Certificates and verification scripts for the Cohn-Elkies bound in dimensions 14 and 10

Exact data and stand-alone verification scripts for the Cohn-Elkies linear programming bound for sphere packings in dimensions 14 and 10. They accompany the manuscript "The Cohn-Elkies linear programming bound is not sharp in dimension 14". The archive holds two certificates. The first is a modular form of weight 7 on Gamma_0(36), a sum of forms with characters chi_-3 and chi_-4, which gives a center-density bound of 0.0754569 in dimension 14. The second is a modular form of weight 5 on Gamma_0(64) with character chi_-4, which gives a bound of 0.0572027 in dimension 10. Non-sharpness in dimension 10 was stated earlier in arXiv:2610.24944; the dimension 10 certificate gives a larger dual bound. Each folder contains the certificate (exact rational coordinates), a Python script that rechecks every inequality the argument uses in exact arithmetic (PARI/GP through cypari, python-flint, mpmath), the saved output of a run in a clean folder, and a notes file that states the claim and lists the trusted inputs. SHA-256 checksums for all files are in SHA256SUMS.txt inside the archive.