rapidhash-v3: standalone fixed-pair reproduction

Paper pairs A (32 B) and D (48 B), in standard, micro and nano v3. The supplied C++ implementation is specialized to C with unprotected multiplication, little-endian reads and the unrolled standard path. All three complete implementations, including their long paths, pass their own SMHasher3 value. Protected variants and the 16-byte null case are not scored or inferred here. Two key models: default (uniformly sampled 64-bit API seed, shipped eight-word rapid_secret; the historical experiment and the article’s default-secret control) and random-secret (uniform seed and eight uniform secret words per trial through the rapidhash_internal-equivalent bodies, 576 hidden bits; the model the article scores, added 2026-09-19).

Build and run

cc -O2 -std=c11 -o rapidhash_v3_verify rapidhash_v3_verify.c -lm
./rapidhash_v3_verify 20
./rapidhash_v3_verify 20 1 random-secret   # random-secret model: seed + eight secret words per trial
./rapidhash_v3_verify 30 1 random-secret   # 2^30 keys per case, about 4 min

Arguments: [log2 N (0..40), default 20] [RNG seed, default 1] [default|random-secret]. The program samples exactly N = 2^log2N seeds per pair and variant. Everything is single-threaded. It requires a C11 compiler; exact 128-bit products use the GCC/Clang __uint128_t extension where applicable. It reads no external files and writes only stdout/stderr.

Implementation and validation

Adapted from paper_rows/rapid_v3_port.h (validated verbatim SMHasher3 bodies) and collision_driver.cpp in the supplied workspace, credited in the C header. Loads are explicit little-endian and work on either host byte order. Algorithm notices are retained. NMHASH’s 16-bit products use unsigned 32-bit intermediates to avoid signed integer-promotion overflow.

The SMHasher3 _ComputedVerifyImpl procedure hashes byte prefixes of lengths 0..255 with seeds 256..1, concatenates their encoded outputs, hashes that array with seed 0, and reads the first four output bytes little-endian. Thus the check exercises the complete long-input path as well as short inputs. No seed fixup is applied. For fasthash32, both upstream 32-bit and SMHasher3 64-bit seed interfaces are tested; the verification inputs fit either width.

Every recorded witness below is asserted against its expected output before sampling. In random-secret mode the program additionally asserts the recorded random-model witness for the three 32-byte cases: seed 27d3b5addafed424 with secret words 8201394795b91ef9, bc80d672c2c377f6, 5afd557e26c19903, a3a9fab4fc0d80e2, 5108fe3feb9bd088, 6742ee43cec628a4, 2267c78c10996237, d96b61ed51f62b33 hashes both messages to d832bac31b8fda6c (from the 2026-09-19 verification against the unmodified upstream tag, ../../records/witness-searches/random-secret/rapid3/verify/logs/10_pairA_random_2p30.txt). A validation mismatch, wrong output, identical built-in messages, or any counterexample to an every-seed claim makes the program fail.

Pairs and mechanism

Paper pairs A (32 B) and D (48 B), in standard, micro and nano v3. The supplied C++ implementation is specialized to C with unprotected multiplication, little-endian reads and the unrolled standard path. All three complete implementations, including their long paths, pass their own SMHasher3 value. Protected variants and the 16-byte null case are not scored or inferred here.

Sampling and expected output

The RNG is xoshiro256**, initialized from four splitmix64 outputs with default seed 1. Each case restarts the same stream, so counts across cases are deliberately correlated (in random-secret mode each trial draws the seed and then the eight secret words from that stream, so all six cases see the same keys). Seeds are truncated only for 32-bit APIs. These are reproducible samples of the specified seed domain, not a fresh exhaustive enumeration. Historical larger measurements remain in the article and supplied records; this run does not replace them.

For rare paper fold differentials, zero at 2^20 is expected: the program still verifies and prints a known colliding seed, explicitly outside the sample count. It reports no probability/score estimate from a zero-hit run. For every-seed cases it checks every trial. The sampled score uses L = ceil(max(input lengths)/8).

The article’s score for rapidhash v3 uses the random-secret model: pooled 2386 / 2^37.83 = 2^-26.61, cap 28.6 bits [28.5, 28.7] (search harness and independent verifier, the latter on the unmodified upstream tag rapidhash_v3), recorded in ../../records/witness-searches/random-secret/rapid3/. The fold differential never uses the secret value, so the shipped secret gives the same rate (pooled 539 / 2^35.64); the shipped secret additionally admits the every-seed annihilation (the word at len-16 equal to secret[1] ^ len), which the random-secret model excludes.

The following output was built and run on the Xeon (2026-09-19, nice -n 10 taskset -c 24-31); run_2p20.txt contains the same output. Reference counts of the default mode, in order: 0 0 0 0 0 0. The random-secret smoke run ./rapidhash_v3_verify 20 1 random-secret prints 0 0 0 0 0 0 (run_2p20_random_secret.txt); the 2^30 run printed 12 / 2^30 = 2^-26.415 for every case (run_2p30_random_secret.txt; the six cases share the key stream and the same first-fold event, so their counts coincide), consistent with the pooled 2^-26.61 above.

