{"paper":{"title":"Multicomponent pentagon maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Necessary and sufficient conditions turn maps obeying associative-like conditions on n-ary magmas into pentagon maps.","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Pavlos Kassotakis","submitted_at":"2026-04-08T15:54:50Z","abstract_excerpt":"We provide necessary and sufficient conditions for maps that satisfy associative-like conditions on families of n-ary magmas to be pentagon maps. We obtain parametric-pentagon maps and we propose a procedure that generates families of multicomponent pentagon and entwining pentagon maps from a given pentagon map."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We provide necessary and sufficient conditions for maps that satisfy associative-like conditions on families of n-ary magmas to be pentagon maps.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The maps under consideration already satisfy the stated associative-like conditions on families of n-ary magmas.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Necessary and sufficient conditions are derived for maps on n-ary magmas satisfying associative-like properties to be pentagon maps, together with a procedure that produces multicomponent and entwining pentagon maps from any given pentagon map.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Necessary and sufficient conditions turn maps obeying associative-like conditions on n-ary magmas into pentagon maps.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f6f9971cac0df85997f6a3cb8ddb4f3fa22f9ad412d1a83778462514312e8cde"},"source":{"id":"2604.07231","kind":"arxiv","version":2},"verdict":{"id":"5a2520e0-e4f4-4046-99bb-8d5822994b27","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T17:49:03.846307Z","strongest_claim":"We provide necessary and sufficient conditions for maps that satisfy associative-like conditions on families of n-ary magmas to be pentagon maps.","one_line_summary":"Necessary and sufficient conditions are derived for maps on n-ary magmas satisfying associative-like properties to be pentagon maps, together with a procedure that produces multicomponent and entwining pentagon maps from any given pentagon map.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The maps under consideration already satisfy the stated associative-like conditions on families of n-ary magmas.","pith_extraction_headline":"Necessary and sufficient conditions turn maps obeying associative-like conditions on n-ary magmas into pentagon maps."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.07231/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}