{"paper":{"title":"Producing Quality Pseudorandomness with a Generalized Gauss Continued-Fraction Map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The family of r-continued-fraction maps generates pseudorandom sequences that outperform the Mersenne Twister on standard statistical test suites.","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.DS","authors_text":"Benjamin V. Holt","submitted_at":"2026-05-06T19:00:30Z","abstract_excerpt":"Well-known chaotic maps, such as the logistic and tent maps, have been used to generate cryptographically secure pseudorandomness, yet we know of no efforts which attempt to utilize the Gauss continued-fraction map, a known chaotic map, as a starting point for producing quality pseudorandom output. In this paper, we consider the family of $r$-continued-fraction maps, which generalize the Gauss map, and use them to generate pseudorandom output which outperforms many standard generators, such as the Mersenne Twister, in statistical quality, as ascertained by the use of the Dieharder, PractRand, "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the family of r-continued-fraction maps ... generate pseudorandom output which outperforms many standard generators, such as the Mersenne Twister, in statistical quality, as ascertained by use of the Dieharder, PractRand, and TestU01 suites.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That finite-precision computer implementations of the r-continued-fraction maps preserve enough of the underlying chaotic mixing properties to avoid introducing detectable patterns or biases that the statistical test suites would miss.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Generalized r-continued-fraction maps produce pseudorandom output that outperforms the Mersenne Twister and other standard generators on Dieharder, PractRand, and TestU01 test suites.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The family of r-continued-fraction maps generates pseudorandom sequences that outperform the Mersenne Twister on standard statistical test suites.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7911ee0f0e6f3290643b65f71649e1b8f5769c0a0e7dd91ab83353af8b557085"},"source":{"id":"2605.05378","kind":"arxiv","version":2},"verdict":{"id":"247c4ade-af78-40a5-ab9c-e5a73e488e40","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T15:49:32.127666Z","strongest_claim":"the family of r-continued-fraction maps ... generate pseudorandom output which outperforms many standard generators, such as the Mersenne Twister, in statistical quality, as ascertained by use of the Dieharder, PractRand, and TestU01 suites.","one_line_summary":"Generalized r-continued-fraction maps produce pseudorandom output that outperforms the Mersenne Twister and other standard generators on Dieharder, PractRand, and TestU01 test suites.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That finite-precision computer implementations of the r-continued-fraction maps preserve enough of the underlying chaotic mixing properties to avoid introducing detectable patterns or biases that the statistical test suites would miss.","pith_extraction_headline":"The family of r-continued-fraction maps generates pseudorandom sequences that outperform the Mersenne Twister on standard statistical test suites."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.05378/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T10:33:37.241423Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T21:01:19.447397Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T13:37:51.549818Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"fe79f23eeec803c909bef40f73c1f7fddb250bb4a008247fc236c38c0d0c3261"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}