NS83 applies Burnol’s established dual-vector argument with explicit extra Hardy operators. This is a logarithmic asymptotic LOWER bound for squared error, not the missing upper bound or a proof of convergence. It gives no finite-size onset and no asymptotic equality. Its order q is fixed.
The certified script evaluates ten positive critical-zero enclosures and both-conjugate weights for q=1,2,3, with weight one per zero. Omitted terms are nonnegative; this subset is not asserted to approximate the full sum. It also checks exact rational Hilbert inverse corners for multiplicities 1..8; the all-multiplicity identity is analytic, not inferred from this list.
PYTHONDONTWRITEBYTECODE=1 .venv/bin/python evidence/v166/ns83/certify_constants.py --bits 256
PYTHONDONTWRITEBYTECODE=1 .venv/bin/python evidence/v166/ns83/certify_constants.py --bits 384
PYTHONDONTWRITEBYTECODE=1 .venv/bin/python evidence/v166/verify_replays.py
maxima --very-quiet -b evidence/v166/ns83/exact-checks.mac
pyright evidence/v166
./manuscript/build.sh
python3 tools/verify_manifest.py v166
There are 43 precision enclosure matches and 33 exact Maxima checks. No numerical onset N0 is claimed. This theorem does not imply a pointwise bound on each block gain, and does not restrict the earlier uniform capture of available gain. Original cofinal arithmetic decay, Weil floor, G2 and RH remain open. Local self-review only, with literature inputs explicit.