t1ha2-64 (t1ha2_atonce, 64-bit output, 64-bit seed): fixed message pairs under random seeds validation: upstream KAT 81/81 ok; SMHasher3 verification 0x8F16C948 (want 0x8F16C948) ok rng: xoshiro256** seeded by splitmix64(1 + pair index) pair F60 (selected pair) m1 (13 bytes) = c4c0cc2284cd239ede36a18fa6 m2 (16 bytes) = fbc31866049ec02dea0c4e2be580d3cf mechanism: 13-byte vs 16-byte messages: 5-digit route +2^60+2^54-2^48-2^9-2^1; 24 fixed bits of L, measured carry cancellation uniform seeds: N = 2^20.00 (1048576): 0 collisions, rate unestimated (zero observed in 2^20.00 trials) (expected at the published 2^-28.19: 0.003) seed class: (L & a5845081f808f44a) == 2080000118003408, L = lo(((seed ^ l0) + t) * P1), density 2^-24 conditional: N = 2^20.00 seeds in the class: 57150 collisions, rate 2^-4.20 => estimated class contribution = 2^-24 * 2^-4.20 = 2^-28.20 (published 2^-28.19) first class colliding seed: 62287e4a66a54435 explicit seed 4c240c2749cd4915: H(m1) = c35b49165b1a4480 H(m2) = c35b49165b1a4480 COLLIDE (L = 60980e4d1a6137ac, in class: yes) pair A (historical control) m1 (16 bytes) = 406b68c281a55e00158ed10a0d96f8ff m2 (11 bytes) = d1d86241d24d9f990323e0 mechanism: 16-byte vs 11-byte messages: a signed-digit difference in word 0 (public (len+w0)*P2 shift) is cancelled by the tail word's carry pattern through P1; only 26 bits of L and 4 carry signs depend on the seed uniform seeds: N = 2^20.00 (1048576): 0 collisions, rate unestimated (zero observed in 2^20.00 trials) (expected at the published 2^-30.00: 0.001) seed class: (L & 7f868a5066451822) == 16808a1062000020, L = lo(((seed ^ l0) + t) * P1), density 2^-26 conditional: N = 2^20.00 seeds in the class: 65785 collisions, rate 2^-3.99 => estimated class contribution = 2^-26 * 2^-3.99 = 2^-29.99 (published 2^-30.00) first class colliding seed: 496126831f847b53 explicit seed 3c805cc67a687f30: H(m1) = f2a1196d24fddaab H(m2) = f2a1196d24fddaab COLLIDE (L = 96b1df91fb0202ed, in class: yes) pair B (same mechanism, second digit route) m1 (13 bytes) = 9858cabfcf20f692468be82bd3 m2 (16 bytes) = 95589a09e664a742a4ac26262cc7fdfc mechanism: 13-byte vs 16-byte messages: 4-digit route +2^56-2^46-2^20+2^50 on the word-0 product, tail difference chosen so the P1 carries cancel it; 27 bits of L and 4 carry signs fixed uniform seeds: N = 2^20.00 (1048576): 0 collisions, rate unestimated (zero observed in 2^20.00 trials) (expected at the published 2^-31.01: 0.000) seed class: (L & 4d4ce1e6964c5012) == 4c408040000c1012, L = lo(((seed ^ l0) + t) * P1), density 2^-27 conditional: N = 2^20.00 seeds in the class: 65084 collisions, rate 2^-4.01 => estimated class contribution = 2^-27 * 2^-4.01 = 2^-31.01 (published 2^-31.01) first class colliding seed: e8b3965dc46f5b7a explicit seed d870b802f1050157: H(m1) = 63cf67ba079a2997 H(m2) = 63cf67ba079a2997 COLLIDE (L = de608850619f1396, in class: yes)