Improve C10c lower bound to 4/sqrt(6)

[sebastian-griego]

Summary

This updates constants/10c.md with a finite-dimensional certificate giving

C_{10c} >= 4/sqrt(6) ≈ 1.632993.

The certificate uses a 6 by 6 sign matrix A with

disc(A) = min_{x in {±1}^6} ||Ax||_∞ = 4.

This improves the previously displayed lower bound of sqrt(2).

Certificate

The added certificate gives the explicit matrix

 1   1   1   1   1   1
-1  -1  -1   1   1   1
-1   1   1  -1   1   1
-1   1  -1   1  -1   1
 1   1  -1  -1   1   1
 1  -1   1  -1  -1   1

The page includes a finite Hamming-covering verification showing that every sign vector satisfies

||Ax||_∞ >= 4.

Equality is attained, for example at

x = (1,-1,1,1,1,1)^T,

where

Ax = (4,2,0,-2,0,2)^T.

Therefore disc(A) = 4, giving the claimed lower bound.

Verification

The certificate was checked by exhaustive enumeration of all 2^6 = 64 sign vectors. The computation confirms that the minimum value of ||Ax||_∞ is exactly 4.

Changed file

• constants/10c.md

AI assistance disclosure

The construction, patch, PR text, and verification script were prepared with assistance from ChatGPT 5.5 Pro. The submitter rechecked the construction and arithmetic before submission.