{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DBCZMBTLMSWOVFXHS3I5SBIYIB","short_pith_number":"pith:DBCZMBTL","schema_version":"1.0","canonical_sha256":"184596066b64acea96e796d1d9051840408170f6c6bf894ca8bc5c7867149748","source":{"kind":"arxiv","id":"1706.09066","version":1},"attestation_state":"computed","paper":{"title":"On the complexity of finding internally vertex-disjoint long directed paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Ana Karolinna Maia, Ana Silva, Ignasi Sau, J\\'ulio Ara\\'ujo, Victor A. Campos","submitted_at":"2017-06-27T22:17:20Z","abstract_excerpt":"For two positive integers $k$ and $\\ell$, a $(k \\times \\ell)$-spindle is the union of $k$ pairwise internally vertex-disjoint directed paths with $\\ell$ arcs between two vertices $u$ and $v$. We are interested in the (parameterized) complexity of several problems consisting in deciding whether a given digraph contains a subdivision of a spindle, which generalize both the Maximum Flow and Longest Path problems. We obtain the following complexity dichotomy: for a fixed $\\ell \\geq 1$, finding the largest $k$ such that an input digraph $G$ contains a subdivision of a $(k \\times \\ell)$-spindle is p"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.09066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-06-27T22:17:20Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"53d8e5587ba47fff49116795271ef09e87b3b1359f3cc8b519cf9fd1af6437b4","abstract_canon_sha256":"d2fd897008c7bc226cf44d5144351259a8574ac2a58aca801a0f18964acd1acf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:19.995109Z","signature_b64":"a2xZrl/eR7Qra+i1bajCWxqaFBQKT6qg0kSB10Vro99/JGPzeNtovaOphl6N6kufgAnnblUS1WIU4iSd6ueiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"184596066b64acea96e796d1d9051840408170f6c6bf894ca8bc5c7867149748","last_reissued_at":"2026-05-18T00:41:19.994287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:19.994287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the complexity of finding internally vertex-disjoint long directed paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Ana Karolinna Maia, Ana Silva, Ignasi Sau, J\\'ulio Ara\\'ujo, Victor A. Campos","submitted_at":"2017-06-27T22:17:20Z","abstract_excerpt":"For two positive integers $k$ and $\\ell$, a $(k \\times \\ell)$-spindle is the union of $k$ pairwise internally vertex-disjoint directed paths with $\\ell$ arcs between two vertices $u$ and $v$. We are interested in the (parameterized) complexity of several problems consisting in deciding whether a given digraph contains a subdivision of a spindle, which generalize both the Maximum Flow and Longest Path problems. We obtain the following complexity dichotomy: for a fixed $\\ell \\geq 1$, finding the largest $k$ such that an input digraph $G$ contains a subdivision of a $(k \\times \\ell)$-spindle is p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09066","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.09066","created_at":"2026-05-18T00:41:19.994434+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.09066v1","created_at":"2026-05-18T00:41:19.994434+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09066","created_at":"2026-05-18T00:41:19.994434+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBCZMBTLMSWO","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBCZMBTLMSWOVFXH","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBCZMBTL","created_at":"2026-05-18T12:31:10.602751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DBCZMBTLMSWOVFXHS3I5SBIYIB","json":"https://pith.science/pith/DBCZMBTLMSWOVFXHS3I5SBIYIB.json","graph_json":"https://pith.science/api/pith-number/DBCZMBTLMSWOVFXHS3I5SBIYIB/graph.json","events_json":"https://pith.science/api/pith-number/DBCZMBTLMSWOVFXHS3I5SBIYIB/events.json","paper":"https://pith.science/paper/DBCZMBTL"},"agent_actions":{"view_html":"https://pith.science/pith/DBCZMBTLMSWOVFXHS3I5SBIYIB","download_json":"https://pith.science/pith/DBCZMBTLMSWOVFXHS3I5SBIYIB.json","view_paper":"https://pith.science/paper/DBCZMBTL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.09066&json=true","fetch_graph":"https://pith.science/api/pith-number/DBCZMBTLMSWOVFXHS3I5SBIYIB/graph.json","fetch_events":"https://pith.science/api/pith-number/DBCZMBTLMSWOVFXHS3I5SBIYIB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBCZMBTLMSWOVFXHS3I5SBIYIB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBCZMBTLMSWOVFXHS3I5SBIYIB/action/storage_attestation","attest_author":"https://pith.science/pith/DBCZMBTLMSWOVFXHS3I5SBIYIB/action/author_attestation","sign_citation":"https://pith.science/pith/DBCZMBTLMSWOVFXHS3I5SBIYIB/action/citation_signature","submit_replication":"https://pith.science/pith/DBCZMBTLMSWOVFXHS3I5SBIYIB/action/replication_record"}},"created_at":"2026-05-18T00:41:19.994434+00:00","updated_at":"2026-05-18T00:41:19.994434+00:00"}