602.12217), 12 Feb 2026. - [11b](https://teorth.github.io/optimizationproblems/constants/11b.html) **solved:** $C_{11b} = 0.5$ by [P. Durcik, P. Ivanisvili, J. Roos, X. Xie](https://arxiv.org/abs/2602.20462), 24 Feb 2026. - [3c](https://teorth.github.io/optimizationproblems/constants/3c.html) **improved lower bound:** $C_{3c} \geq 1.67471$ by T. Astor (paper coming soon). From 9e5a2c3db8952b128f7b5c457887a917213f23b8 Mon Sep 17 00:00:00 2001 From: Dank1995 Date: Wed, 9 Sep 2026 12:50:07 +1000 Subject: [PATCH 3/3] Update Zenodo link to v1.1 --- constants/21a.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/constants/21a.md b/constants/21a.md index f295b5fc..35d49b6a 100644 --- a/constants/21a.md +++ b/constants/21a.md @@ -57,4 +57,4 @@ Newman showed in [N1976] that there exists a finite constant $C_{21}$ (the de Br - [D2020] Dobner, Alexander. "A New Proof of Newman's Conjecture and a Generalization." [arXiv:2005.05142](https://arxiv.org/abs/2005.05142) - [MI2026] Mosaic Intelligence. "A certified unconditional upper bound Λ ≤ 0.1965 for the de Bruijn–Newman constant." 2026. Paper and certificate bundle: https://doi.org/10.5281/zenodo.20724170 - [MI2026b] Mosaic Intelligence. "A certified unconditional upper bound Λ ≤ 0.1875 for the de Bruijn–Newman constant." 2026. Paper and certificate bundle: https://doi.org/10.5281/zenodo.21175533 -- [Z2026] Daniel Martin Kornaus. "A computer-assisted unconditional upper bound $\Lambda < 0.172422$ for the de Bruijn-Newman constant." 2026. Paper, theorem certificate, and full replay bundle: https://zenodo.org/records/22337308 +- [Z2026] Daniel Martin Kornaus. "A computer-assisted unconditional upper bound $\Lambda < 0.172422$ for the de Bruijn-Newman constant." 2026. Paper, theorem certificate, and full replay bundle:https://zenodo.org/records/22658444