{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UQVE3SDQRRX76HYDG6CKY36QX5","short_pith_number":"pith:UQVE3SDQ","schema_version":"1.0","canonical_sha256":"a42a4dc8708c6fff1f033784ac6fd0bf5c0db2b665d22d13da2f69bc24f4a0ff","source":{"kind":"arxiv","id":"2603.17424","version":2},"attestation_state":"computed","paper":{"title":"Lattice Structure and Efficient Basis Construction for Strongly Connected Orientations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Olha Silina, Siyue Liu","submitted_at":"2026-03-18T07:02:02Z","abstract_excerpt":"Let $\\vec{G}=(V,E^+\\cup E^-)$ be a bidirected graph whose underlying undirected graph $G=(V,E)$ is $2$-edge-connected. A strongly connected orientation (SCO) is defined as a subset of arcs that contains exactly one of $e^+,e^-$ for every $e\\in E$ and induces a strongly connected subgraph of $\\vec{G}$. Given a family $\\mathcal{F}$ of proper subsets of $V$, we call an SCO tight if there is exactly one arc entering $U$ for every $U\\in \\mathcal{F}$. We give a polynomial-time algorithm to construct a set $\\mathcal{B}$ consisting of tight SCO's which forms an integral basis for the linear hull of ti"},"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":"2603.17424","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-18T07:02:02Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"0e3bebf2001fa1fd66bf63a132cdfc7182018fd09c8cef7ff4e82fbd538e3d53","abstract_canon_sha256":"84070a76e46576864c62ab67f531082fb309e7e9bb71db5c088abe63a3a96ff1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:28.086771Z","signature_b64":"snqf/FEyod96AtO/mNG00e39/m8ECbytmofkhMPqW7uMtCo6RRRTZrb31cKhm1cAcEH83lHiGFIEJB5dYm8GAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a42a4dc8708c6fff1f033784ac6fd0bf5c0db2b665d22d13da2f69bc24f4a0ff","last_reissued_at":"2026-05-26T01:03:28.085688Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:28.085688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lattice Structure and Efficient Basis Construction for Strongly Connected Orientations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Olha Silina, Siyue Liu","submitted_at":"2026-03-18T07:02:02Z","abstract_excerpt":"Let $\\vec{G}=(V,E^+\\cup E^-)$ be a bidirected graph whose underlying undirected graph $G=(V,E)$ is $2$-edge-connected. A strongly connected orientation (SCO) is defined as a subset of arcs that contains exactly one of $e^+,e^-$ for every $e\\in E$ and induces a strongly connected subgraph of $\\vec{G}$. Given a family $\\mathcal{F}$ of proper subsets of $V$, we call an SCO tight if there is exactly one arc entering $U$ for every $U\\in \\mathcal{F}$. We give a polynomial-time algorithm to construct a set $\\mathcal{B}$ consisting of tight SCO's which forms an integral basis for the linear hull of ti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.17424","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.17424/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.17424","created_at":"2026-05-26T01:03:28.085811+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.17424v2","created_at":"2026-05-26T01:03:28.085811+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.17424","created_at":"2026-05-26T01:03:28.085811+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQVE3SDQRRX7","created_at":"2026-05-26T01:03:28.085811+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQVE3SDQRRX76HYD","created_at":"2026-05-26T01:03:28.085811+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQVE3SDQ","created_at":"2026-05-26T01:03:28.085811+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/UQVE3SDQRRX76HYDG6CKY36QX5","json":"https://pith.science/pith/UQVE3SDQRRX76HYDG6CKY36QX5.json","graph_json":"https://pith.science/api/pith-number/UQVE3SDQRRX76HYDG6CKY36QX5/graph.json","events_json":"https://pith.science/api/pith-number/UQVE3SDQRRX76HYDG6CKY36QX5/events.json","paper":"https://pith.science/paper/UQVE3SDQ"},"agent_actions":{"view_html":"https://pith.science/pith/UQVE3SDQRRX76HYDG6CKY36QX5","download_json":"https://pith.science/pith/UQVE3SDQRRX76HYDG6CKY36QX5.json","view_paper":"https://pith.science/paper/UQVE3SDQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.17424&json=true","fetch_graph":"https://pith.science/api/pith-number/UQVE3SDQRRX76HYDG6CKY36QX5/graph.json","fetch_events":"https://pith.science/api/pith-number/UQVE3SDQRRX76HYDG6CKY36QX5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQVE3SDQRRX76HYDG6CKY36QX5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQVE3SDQRRX76HYDG6CKY36QX5/action/storage_attestation","attest_author":"https://pith.science/pith/UQVE3SDQRRX76HYDG6CKY36QX5/action/author_attestation","sign_citation":"https://pith.science/pith/UQVE3SDQRRX76HYDG6CKY36QX5/action/citation_signature","submit_replication":"https://pith.science/pith/UQVE3SDQRRX76HYDG6CKY36QX5/action/replication_record"}},"created_at":"2026-05-26T01:03:28.085811+00:00","updated_at":"2026-05-26T01:03:28.085811+00:00"}