The two pieces of shared vocabulary the catalog's problems are stated with. On a CNF structure of the NP core's vocabulary, IsCl, PosIn, NegIn and OccIn read off clauses and the signed occurrences of variables in them, and LitTrue evaluates a literal under an assignment; the satisfiability variants (3SAT, NAE-SAT, 1-in-SAT) are written with these. On a structure carrying a set of bit positions and an order on them, bitRank is the number of positions strictly below a position and binNum decodes a set of positions as the number whose binary digits they are; the problems written in binary (Knapsack, Partition, 0-1 integer programming, job sequencing) compare numbers decoded this way. Both decoders are total, defined for an arbitrary relation in place of the order, so that isomorphism-invariance is a plain transport statement.