{"paper":{"title":"Characterization of cactus-expandable digraphs via doubly bidirectionally connected pairs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"A digraph with a doubly bidirectionally connected pair admits no cactus expansion.","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hiroki Kodama","submitted_at":"2023-12-28T19:05:12Z","abstract_excerpt":"Azuma et al.\\ showed that a strongly connected digraph without a doubly bidirectionally connected pair is cactus-expandable. We prove the converse: if a digraph has a doubly bidirectionally connected pair, then no expansion of it is a cactus digraph. Combined with the theorem of Azuma et al., this yields a characterization of strongly connected cactus-expandable digraphs."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"If a digraph has a doubly bidirectionally connected pair, then no expansion of it is cactus.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The definitions and prior result from Azuma et al. on cactus-expandability for digraphs without such pairs are taken as given and correctly applied to the converse case.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"If a digraph has a doubly bidirectionally connected pair, then no expansion of it is cactus.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A digraph with a doubly bidirectionally connected pair admits no cactus expansion.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c023de4721a47f2d3df5914d171cbf5ed7dc15eaf3679983bc6f8b931f1ec5f0"},"source":{"id":"2312.17327","kind":"arxiv","version":4},"verdict":{"id":"9c911906-9d51-44fa-9628-8295eca1de86","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T04:53:00.557350Z","strongest_claim":"If a digraph has a doubly bidirectionally connected pair, then no expansion of it is cactus.","one_line_summary":"If a digraph has a doubly bidirectionally connected pair, then no expansion of it is cactus.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The definitions and prior result from Azuma et al. on cactus-expandability for digraphs without such pairs are taken as given and correctly applied to the converse case.","pith_extraction_headline":"A digraph with a doubly bidirectionally connected pair admits no cactus expansion."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.17327/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"}