Reports identify this algorithm with statistical_profile.name = "paired-v2".
The former NumPy-dependent paired-v1 is unsupported: verification rejects it
instead of interpreting an old artifact using a different sampler. Rebuild a
report under a new explicit report configuration to adopt v2; do not relabel
an existing report. Worker evidence and run manifests are unchanged.
The ordered population is candidate-minus-reference binary64 deltas, ordered
by the common subjects’ content references. For each of the independent ASCII
domains observed and null, construct this byte prefix:
b"assay/paired-v2\0" + ASCII(decimal seed) + b"\0" + domain + b"\0"
Append a 16-byte unsigned big-endian counter starting at zero, hash with SHA-256,
and increment the counter for each block. Consume each digest as four unsigned
64-bit big-endian integers, in byte order. For population size n, reject words
at least 2**64 - (2**64 % n); otherwise the sample index is word % n.
Each bootstrap replicate consumes exactly n accepted indices. Both domains
generate bootstrap_samples replicates. This definition is independent of
NumPy, host byte order, vectorization, and batching.
bootstrap_samples must be an integer from 100 through 100,000 inclusive;
the wire schema and both public statistical entry points enforce this bound.
This limits replicate allocation, not total verification cost: CPU work still
scales with subject count, candidate count, and the number of reports verified.
Convert each finite binary64 delta to its exact integer ratio. Their denominators
are powers of two; use the largest denominator D and scale numerators to a
common integer population x. All replicate sums use arbitrary-precision
integers, with no intermediate floating-point summation or centering.
Let T = sum(x). The reported paired effect is the rational T / (n * D),
converted once to binary64. Sort the observed replicate sums. The percentile
endpoints use linear interpolation at exact ranks (B - 1) / 40 and
39 * (B - 1) / 40, then divide by n * D and convert once to binary64.
For each null replicate sum S, count abs(S - T) >= abs(T). The two-sided
p-value is (1 + count) / (B + 1), converted once to binary64. Fraction-to-float
conversion uses Python’s correctly rounded rational conversion.
This specifies the bootstrap and paired-effect arithmetic. Existing report rules still aggregate evaluator repeats before worker repeats, use the declared mean/median rules, require ten common subjects for inference, and apply Holm once to the complete candidate family. Reporting uses only the paired-effect and bootstrap primitives, not a second per-candidate aggregation pipeline.
Memory is O(n + B), without an n-by-B matrix; null replicate sums are counted and discarded. This trades NumPy vectorization for an explicitly reproducible algorithm. Exact sampler and hexadecimal float vectors are enforced in tests on both supported CI Python versions.