The 6x3 checksum of 15 matchings, 3375 triples, and 8 S6 x S3 orbits is verified, and the 8x3 frontier of 105 matchings and 1,157,625 triples partitions into exactly 31 S8 x S3 orbits with matching Burnside and orbit-stabilizer counts.
hunts/r_322dae (Record 51 of 98 in chronological sequence)
Guiding Question
What is the exact orbit census and stabilizer decomposition of the 1157625 monochromatic matching triples in the Krenn-Gu 8x3 problem under S8 x S3 symmetry?
Method & Verification
The 31 orbits were obtained both by exhaustive disjoint partition of the 1,157,625 triples and by Burnside evaluation over S8 x S3 conjugacy classes, after a 6x3 calibration against the known 8-orbit checksum.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
Later hunt r_044dd2 withdraws the claim that these 31 orbits quotient the full 252-variable polynomial system; they remain an exhaustive outer branch cover. That correction is not retrofitted into this row's headline. Evidence is combinatorial exactness, not a Lean kernel check.
Date Provenance
commit 892010f501d8ab6aea27136a1a1cc5fdb46ff9b5, hunts/r_322dae/RESULTS.md, author 2026-08-21T23:30:26-05:00