xxh3-64: standalone fixed-pair reproduction
XXH3-64, xxHash 0.8.3, default public secret/constants, uniformly sampled 64-bit API seeds. The scored base-1143 pair is a 32-byte pair checked by xxh3_64_32B_check.c; see CHECK_32B.md. The historical xxh3_64_verify.c driver also contains pair A and a 128-byte supporting pair.
Build and run
cc -O2 -std=c11 -o xxh3_64_verify xxh3_64_verify.c -lm
./xxh3_64_verify # default 2^20-seed smoke run
./xxh3_64_verify 20 1 # explicit sample size and RNG seed
./xxh3_64_verify 30 1 # optional larger sample, a different stream from historical recordsArguments: [log2 N (0..40), default 20] [RNG seed, default 1]. Each pair receives exactly N seeds. The program runs in one thread, reads no files, and writes only stdout/stderr. GCC/Clang C11 and libm suffice; the transcribed multiplication code uses the unsigned __int128 extension.
Implementation and startup validation
The C file embeds ../../ref/xxhash.h verbatim with XXH_INLINE_ALL and calls XXH3_64bits_withSeed. No external header or library is required. The embedded version must be 803. Header SHA-256:
17973c0dc49d9854ca26caa191f0e12f7a424b68858d9a78de3860d959d85e4bStartup recomputes SMHasher3 verification 0x1AAEE62C, read from SMHasher3 hashes/xxhash.cpp (commit 7ad8939d). Verification encodes outputs in canonical big-endian order (high half first for 128 bits), matching that wrapper.
The SMHasher3 check hashes byte prefixes of lengths 0..255 with seeds 256..1, concatenates the encoded outputs, hashes that array with seed 0, and reads the first four output bytes little-endian. It therefore exercises short and long input paths. No seed fixup is applied.
It additionally checks all ten official XXH3-64 sanity vectors: lengths 12, 24, 48, 80 and 195 with seeds 0 and PRIME64 = 11400714785074694797 (0x9e3779b185ebca8d). These are transcribed from xxHash cli/xsum_sanity_check.c. The buffer starts with byteGen = 2654435761; each byte is byteGen >> 56, followed by byteGen *= PRIME64 modulo 2^64.
Before sampling, each recorded colliding seed is hashed on both messages and checked against its literal expected output. A mismatch exits nonzero. These witnesses are separate from the random sample and never added to its collision count.
Pairs and historical measurements
Both pairs complement their first two words and leave the suffix unchanged. In these length paths, equality of the first 16-byte multiplication fold survives the common sum and final avalanche. The exact 128-byte messages come from ../../xxh3_128b_pairs.json: id 1143, variant 0, tail 0, length 128, stages confirm1 and confirm2 (identical messages). This is the selected base-1143 pair, not the 128-byte extension of pair A in supplied_rows.json.
Historical measurements supplied with the package: A: 11 / 2^30 = 2^-26.540568; base-1143: 504 / 2^30 = 2^-21.022720 and 526 / 2^30 = 2^-20.961081. The 32-byte pair, seed and output literals come from ../../rows.json (also retained in supplied_rows.json). The base-1143 records, where applicable, come from ../../xxh3_128b_pairs.json. These historical 2^30 counts were not rerun here. Their original sampling streams differ from this standalone program; running with argument 30 estimates the same seed-domain probability but need not give the same counts.
2^20 is only a smoke run, not a useful estimate of these rare-event rates. Expected hits at that size are near zero (about 0.5 for base-1143, below 0.012 for the other pairs). Zero hits reports log2(sample rate) = -inf, not evidence that the population collision probability is zero. An isolated hit is also a noisy estimate.
Sampling and EXPECTED output
The RNG is xoshiro256, initialized from four splitmix64 outputs with seed 1 by default. Seeds use all 64 bits and no secret words are randomized. Each pair restarts the same stream; multiple pair results are deliberately correlated. make check compares the exact deterministic 2^20 counts, in printed order: 0 0**.
