The corpus, as data

Every knot here, with the invariants our pipeline computes — and with two things the standard catalogues do not tabulate: the Bar-Natan–van der Veen θ cluster-hash, and, for knots beyond the named range, a crossing-number statement.

KnotInfo names knots through 13 crossings; Benjamin Burton’s census completely enumerates prime knots through 19. We compare each of our knots against both. A match in the census reveals its exact minimal crossing number; absence from the complete census through c crossings is a proof that its crossing number exceeds c (our knots are hyperbolic, hence prime, so if they were that small they would appear). 400 knots in this table carry a proven lower bound — from absence in the complete census, from the span of the Jones polynomial (Kauffman–Murasugi–Thistlethwaite), or from the genus; they read ‘L ≤ c ≤ N’. A bare ‘≤ c’ entry is an honest upper bound, not a final crossing number. Only knots with a proven L ≥ 21 are marked novel.