Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines split EVENLY into two line-operation types (in the natural F_11 parameterization x ◇ y = (1-α)x + αy):
• 6 parallel classes use α = 6 (the F_11 midpoint quasigroup x ◇ y = 6(x+y) mod 11, which is commutative).
• 6 parallel classes use α = 7 (the non-commutative operation x ◇ y = 5x + 7y mod 11).
Globally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. The display reorder presents points as (h, v) ∈ F_11 × F_11; all 11 diagonal 11×11 blocks render as the identical F_11(α=6) Cayley table, and the 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation. Compare 985e14d6, which has the same combinatorial AG(2, 11) structure but an uneven 8 × α=6 / 4 × α=8 split.
[text written by Claude]
dwrensha · 2026-05-13 11:40:13
Size-121 idempotent right-cancellative magma whose 2-generated sub-quasigroups are exactly the 132 lines of the affine plane AG(2, 11). The 12 parallel classes of lines split EVENLY into two line-operation types (in the natural F_11 parameterization x ◇ y = (1-α)x + αy):
• 6 parallel classes use α = 6 (the F_11 midpoint quasigroup x ◇ y = 6(x+y) mod 11, which is commutative).
• 6 parallel classes use α = 7 (the non-commutative operation x ◇ y = 5x + 7y mod 11).
Globally NOT medial. Each pair of distinct points lies on a unique 11-element sub-quasigroup. The display reorder presents points as (h, v) ∈ F_11 × F_11; all 11 diagonal 11×11 blocks render as the identical F_11(α=6) Cayley table, and the 11 'vertical' lines (one point per block-row) carry the F_11(α=7) operation. Compare 985e14d6, which has the same combinatorial AG(2, 11) structure but an uneven 8 × α=6 / 4 × α=8 split.
dwrensha · 2026-05-13 11:45:48
dwrensha · 2026-05-13 11:40:13