The following EXPECTED block is the actual local default run, also saved in run_2p20.txt:
SMHasher3 XXH3-64 0.8.3: 1AAEE62C expected 1AAEE62C PASS
XXH3 sanity len=12 seed=0000000000000000: a713daf0dfbb77e7 expected a713daf0dfbb77e7 PASS
XXH3 sanity len=12 seed=9e3779b185ebca8d: e7303e1b2336de0e expected e7303e1b2336de0e PASS
XXH3 sanity len=24 seed=0000000000000000: a3fe70bf9d3510eb expected a3fe70bf9d3510eb PASS
XXH3 sanity len=24 seed=9e3779b185ebca8d: 850e80fc35bdd690 expected 850e80fc35bdd690 PASS
XXH3 sanity len=48 seed=0000000000000000: 397da259ecba1f11 expected 397da259ecba1f11 PASS
XXH3 sanity len=48 seed=9e3779b185ebca8d: adc2cbaa44acc616 expected adc2cbaa44acc616 PASS
XXH3 sanity len=80 seed=0000000000000000: bcdefbbb2c47c90a expected bcdefbbb2c47c90a PASS
XXH3 sanity len=80 seed=9e3779b185ebca8d: c6dd0cb699532e73 expected c6dd0cb699532e73 PASS
XXH3 sanity len=195 seed=0000000000000000: cd94217ee362ec3a expected cd94217ee362ec3a PASS
XXH3 sanity len=195 seed=9e3779b185ebca8d: ba68003d370cb3d9 expected ba68003d370cb3d9 PASS
paper pair A / XXH3-64 0.8.3
M (32 B) = 9bd4604137366abec688a63706aa4a2188d35499de169df633e0964e8c04600c
M' (32 B) = 642b9fbec8c99541397759c8f955b5de88d35499de169df633e0964e8c04600c
recorded colliding seed cd362ec99e1e6259: H(M)=bf1f613669d6c8ae H(M')=bf1f613669d6c8ae
collisions = 0 / 1048576; rate = 0; log2(rate) = -inf (zero hits; no population-rate estimate)
no sampled collision; the recorded witness above was checked separately
base-1143 pair / XXH3-64 0.8.3
M (128 B) = 8912a3da9fc464368202a1be238b7d11a56186f8dc03bd1f78bfbd2ba3386ced7093d3639fc8f076abe3f9a757e5c84290720e6340b2e7820a16a5633b9b0344773006232e3abc7d4727eafba248b46cf2a6516698382bd2fa890528924cd1b618df4aa87d1af4bcec13f92bf8a1163e657fb0885deddf709a0252fbe3ae169d
M' (128 B) = 76ed5c25603b9bc97dfd5e41dc7482eea56186f8dc03bd1f78bfbd2ba3386ced7093d3639fc8f076abe3f9a757e5c84290720e6340b2e7820a16a5633b9b0344773006232e3abc7d4727eafba248b46cf2a6516698382bd2fa890528924cd1b618df4aa87d1af4bcec13f92bf8a1163e657fb0885deddf709a0252fbe3ae169d
recorded colliding seed c8eae1baae13330b: H(M)=448e3716c8effb94 H(M')=448e3716c8effb94
collisions = 0 / 1048576; rate = 0; log2(rate) = -inf (zero hits; no population-rate estimate)
no sampled collision; the recorded witness above was checked separatelyAttribution and licensing
The embedded xxHash header retains Yann Collet’s copyright and full BSD 2-Clause license verbatim. Driver additions are Copyright (c) 2026 Thomas Dybdahl Ahle, MIT, with the full notice in the C file. The supplied collision_driver.cpp, harness/hashes.h, and JSON evidence records are credited as the sources of the implementation and reproduction data.
Scored-pair reproduction:
cc -O3 -std=c11 xxh3_64_32B_check.c -lm -o check
./check 20The scored pair and score are unchanged; a stronger candidate is under separate verification.