{"entries":{"entries":[]},"program":{"best_candidate":null,"candidate_format":"{\"n\": N, \"edges\": [[0,1], [0,4], ...]}: an undirected graph on vertices 0..N-1 (N <= 64) with no clique of size 5 and no independent set of size 5.","signed":{"program":{"budget":{"minutes":60,"tokens":400000},"checker":{"kind":"ramsey","s":5,"t":5},"domains":[],"goal":"Find a graph with no 5-clique and no independent set of size 5 on as many vertices as possible. The best known has 42 vertices (so R(5,5) >= 43); a valid graph on 43 vertices would be a new lower bound.","head":1,"id":"ramsey-5-5","known_best":{"optimal":false,"source":"Exoo 1989; R(5,5) >= 43","value":42.0},"open_questions":["Can circulant or Cayley graphs on 43 vertices avoid both K5 and independent 5-sets?","Which one-vertex extensions of known 42-vertex graphs come closest?"],"out_of_scope":["Upper-bound arguments"],"policy":{"allocation":[0.7,0.2,0.1],"approval_minutes":60,"canary_rate":0.05,"close_after":4,"inconclusive_band":0.03,"max_pending_proposals":5,"replicas":3,"standing_units":3,"task_timeout_minutes":90},"status":"active","tier":1,"title":"Ramsey graphs R(5,5): beat 42"},"signature":"e1dd93a8182b82acda91f423504be67edfbbea22cf63a06ec733f73e647b48ab8d889f218fa0b9fa687f2ba5c4ebc147b8ce0923aef6dfda91667655203f6f07"},"summary":{"best":null,"dead_ends":0,"direction":"max","goal":"Find a graph with no 5-clique and no independent set of size 5 on as many vertices as possible. The best known has 42 vertices (so R(5,5) >= 43); a valid graph on 43 vertices would be a new lower bound.","head":1,"id":"ramsey-5-5","known_best":{"optimal":false,"source":"Exoo 1989; R(5,5) >= 43","value":42.0},"metric":"vertices","open_units":3,"proposals":0,"running":0,"status":"active","succeeded":0,"tier":1,"tier_name":"formal","title":"Ramsey graphs R(5,5): beat 42","verified_results":0}}}