{"targets":[{"slug":"riemann-hypothesis","name":"The Riemann Hypothesis","statement":"Every nontrivial zero of the Riemann zeta function has real part 1/2.","status":"open","node_count":81,"edge_count":83,"paper_edge_count":63,"composed_count":4,"novel_count":1,"sufficient_count":6,"last_run_at":"2026-08-13T12:30:24.983102+00:00"},{"slug":"abc-conjecture","name":"The abc Conjecture","statement":"For every epsilon > 0, only finitely many coprime triples a + b = c satisfy c > rad(abc)^(1+epsilon).","status":"open","node_count":5,"edge_count":4,"paper_edge_count":4,"composed_count":0,"novel_count":0,"sufficient_count":0,"last_run_at":"2026-08-13T12:30:24.526552+00:00"},{"slug":"birch-swinnerton-dyer","name":"Birch and Swinnerton-Dyer","statement":"For every elliptic curve over Q, the rank of the Mordell-Weil group equals the order of vanishing of its L-function at s = 1.","status":"open","node_count":2,"edge_count":1,"paper_edge_count":1,"composed_count":0,"novel_count":0,"sufficient_count":0,"last_run_at":"2026-08-13T12:30:24.567968+00:00"},{"slug":"collatz","name":"The Collatz Conjecture","statement":"Iterating n to n/2 for even n and 3n+1 for odd n reaches 1 from every positive integer.","status":"open","node_count":1,"edge_count":0,"paper_edge_count":0,"composed_count":0,"novel_count":0,"sufficient_count":0,"last_run_at":"2026-08-13T12:30:24.611251+00:00"},{"slug":"goldbach","name":"Goldbach's Conjecture","statement":"Every even integer greater than 2 is a sum of two primes.","status":"open","node_count":2,"edge_count":1,"paper_edge_count":1,"composed_count":0,"novel_count":0,"sufficient_count":1,"last_run_at":"2026-08-13T12:30:24.649417+00:00"},{"slug":"hodge-conjecture","name":"The Hodge Conjecture","statement":"On a nonsingular complex projective variety, every rational Hodge class is a rational combination of classes of algebraic cycles.","status":"open","node_count":1,"edge_count":0,"paper_edge_count":0,"composed_count":0,"novel_count":0,"sufficient_count":0,"last_run_at":"2026-08-13T12:30:24.684740+00:00"},{"slug":"navier-stokes","name":"Navier-Stokes Regularity","statement":"Smooth, globally defined solutions exist for the three-dimensional incompressible Navier-Stokes equations with smooth initial data.","status":"open","node_count":1,"edge_count":0,"paper_edge_count":0,"composed_count":0,"novel_count":0,"sufficient_count":0,"last_run_at":"2026-08-13T12:30:24.739129+00:00"},{"slug":"p-vs-np","name":"P versus NP","statement":"Whether every language decidable in nondeterministic polynomial time is decidable in deterministic polynomial time.","status":"open","node_count":5,"edge_count":4,"paper_edge_count":4,"composed_count":0,"novel_count":0,"sufficient_count":1,"last_run_at":"2026-08-13T12:30:24.833851+00:00"},{"slug":"twin-primes","name":"The Twin Prime Conjecture","statement":"There are infinitely many primes p such that p + 2 is prime.","status":"open","node_count":2,"edge_count":1,"paper_edge_count":1,"composed_count":0,"novel_count":0,"sufficient_count":1,"last_run_at":"2026-08-13T12:30:25.039919+00:00"},{"slug":"yang-mills-mass-gap","name":"Yang-Mills Mass Gap","statement":"For every compact simple gauge group, quantum Yang-Mills theory on R^4 exists and has a mass gap greater than zero.","status":"open","node_count":1,"edge_count":0,"paper_edge_count":0,"composed_count":0,"novel_count":0,"sufficient_count":0,"last_run_at":"2026-08-13T12:30:25.191049+00:00"}]}