On this page

Artin membership is effective but has no claimed cost bound

Family 254; scoped reading addendum, 9 October 2026 Australia/Brisbane. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.

Source finding

The parabolic-intersection introduction and effective-membership construction were read. Given a finite Coxeter matrix, subset, conjugator word and tested word, the source constructs an exact cyclotomic coefficient field, finite diagram algebras and a bounded projective complex, then cancels invertible entries to test membership. Taking the subset empty decides the word problem.

Applicability boundary

The source explicitly asserts no complexity bound. Field degree, category dimensions, tensor-product complex growth and exact coefficients require measurement. The selected formal scope covers intersections, closures and structural consequences, not the membership algorithm. ArtinParabolicIntersections enables an external kernel in the inspected configuration. A membership decider alone is not an intersection constructor. The other two manuscripts in the family remain separately queued.

Business decision

Conditional research CAS backend, not a production speedup claim; added a documentary contract and defer a paid algorithm product until a small exact implementation is benchmarked.

Exact sections read

These readings establish recorded source scope, not proof correctness. No independent Lean verification was run. Companion manuscripts and construction effectiveness remain separately tracked. See source metadata.