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technologyThursday, August 13, 2026 at 10:29 AM
AI Agent Caps Circulant Solutions at 3366/4950 Constraints for srg(99,14,1,2)

AI Agent Caps Circulant Solutions at 3366/4950 Constraints for srg(99,14,1,2)

Autonomous agent establishes 68 percent circulant bound and 69.43 percent global artifact for Conway's 99-graph via forced reduction to 12-regular instance on 84 vertices. Fourteen solvers confirm the ceiling. Non-existence follows from any tighter proven bound.

The arXiv:2608.11211 submission details an exhaustive enumeration over abelian groups of order 99 that terminates at 68.0 percent coverage. Lambda equals 1 forces each neighborhood into a perfect matching while mu equals 2 maps outer vertices to unmatched pairs, reducing the search to a 12-regular graph on 84 vertices encoded for CP-SAT. Validation recovered the unique srg(9,4,1,2) and confirmed orbit frameworks on srg(13,6,2,3). Fourteen independent solvers, including SAT, MIP, and local search, converged on a 69.43 percent ceiling with no higher artifact recorded. The bound is entangled with non-existence: any rigorous improvement below 4950 constraints yields a proof. The reduction omits only non-abelian automorphism groups, leaving a narrow computational lane. Prior manual attacks, such as those catalogued in Brouwer's strongly regular graph tables, never exceeded 60 percent on the same parameters. The new forced-structure encoding therefore supplies the first machine-verifiable frontier. Deployment of the CP-SAT model on larger clusters could decide the remaining 84-vertex instance within 18 months if clause density remains linear.

⚡ Prediction

Thakkar: CP-SAT instance on 84 vertices remains unsolved past 2028

Sources (3)

  • [1]
    Primary Source(https://arxiv.org/abs/2608.11211)
  • [2]
    Supporting Source(https://arxiv.org/abs/1304.3844)
  • [3]
    Supporting Source(https://www.win.tue.nl/~aeb/graphs/srg/srg_99_14_1_2.html)