CERTIFIED COMPUTATION · FRESH REPLACEMENT WITNESSES
NS-44: the stipulated 10⁻⁸D comparison fails
22 September 2026 · version 1 · λ=5, literal Q16 tail
Exact dyadic vectors supported on modes 17 through 128 pass fresh interval verification at 320 and 448 bits, in both parities. Every coordinate is an integer divided by 260.
For each vector, the verifier proves q[v] > 0 and q[v] − 10⁻⁸D[v] < 0, with D[v] > 0. The comparison T ≥ 10⁻⁸D therefore fails. The complete Weil energies of these witnesses are positive.
| Parity | q[v] | q[v]/D[v] | q[v] − 10⁻⁸D[v] |
|---|---|---|---|
| Even | 1.55884794745770125919e−17 | 6.42352441565298054355e−18 | −2.42677982613055495503e−8 |
| Odd | 2.73181237557136479370e−17 | 1.11279227533041427672e−17 | −2.45491672892884303058e−8 |
Table decimals are shortened displays of interval results. The complete certified ratio enclosures follow; no finite decimal is asserted to equal the underlying scalar exactly.
Even · complete 448-bit ratio enclosure
[6.4235244156529805435524569703242929577471031414566951511421938983280411697654828869896900689753055118885839140524e-18 +/- 8.40e-131]
Odd · complete 448-bit ratio enclosure
[1.11279227533041427671889054235119593489450463585403682397972153106386274380693016313286838599893918701248166739881e-17 +/- 6.17e-131]
D[v]=Σ anvn² uses the complete archimedean diagonal an=−An. It is neither the arithmetic/pole diagonal dn nor the ordinary L² norm. The exact dyadic vectors are not renormalized during verification; their ordinary norms are near one, and all conclusions are homogeneous.
Replay and its scope
Each precision rebuilds the analytic Arb coefficients in a new empty temporary cache, retaining the 96-term analytic remainder. Float eigensolves propose the vectors only. Every sign gate uses interval arithmetic.
A separate signed-index expansion checks the same positive numerator and negative shifted numerator and overlaps the parity-block assembly. The independent scoped review also reran the verifier and a separately written signed double sum. These checks share the audited analytic coefficient routine; they independently check parity and index assembly, not a second derivation of the kernel.
Because every coefficient outside 17:128 is exactly zero, the recorded quadratic is the complete-form value of the witness. No remote-tail bound is needed. An even-source constraint is not part of the literal-tail comparison being tested.
Historical recovery remains OPEN. These new files do not recover the absent v1.27 originals, validate their recorded hashes or reconstruct the original transfer protocol. They supply fresh evidence for this specified comparison failure.
This result is not a negative Weil direction and does not settle complete λ=5 positivity or negativity, another metric, a cofinal floor, G2 or RH. The independent scoped review records no outstanding major or minor finding. No new window or tail metric was introduced.
Replay from the repository root with the existing environment:
.venv/bin/python evidence/ns44_metric_replay/replay.py --verify
Use ordinary assertion mode; do not use Python −O. The proposal option refuses to replace frozen witnesses.
Certificate and hashes · Exact dyadic witnesses · Replay script · Independent review · Reproducibility and scope