Classification: exact finite identities, proved scoped majorant obstruction, certified finite computations, and two open averaged arithmetic inputs. No cofinal gain, new best error, or RH claim.
See argument.tex and ../../audits/averaged-arithmetic-cost-2026-09-23-v1.html.
The diagonal of S is uniformly bounded; signed off-diagonal cancellation is
still unestimated. The absolute-product majorant grows at least linearly,
so averaging cannot prove bounded cost by that particular separation.
Replay from the repository root:
python evidence/ns93_averaged_cost/check_cost.py --bits 256 --output evidence/ns93_averaged_cost/cost-256bits.json
python evidence/ns93_averaged_cost/check_cost.py --bits 384 --output evidence/ns93_averaged_cost/cost-384bits.json
python evidence/ns93_averaged_cost/check_cost.py --bits 384 --sieve-multiplier 2 --output evidence/ns93_averaged_cost/cost-sieve-replay.json
maxima --no-init --very-quiet --quit-on-error --batch=evidence/ns93_averaged_cost/checks.mac > evidence/ns93_averaged_cost/checks-output.txt
maxima --no-init --very-quiet --quit-on-error --batch=evidence/ns94_circle_inversion/checks.mac > evidence/ns94_circle_inversion/checks-output.txt
python evidence/ns93_averaged_cost/verify.py
There is no physical cutoff: these are exact finite scalar sums. Independent quadratic expansions check N16/32/64; the doubled sieve checks table limits. Original Mobius implementation is bound by hash. The author reviewed the analytic squarefree count and constants; Maxima checks finite algebra only. The sufficient averaged criterion is prior descent plus Cauchy-Schwarz, not new arithmetic content. Both historical evidence gaps remain open.