SMHasher3 rapidhash v3: 1FDC65EE expected 1FDC65EE PASS
SMHasher3 rapidhash v3 micro: 6F183D61 expected 6F183D61 PASS
SMHasher3 rapidhash v3 nano: 2C200DC7 expected 2C200DC7 PASS
SMHasher3 checks complete; recorded output assertions follow
key model: uniform 64-bit API seed; shipped public secret words (default)

rapid3_32 / rapidhash v3
M (32 B) = 9bd4604137366abec688a63706aa4a2188d35499de169df633e0964e8c04600c
M' (32 B) = 642b9fbec8c99541397759c8f955b5de88d35499de169df633e0964e8c04600c
recorded colliding seed 3187ae8a8617e034: H(M)=a7ee6375a78a86f0 H(M')=a7ee6375a78a86f0
collisions = 0 / 1048576; rate = 0; no rate/score estimate from zero hits (resolution 1/N)
no sampled collision; the recorded witness above was checked separately

rapid3_48 / rapidhash v3
M (48 B) = 9bd4604137366abec688a63706aa4a2188d35499de169df633e0964e8c04600c48c651edae76208e840fc51f1cccbb02
M' (48 B) = 642b9fbec8c99541397759c8f955b5de88d35499de169df633e0964e8c04600c48c651edae76208e840fc51f1cccbb02
recorded colliding seed 3187ae8a8617e034: H(M)=b52b5b5759f1d08a H(M')=b52b5b5759f1d08a
collisions = 0 / 1048576; rate = 0; no rate/score estimate from zero hits (resolution 1/N)
no sampled collision; the recorded witness above was checked separately

rapid3_micro_32 / rapidhash v3 micro
M (32 B) = 9bd4604137366abec688a63706aa4a2188d35499de169df633e0964e8c04600c
M' (32 B) = 642b9fbec8c99541397759c8f955b5de88d35499de169df633e0964e8c04600c
recorded colliding seed 3187ae8a8617e034: H(M)=a7ee6375a78a86f0 H(M')=a7ee6375a78a86f0
collisions = 0 / 1048576; rate = 0; no rate/score estimate from zero hits (resolution 1/N)
no sampled collision; the recorded witness above was checked separately

rapid3_micro_48 / rapidhash v3 micro
M (48 B) = 9bd4604137366abec688a63706aa4a2188d35499de169df633e0964e8c04600c48c651edae76208e840fc51f1cccbb02
M' (48 B) = 642b9fbec8c99541397759c8f955b5de88d35499de169df633e0964e8c04600c48c651edae76208e840fc51f1cccbb02
recorded colliding seed 3187ae8a8617e034: H(M)=b52b5b5759f1d08a H(M')=b52b5b5759f1d08a
collisions = 0 / 1048576; rate = 0; no rate/score estimate from zero hits (resolution 1/N)
no sampled collision; the recorded witness above was checked separately

rapid3_nano_32 / rapidhash v3 nano
M (32 B) = 9bd4604137366abec688a63706aa4a2188d35499de169df633e0964e8c04600c
M' (32 B) = 642b9fbec8c99541397759c8f955b5de88d35499de169df633e0964e8c04600c
recorded colliding seed 3187ae8a8617e034: H(M)=a7ee6375a78a86f0 H(M')=a7ee6375a78a86f0
collisions = 0 / 1048576; rate = 0; no rate/score estimate from zero hits (resolution 1/N)
no sampled collision; the recorded witness above was checked separately

rapid3_nano_48 / rapidhash v3 nano
M (48 B) = 9bd4604137366abec688a63706aa4a2188d35499de169df633e0964e8c04600c48c651edae76208e840fc51f1cccbb02
M' (48 B) = 642b9fbec8c99541397759c8f955b5de88d35499de169df633e0964e8c04600c48c651edae76208e840fc51f1cccbb02
recorded colliding seed 3187ae8a8617e034: H(M)=b52b5b5759f1d08a H(M')=b52b5b5759f1d08a
collisions = 0 / 1048576; rate = 0; no rate/score estimate from zero hits (resolution 1/N)
no sampled collision; the recorded witness above was checked separately

Attribution and licensing

The supplied claimant/verifier authors and paper driver are credited by path above and in the source header. Algorithm authors and license notices are preserved in the C file. Driver additions are Copyright (c) 2026 Thomas Dybdahl Ahle, MIT; this does not relicense embedded algorithm code. Pengyhash v0.3 carries GPLv3-or-later, NMHASH BSD 2-Clause, mx3 CC0, and mir/fasthash/MUM/rapidhash MIT notices, as applicable.