{"paper":{"title":"New 3 and 6-Term Functional Dilogarithm Equations from Beta-Type Integrals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The ratio of a sextic arctangent integral to a cubic one equals a rational constant and generates new dilogarithm functional equations.","cross_cats":[],"primary_cat":"math.CA","authors_text":"Cetin Hakimoglu-Brown","submitted_at":"2026-04-27T15:11:28Z","abstract_excerpt":"Building on results by Abouzahra and Lewin, McIntosh, and Kirilov we derive new functional dilogarithm equations and consequent diologarithim ladders. By showing that the ratio of a pair of sextic and cubic integrals equals a rational constant, we construct new 3- and 6-term functional equations, from which we derive an analytic proof of an identity by Loxton-Lewin, as well as a pair of quartic-base dilogarithm ladders, also believed to be new, building on Loxton's result. Finally, we prove conjectured 2-term dilogarithm identities of Bytsko, and extend his result for the Bloch-Wigner function"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By showing that the ratio of a pair of sextic and cubic integrals equals a rational constant, we construct new 3- and 6-term functional equations, from which we derive an analytic proof of an identity by Loxton-Lewin, as well as a pair of quartic-base dilogarithm ladders... Finally, we prove conjectured 2-term dilogarithm identities of Bytsko.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The central step assumes that the ratio of the specific sextic and cubic arctangent integrals is exactly the stated rational constant; if this evaluation contains an undetected error or relies on unstated analytic continuation, the derived functional equations lose their foundation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Ratio of sextic and cubic arctangent integrals equals a rational constant and yields new dilogarithm functional equations plus proofs of several prior conjectures.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The ratio of a sextic arctangent integral to a cubic one equals a rational constant and generates new dilogarithm functional equations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d492f91d850708eb030a79bff57cdc75e08827d09161b5f74206ad5cae9a0b9d"},"source":{"id":"2604.24588","kind":"arxiv","version":3},"verdict":{"id":"d307686e-56dc-49ae-a6d2-406f6d9a1795","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T17:44:59.201714Z","strongest_claim":"By showing that the ratio of a pair of sextic and cubic integrals equals a rational constant, we construct new 3- and 6-term functional equations, from which we derive an analytic proof of an identity by Loxton-Lewin, as well as a pair of quartic-base dilogarithm ladders... Finally, we prove conjectured 2-term dilogarithm identities of Bytsko.","one_line_summary":"Ratio of sextic and cubic arctangent integrals equals a rational constant and yields new dilogarithm functional equations plus proofs of several prior conjectures.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The central step assumes that the ratio of the specific sextic and cubic arctangent integrals is exactly the stated rational constant; if this evaluation contains an undetected error or relies on unstated analytic continuation, the derived functional equations lose their foundation.","pith_extraction_headline":"The ratio of a sextic arctangent integral to a cubic one equals a rational constant and generates new dilogarithm functional equations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.24588/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T06:37:57.164546Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T21:54:58.349269Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"183486fa14a812f0ff9404e704998c96acd8c8b24d2cd3d063fb5c2c43a24645"},"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"}