\$ ./flagmatic --n 6 --r 3 --induced-density 5.9 --dir output/max59 flagmatic version 1.5 ============================================================================ Optimizing for density of 5.9. Using admissible graphs of order 6. Generated 1 type of order 0, with 2 flags of order 3. Generated 1 type of order 2, with 12 flags of order 4. Generated 5 types of order 4, with [64, 64, 64, 64, 64] flags of order 5. Generated 2136 admissible graphs. Approximate floating-point bound is 0.62500000 \$ sage -python scripts/find_sharp_graphs.py --dir output/max59 Floating point bound is 0.625000000006370460. 4 members of H are sharp. 0.624999999987251531 : graph 1 (6:) 0.625000000004181211 : graph 893 (6:123124125126134135136145146156) 0.625000000006370460 : graph 2104 (6:123124125126134135136145146156234235236245246256) 0.625000000005618617 : graph 2134 (6:123124125126134135136145146235236245246256345346356456) Written sharp graphs to flags.py \$ sage -python scripts/check_construction.py --n 6 --r 3 --induced-density 5.9 --vertex-transitive 2:112122 Density of 5.9 is 5/8. 4 graphs of order 6 occur as induced subgraphs of the blow-up: 6: has density 1/32 (0.031250) 6:123124125126134135136145146156 has density 3/16 (0.187500) 6:123124125126134135136145146156234235236245246256 has density 15/32 (0.468750) 6:123124125126134135136145146235236245246256345346356456 has density 5/16 (0.312500) \$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 2:112122 --dir output/max59 Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 2 out of 2 zero eigenvectors for type 2. Constructed 1 out of 1 zero eigenvectors for type 3. Constructed 0 out of 0 zero eigenvectors for type 4. Constructed 0 out of 0 zero eigenvectors for type 5. Constructed 1 out of 1 zero eigenvectors for type 6. Constructed 3 out of 3 zero eigenvectors for type 7. Written zev.py Written field to flags.py \$ sage -python scripts/factor_approximate_q.py --dir output/max59 Floating point bound is 0.625000000006370460. Type 1: smallest eigenvalue is 0.131219837362048564 Type 2: smallest eigenvalue is 0.016288538072509493 Type 3: smallest eigenvalue is 0.144840013734284789 Type 4: smallest eigenvalue is 0.126877809427999783 Type 5: smallest eigenvalue is 0.123613333741116119 Type 6: smallest eigenvalue is 0.049018046075125776 Type 7: smallest eigenvalue is 0.005163244188996869 Written r.py Written qdashf.py \$ sage -python scripts/make_exact_qdash.py '5/8' --denominator 240 --dir output/max59 --diagonalize Type 1: smallest eigenvalue is 0.134726840247339691 Type 2: smallest eigenvalue is 0.013409301550552553 Type 3: smallest eigenvalue is 0.137034063062108274 Type 4: smallest eigenvalue is 0.126160880500172601 Type 5: smallest eigenvalue is 0.121495946233677363 Type 6: smallest eigenvalue is 0.048052766793083290 Type 7: smallest eigenvalue is 0.002360011222993049 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py \$ sage -python scripts/verify_bound.py --dir output/max59 Written q.py Floating point bound (non-sharp graphs) is 0.623737450005478977 Exact bound (just sharp graphs) is 5/8 Bound (all graphs) is 5/8 \$ sage -python scripts/make_certificate.py --dir output/max59 Written certificate to cert.js