carlok — zsh — 88×30

cat _posts/2026-08-29-parsimagma-the-hard-core-splits-exactly-and-a-coverage-number-that-was-understated-by-its-own-denominator.md

parsimagma: the hard core splits exactly, and a coverage number that was understated by its own denominator

The Equational Theories Project’s completed implication graph turns out to be fetchable: finite_graph.json and graph.json are build artifacts the site serves and the repository does not track, and decoding them reproduces the project dashboard exactly, recovering its two remaining open cells, (677, 255) and its dual, without being told. That splits the 1,062 Vampire-unresolved implications precisely — 610 require an infinite model, 450 have a finite counterexample, 2 are still open — which settles the question parsimagma had filed as unanswerable in issue #1474, and corrects its own headline: 610 of those 1,062 admit no finite counterexample at all, so the corpus reaches 411 of 450, not 411 of 1,062. Same measurement, 39% or 91% depending on which denominator you bother to compute. The earlier claim that the circulating figure of 310 sits below a provable floor is withdrawn: counted up to duality the same set is 316, so 310 looks like a dual-class count against an earlier snapshot rather than an error. The graph is also Lean-verified, so it can contradict the engine, and does not: 790 of 790 finite witnesses agree, and 19,392 order-5 laws extracted from a fork’s branch agree too.