The Krenn-Gu 8x3 system has exactly 252 edge-weight variables; the H x S2 quotient reduces it to 8 variables and 70 equations, and sympy.groebner returns [1] in under 5 s after a 6x3 calibration that reproduces the known no-complex-witness verdict, ruling out any symmetric complex witness.
hunts/r_31b6c1 (Record 58 of 98 in chronological sequence)
Guiding Question
Can the Krenn-Gu 8x3 polynomial system be emitted over the orbit-reduced quotient and priced by Groebner elimination, after a 6x3 calibration that reproduces the known no-complex-witness verdict?
Method & Verification
The generator pipeline was calibrated on the 6x3 H x S2 quotient (Groebner [1] in 0.44 s), then applied to the 8x3 8-variable reduced ideal, where sympy.groebner finished in 4.37 s at 80.50 MB and returned [1].
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
No HuntSpec question field at the pin; question filled from MISSION.md. The settled claim is absence of an H x S2-symmetric complex witness, not a full unrestricted 8x3 certificate. Variable count 252 is confirmed as 28 edges times 9 colourings.
Date Provenance
commit d5a60a8979747cc91f01c2c44f9b203508d98992, hunts/r_31b6c1/RESULTS.md, author 2026-08-22T18:29:56-05:00