Verification — What to Test and How

Per-language property tests

#	Test	Pass if
V1	`fnv1a64_known_vectors`	`""` → `0xcbf29ce484222325`; `"a"` → `0xaf63dc4c8601ec8c`; `"foobar"` → `0x85944171f73967e8`
V2	`splitmix64_known_vectors`	`splitmix64(0)` = `0xe220a8397b1dcdaf`; `splitmix64(0xdeadbeef)` = `0x4adfb90f68c9eb9b`
V3	`no_false_negatives`	Insert N=10 000 random keys (seeded); `contains` returns true for every one
V4	`fpr_within_2x`	Build for n=10 000 at fpr=0.01; query 100 000 random absent keys; observed FPR ≤ 2× theoretical
V5	`optimal_k_formula`	`with_fpr(1000, 0.01)` returns `k=7` and `9 580 ≤ m ≤ 9 620` (allow ±0.5%)
V6	`encode_decode_roundtrip`	encode → decode → query the same keys: identical results
V7	`header_layout`	First 4 bytes = `k` LE; next 8 = `m` LE; payload length = ⌈m/8⌉
V8	`empty_filter_rejects_all`	New filter with m=64, k=3; `contains` returns false for 1000 random keys

Cross-language test

scripts/cross_test.sh performs the writer × reader matrix for {go, rust, cpp}²:

Each writer builds a filter for the same fixed-seed key set (1 000 keys).
Filters must be byte-identical (md5sum over filter file).
Each reader opens each writer's filter and runs:
- 1 000 known-present queries → must all return present
- 1 000 known-absent queries (different seed) → results must match across readers

This catches:

Endian or bit-order bugs in the header / bit array.
Hash mismatch (fnv1a64 or splitmix64 differs).
mod m reduction differs (Lemire's u128 trick vs % should yield identical indices).

What "passing" means

All 8 property tests green in all three languages.
cross_test.sh exits 0 with 9 byte-identical filter writers and 9 passing reader runs.
Manual smoke: hexdump of a 4-key filter matches the structure described in docs/observation.md.