Certificates and verifiers for "The bridge index and the nonorientable four-genus of knots with at most thirteen crossings".

Part I (bridge index):
  python3 anc/bridge/verify/verify.py                 # standard library only, 243 certificates
  pip install database_knotinfo
  python3 anc/bridge/verify/verify.py --knotinfo      # also compares with KnotInfo 2026.10.5

Part II (nonorientable four-genus):
  pip install regina database_knotinfo numpy sympy
  python3 anc/crosscap4d/verify/verify.py             # pinch certificates, checked in Regina
  python3 anc/crosscap4d/lower/verify_lower.py --selftest --certificates   # Goeritz-lattice lower bounds

The search programs are in https://github.com/creelie/conjecture-to-choose, release 1.3.0.