Analytic number theory

The Quasi-Riemann Hypothesis

A zero-free half-plane Re(s) > 7/8

199 pages67 claims indexed28 referencesManuscript 2026-09-30

Review API cost estimate

Prepared October 10, 2026. Approximate USD costs for explicit paper-review calls. This is not an invoice reconciliation. No mathematical verdicts are included.

Quasi-Riemann: budget roughly $40–70. Its captured later-panel usage accounts for $29.109806; initial full-manuscript Sol/Astra usage was not retained. Short product paper: $2.162152 for five returned reviews, plus an unknown Qwen timeout charge.

Review Model Usage-backed cost
Quasi-Riemann claude-fable-5-1 $28.229440
Quasi-Riemann gemini-3.1-pro-preview $0.409186
Quasi-Riemann grok-4.7 $0.471180
Product paper claude-fable-5-1 $0.712450
Product paper gemini-3.1-pro-preview $0.229560
Product paper gpt-6-astra $0.977430
Product paper gpt-6.1-sol $0.073356
Product paper grok-4.7 $0.169356

Fable’s quasi-Riemann subtotal includes all eight captured attempts: six token-budget failures and two attempts in the job that eventually returned a review. Final cumulative streaming usage is counted once per attempt. Hidden thinking is already included in its output tokens. Gemini visible and thinking counts are added; xAI uses its reported billed USD ticks. OpenAI cache-write tokens use the write rate instead of being charged twice.

The quasi-Riemann estimate adds the three initial OpenAI application invocations: one Sol high, one Astra max whose output failed parsing, and a separate Astra max rerun. Native usage, caching and retry counts were not preserved for these calls. Parsing failure does not remove the API charge.

The saved manuscript has about 245K tokens under a proxy tokenizer. Under current standard short-context pricing, the three initial OpenAI calls would cost about $15.31 if each consumed its first configured output budget and every input were a cache write; allowing one token-budget retry in each gives about $35.59. These are scenarios under the current adapter, not measurements or hard limits. Adding the captured $29.11 produces approximately $44.42 or $64.70 before unmetered charges. The rounded $40–70 range is a planning estimate. SDK timeout retries, historic adapter differences or a different context tier can move actual charges outside it.

Neither Qwen request returned usage. The older quasi-Riemann cancellation also has an internal retry tracing gap. Their costs remain unknown, rather than zero. Account discounts, credits and taxes are not reconciled.

Scope excludes this Codex conversation/subagents, model-upgrade smoke tests and tiny pipeline tests. Provenance research made no additional explicit reviewer API calls. Existing human-reading materials were not changed.

Rates checked against official OpenAI documentation, OpenAI cache accounting, Anthropic pricing, Gemini pricing, and xAI cost tracking.

Detailed per-attempt usage ledger.

Source record

Additional supporting archive items are identified in the original report. View the manuscript hashes and repository snapshot.