cat _posts/2026-09-06-parsimagma-the-820-infinite-only-pairs-enumerated.md
parsimagma: the 820 infinite-only pairs, enumerated
parsimagma now
enumerates, pair by pair,
every implication that is false in general but holds for every finite magma:
820 ordered pairs — 610 from the unresolved hard core and 210 from the
saturation-refuted set — decoded from the ETP’s closed implication graphs into
data/etp/infinite-only.tsv. The exact split answers the question left open
in the project’s
#1474, and it
makes the corpus’s coverage readable honestly: 610 of the 1062 hard-core pairs
can never be refuted by a finite construction, so the real figure is 411 of
the 450 finitely refutable (91%), with the remaining 39 listed. A differential
test against the ETP’s Lean-verified finite graph agrees on all 797 finite
claims.