# Verification of the generating pair

The original researcher accepts the elementary proof in Lemma 2 and its
application in Theorem 1. The key identity is
`a=s^-2*t*s^-1*t^2`, where `s=u^-1*v` and `t=u*v^-1`.
It follows by reversible multiplication from the first five equations of
the source presentation; it is an ordinary generation statement, not normal
generation. Radu's theorem supplies the noncyclic infinite simple group.

Proposition 3 was checked in both directions. Under the proposed seven
equations, `C^2=E^2` gives `S=C^-1*E=C*E^-1` and `T=A*S*A^-1`. The recovery
formula for A therefore recovers the omitted relation `B^2=D*A^-1*D`.
The other six equations were compared term by term with Radu's equations
6 through 11. The two homomorphisms compose to the identity on every original
generator and on u,v. Seven is an upper bound on the number of defining
equations, not a minimality claim.

The supplementary coset certificate has 146 events and a separate verifier.
The free-word certificate has 40 instructions and is checked by exact stack
cancellation. Its words for a,c,e have lengths 12,13,13 and agree with the
elementary formula. Ten deliberately corrupted controls are rejected across
the two checkers. Three elementary free-word identities are checked exactly.
The 14,049 symmetric-group triples checked through degree four are bounded
regressions, not the proof of the theorem.

Independent external review and proof-assistant verification were not
performed. The broad AIM problem remains unresolved. Full compilation,
page inspection, hashes and isolated replays are recorded separately in
the package manifest, visual QA and reproducibility receipts.