Atomic Coupled Tail Inversion Generates the Endpoint Merge
The missing correspondence between the two endpoint components is simultaneous inversion of both nonrepeated generators. It is Moore-legal and Smith-depth-profile-preserving. Either individual inversion is Moore-illegal on the endpoint stratum, so the correspondence cannot factor through admissible unary intermediates.
After adjoining this atomic coupled constructor to the known local presentation moves, the source groupoid has exactly three components of sizes sixteen, eight, and eight. They coincide with the three reflection-response Smith-depth-profile fibers. It does not preserve the full response matrix.
Thus the endpoint merge is source-generated, but its generator is irreducibly two-port relative to the legal state category.
Evidence:
- research/strominger/the-atomic-coupled-tail-inversion-generates-the-endpoint-merge.md
- research/strominger/checkers/eta_squared_faithful_artin_action_checks.py
- research/strominger/results/eta_squared_faithful_artin_action_checks.json
Verification after the observation-level audit: sixty-seven of sixty-seven exact gates pass.