Carrier: F_131 x F_5, encoded by 5*x+u. QR/NQR fiber extension. Base operation on F_131: x o y = 54x + 78y (mod 131), where beta=53 is a primitive 5th root and both -1 and beta+1 are quadratic non-residues. For d=y-x: the fiber law is 2u+4v (mod 5) when d=0, right projection v when d is a nonzero quadratic residue, and -u-v (mod 5) when d is a non-residue. Direct check of the 655x655 table: Eq 677 and Eq 255 hold; fully idempotent; left-cancellative; not right-cancellative; nonmedial. Right-cancellation witness: 10*0=540=11*0. Medial witness: (0*0)*(1*5)=290, while (0*1)*(0*5)=291. This is not a direct product: the fiber operation depends on the QR/NQR class of the base difference.
omegaestable · 2026-08-17 04:08:23