{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KFR43SP4SGLHGJL2VH5UJDIIE4","short_pith_number":"pith:KFR43SP4","schema_version":"1.0","canonical_sha256":"5163cdc9fc919673257aa9fb448d082715a068e14c9307512a9ce6a744b469b6","source":{"kind":"arxiv","id":"2407.17821","version":1},"attestation_state":"computed","paper":{"title":"Integral Biflow Maximization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guoli Ding, Mengxi Yang, Rongchuan Tao, Wenan Zang","submitted_at":"2024-07-25T07:24:13Z","abstract_excerpt":"Let $G=(V,E)$ be a graph with four distinguished vertices, two sources $s_1, s_2$ and two sinks $t_1,t_2$, let $c:\\, E \\rightarrow \\mathbb Z_+$ be a capacity function, and let ${\\cal P}$ be the set of all simple paths in $G$ from $s_1$ to $t_1$ or from $s_2$ to $t_2$. A biflow (or $2$-commodity flow) in $G$ is an assignment $f:\\, {\\cal P}\\rightarrow \\mathbb R_+$ such that $\\sum_{e \\in Q \\in {\\cal P}}\\, f(Q) \\le c(e)$ for all $e \\in E$, whose value is defined to be $\\sum_{Q \\in {\\cal P}}\\, f(Q)$. A bicut in $G$ is a subset $K$ of $E$ that contains at least one edge from each member of ${\\cal 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":"2407.17821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-07-25T07:24:13Z","cross_cats_sorted":[],"title_canon_sha256":"b50e034d67adacbcb2c854417b161afc8f5b9839fdbe8fd81ac4840ff439a41c","abstract_canon_sha256":"cf4f5c40618594e24c02f41454ec6aaeeab4a77aab9779e61a5c56110d631341"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:48:22.098499Z","signature_b64":"Z/cjbbQoSaXzWePB57m/rN8N+laGPbyHChZ51t9rcLRRZDCAcYvBK1GWS2BWbZnH23veMUqTv8Z2t4JFLn2YCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5163cdc9fc919673257aa9fb448d082715a068e14c9307512a9ce6a744b469b6","last_reissued_at":"2026-07-05T08:48:22.098030Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:48:22.098030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral Biflow Maximization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guoli Ding, Mengxi Yang, Rongchuan Tao, Wenan Zang","submitted_at":"2024-07-25T07:24:13Z","abstract_excerpt":"Let $G=(V,E)$ be a graph with four distinguished vertices, two sources $s_1, s_2$ and two sinks $t_1,t_2$, let $c:\\, E \\rightarrow \\mathbb Z_+$ be a capacity function, and let ${\\cal P}$ be the set of all simple paths in $G$ from $s_1$ to $t_1$ or from $s_2$ to $t_2$. A biflow (or $2$-commodity flow) in $G$ is an assignment $f:\\, {\\cal P}\\rightarrow \\mathbb R_+$ such that $\\sum_{e \\in Q \\in {\\cal P}}\\, f(Q) \\le c(e)$ for all $e \\in E$, whose value is defined to be $\\sum_{Q \\in {\\cal P}}\\, f(Q)$. A bicut in $G$ is a subset $K$ of $E$ that contains at least one edge from each member of ${\\cal P}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17821","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.17821/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":"2407.17821","created_at":"2026-07-05T08:48:22.098088+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.17821v1","created_at":"2026-07-05T08:48:22.098088+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.17821","created_at":"2026-07-05T08:48:22.098088+00:00"},{"alias_kind":"pith_short_12","alias_value":"KFR43SP4SGLH","created_at":"2026-07-05T08:48:22.098088+00:00"},{"alias_kind":"pith_short_16","alias_value":"KFR43SP4SGLHGJL2","created_at":"2026-07-05T08:48:22.098088+00:00"},{"alias_kind":"pith_short_8","alias_value":"KFR43SP4","created_at":"2026-07-05T08:48:22.098088+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/KFR43SP4SGLHGJL2VH5UJDIIE4","json":"https://pith.science/pith/KFR43SP4SGLHGJL2VH5UJDIIE4.json","graph_json":"https://pith.science/api/pith-number/KFR43SP4SGLHGJL2VH5UJDIIE4/graph.json","events_json":"https://pith.science/api/pith-number/KFR43SP4SGLHGJL2VH5UJDIIE4/events.json","paper":"https://pith.science/paper/KFR43SP4"},"agent_actions":{"view_html":"https://pith.science/pith/KFR43SP4SGLHGJL2VH5UJDIIE4","download_json":"https://pith.science/pith/KFR43SP4SGLHGJL2VH5UJDIIE4.json","view_paper":"https://pith.science/paper/KFR43SP4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.17821&json=true","fetch_graph":"https://pith.science/api/pith-number/KFR43SP4SGLHGJL2VH5UJDIIE4/graph.json","fetch_events":"https://pith.science/api/pith-number/KFR43SP4SGLHGJL2VH5UJDIIE4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KFR43SP4SGLHGJL2VH5UJDIIE4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KFR43SP4SGLHGJL2VH5UJDIIE4/action/storage_attestation","attest_author":"https://pith.science/pith/KFR43SP4SGLHGJL2VH5UJDIIE4/action/author_attestation","sign_citation":"https://pith.science/pith/KFR43SP4SGLHGJL2VH5UJDIIE4/action/citation_signature","submit_replication":"https://pith.science/pith/KFR43SP4SGLHGJL2VH5UJDIIE4/action/replication_record"}},"created_at":"2026-07-05T08:48:22.098088+00:00","updated_at":"2026-07-05T08:48:22.098088+00:00"}