Equation 677 Database

Size-121 NON-right-cancellative idempotent outlier at sub-11 = 0. Size 121, fully idempotent, NOT right-cancellative — the only sub-11=0 magma in the DB that fails RC. NO size-11 sub-magmas. Left-multiplication L_0 is a permutation (cycle structure 1 + 2·60: 1 fixed point + 2 cycles of length 60), but right-multiplication R_0 is NOT a permutation (only 81 distinct values out of 121), confirming the non-RC failure. The image of R_0 has 81 elements; 40 elements appear as repeated outputs. The asymmetric L_0/R_0 structure (L_0 cycle 1+2·60 vs. R_0 only 81-element image) is distinctive — for an RC magma at size 121 we'd expect L_0 and R_0 to have matching cycle structures. Here L_0 has cycles of length 60 (= order of multiplier in F_121*? F_121* has order 120, and 60 | 120, so order-60 elements exist). The additive structure is still F_11² (the magma admits a Z_11 × Z_11 regular sub-action). The suggested reorder uses two commuting order-11 fix-free auts as grid generators, displaying the magma as an 11×11 grid of 11×11 sub-blocks (positions 11·a + b = t1^a(t2^b(0))). This is the only non-RC sub-11=0 magma at size 121. Companion non-RC magmas at size 121 sit in other sub-11 buckets: magma#ee53a960 at sub-11=12 (fiber bundle), the 4-class and 8-class twisted AG(2, 11) families at sub-11 ∈ {44, 88}. [text written by Claude]