riemann

v1.63 evidence: full arithmetic sampling and finite-block efficiency

Incremental NS-78–80 evidence only. RH/G2 remain open. Local self-review only.

• ns78/: uniform complete norm comparison, exact sample/divisor inversion, physical-cell integration, and analytic physical and sample tails.
• ns79/: tail-balanced feedback and endpoint-augmented span. Complete true energies and old projections; the last jump is deliberately not cancelled.
• ns80/: full arithmetic Gram comparison, Schur transfer and uniform ideal block efficiency. Analytic theorem and exact rational Maxima checks; no numerical implementation or finite-prefix substitute for its inverse.
• proof.tex is integrated verbatim into the live manuscript.
• Dated HTML files give the readable update and local self-review.

Reproduce

PYTHONDONTWRITEBYTECODE=1 .venv/bin/python evidence/v163/verify_replays.py
pyright evidence/v163
./manuscript/build.sh
python3 tools/verify_manifest.py v163

NS78: certify_cells.py --bits 256 --sizes 16 64 256 --output <new-path>; repeat at 384 bits. Replay N=256 with --cell-stop 131072 --kernel-cutoff 256. The default cell stop is 65536; all cells beyond it are bounded, not omitted. The initial kernel series cutoff is 128 with full order-24 tail. The accurate finite norm, main tail and analytic radius are archived separately; printed combined balls can be wider due to decimal rounding.

NS79: `certify_balanced.py –bits 256 –sizes 16 32 64 128 256 –output

`; repeat at 384 bits. Replay N=256 with `--cutoff 256`. Every inherited scientific dependency is hash-checked. All solves retain Arb balls; no midpoint solve is used. Run the three Maxima files and require PASS counts 30, 16 and 10. NS80 uses exact rational constants, so no floating-point replay is needed. A uniform fraction of available block gain does not prove zero limiting error. No new Weil window, original uniform floor, G2 or RH proof.

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