Ergodic theory and translation surfaces

Weakly mixing polygonal billiards

Jon Chaika and Giovanni Forni

41 pages51 claims indexed35 referencesManuscript 2025-08-14

Coverage and cost

One full-paper Sol high assessment and eight targeted requests were made. Four targeted requests returned usable assessments (three Sol high, one Gemini HIGH). Two Opus max reviews and one Gemini HIGH review exhausted their output allowances; one targeted Sol response failed its source-quote validation. Three arbitration requests returned no accepted verdicts: one Opus cap and two Gemini reference-annotation inconsistencies. The latter are not evidence by themselves that a later theorem was used in the mathematical reasoning.

The Opus targeted/arbitration caps were 49,152 tokens, Gemini 32,768, targeted Sol 16,384, and full-paper Sol 32,768. Caps include billed reasoning. All twelve attempts are recorded in attempts.json; raw provider envelopes and rejected response text are excluded. Initial reviewers saw the frozen v2 source without Astra's supplied analysis. The journal PDF was compared afterward.

Total usage-based conservative API accounting: $3.9399455 out of $10 authorized. It includes failed attempts and uses the native runner's conservative batch rates. This is not an invoice; storage charges and taxes are outside this token accounting. No generation retries or additional repair search were run.

Source record

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