Steiner system S(6,7,23): four automorphism groups eliminated via Kramer-Mesner

Partial progress on Open Subproblem 1 from Epoch AI's FrontierMath
(https://epoch.ai/frontiermath/open-problems/large-steiner-systems):
construct a Steiner system with t > 5.

Using Kramer-Mesner reductions, I have computationally eliminated four
candidate automorphism groups for S(6,7,23):

- M₂₃: trivial 3×4 KM matrix, no exact cover (category: research solved)
- AGL(1,23): structural uncoverable row (category: research solved)
- Z₂₃⋊Z₁₁: exhaustive DLX search, 11M nodes, UNSAT (category: research solved)
- D₂₃: divisibility-2 obstruction (category: research solved)

The Z₂₃ case (4389×10648 KM matrix) remains open and is currently
running under CP-SAT with 80 workers (category: research open).

Related to #3524. References the FrontierMath large Steiner systems
open problem. I plan to contribute Lean formalizations of these results.

The issue names no repository files, tests, or Lean entry points. Start by reading the linked FrontierMath problem and related issue #3524, then review the four Kramer–Mesner eliminations and the open Z₂₃ case. Done means formalizing the reported results in Lean, as proposed in the issue.

Written by the indexing model from the issue text.