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Update constant 45a #125

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Update 45a
andrew-yoo Jul 2, 2026
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Update README
andrew-yoo Jul 2, 2026
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2 changes: 1 addition & 1 deletion README.md
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Expand Up @@ -77,7 +77,7 @@ Bounds for which the level of available verification is currently at minimal lev
| [42](https://teorth.github.io/optimizationproblems/constants/42a.html) | Turan's pure power sum constant | 0.5 | 0.69368 |
| [43](https://teorth.github.io/optimizationproblems/constants/43a.html) | Gilbert-Pollak conjecture (Steiner ratio) | 0.8559 | 0.86602540378 |
| [44](https://teorth.github.io/optimizationproblems/constants/44a.html) | Maximal number of relevant variables in degree-$d$ Boolean functions | 1.5 | 4.394 |
| [45](https://teorth.github.io/optimizationproblems/constants/45a.html) | Density of odd integers that are the sum of a prime and a power of two | 0.107648 | <0.490248930138966 |
| [45](https://teorth.github.io/optimizationproblems/constants/45a.html) | Density of odd integers that are the sum of a prime and a power of two | 0.107648 | 0.490180063290061 |
| [46](https://teorth.github.io/optimizationproblems/constants/46a.html) | Fourier restriction constant for the 2-sphere | 3 | $\frac{22}{7}\approx 3.142857$ |
| [47](https://teorth.github.io/optimizationproblems/constants/47a.html) | Centered Hardy-Littlewood maximal constant in dimension $2$ | $\frac{11+\sqrt{61}}{12}\approx 1.5675208$ | 4 |
| [48](https://teorth.github.io/optimizationproblems/constants/48a.html) | One-dimensional convex sub-Gaussian comparison constant | $\approx 5.33386$ | $\approx 5.33386$ |
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6 changes: 3 additions & 3 deletions constants/45a.md
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Expand Up @@ -12,8 +12,8 @@ $C_{45}$ is the asymptotic density (if it exists) of the set of odd integers tha
| $<0.5$ | [E1950] | Used covering systems |
| $0.490941$ | [HR2006] | |
| $0.490341088858244$ | [CDL2024] | |
| $<0.490249407811155$ | [G2026] | 36-prime finite obstruction certificate with exact cluster-update verification. |
| $<0.490248930138966$ | [Y2026] | |
| $0.490249407811155$ | [G2026] | 36-prime finite obstruction certificate with exact cluster-update verification. |
| $0.490180063290061$ | [Y2026] | |

## Known lower bounds

Expand Down Expand Up @@ -83,7 +83,7 @@ The external verifier independently recomputes the 13-prime seed histogram from

- [G2026] Griego, Sebastian. 36-prime obstruction certificate for Romanoff's constant upper-density bound, 2026. [Code and verification](https://github.com/sebastian-griego/c45-romanoff-certificate/tree/v1-c45-certificate).
- [G2026-ub-0-490249407811155] **loc:** external verifier repository, `verify_all.sh`. **quote:** "The exact rational verifier proves the upper-density bound \(\overline d(A)<0.490249407811155\)."
- [Y2026] Yoo, Andrew, "An improved upper bound on Romanoff's constant," 2026. https://github.com/andrew-yoo/romanoff/tree/v2.
- [Y2026] Yoo, Andrew, "An improved upper bound on Romanoff's constant," 2026. https://github.com/andrew-yoo/romanoff/tree/v3.


## Contribution notes
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