r2_families_fp.py -- verification run 2, KOU-15.75
[1] Lemma 3.2 for all 17983 odd primes p < 200000: failures 0
[2] brute-force roots and root finder for odd p < 3000: failures 0
[3] Lemma 3.3 (D takes (p+1)/2 values, meets the squares; construction works): 79214 cases (5 <= p <= 700, all t, both x), failures 0
[4] families with explicit matrices: 476 primes (all 5<=p<=3000 and 48 primes near 10^6, 10^9, 10^12, 10^18); instances L1 (K and O) 1072, L2 (K) 2032 (each root, plain and conjugated pair); y not found 0; failures 0
[5] negative controls (t not a root of g): 41 cases, unexpected passes 0
[6] example p=17, t=2, x=[[0,-1],[1,0]], y=[[1,2],[0,1]] (K): u_2 = (15, 1, 12, 2), u_3 = (2, 16, 5, 15), -u_3 = (15, 1, 12, 2)
    example p=7, t=2, x=[[0,-1],[1,1]], y=[[1,1],[0,1]] (K): u_2 = (1, 6, 1, 0), u_4 = (1, 6, 1, 0)  (text: [[1,-1],[1,0]] = (1,6,1,0) mod 7)
TOTAL failures: 0   (time 8.2s)
