{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:E63QCKHV3QPN3KVBM3MPQXLFRC","short_pith_number":"pith:E63QCKHV","schema_version":"1.0","canonical_sha256":"27b70128f5dc1eddaaa166d8f85d658895cdb6ec293dfb3079a287a05f97415f","source":{"kind":"arxiv","id":"math/0511307","version":2},"attestation_state":"computed","paper":{"title":"A note on Rees algebras and the MFMC property","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"C. E. Valencia, I. Gitler, R. H. Villarreal","submitted_at":"2005-11-11T17:18:56Z","abstract_excerpt":"We study irreducible representations of Rees cones and characterize the max-flow min-cut property of clutters in terms of the normality of Rees algebras and the integrality of certain polyhedra. Then we present some applications to combinatorial optimization and commutative algebra. As a byproduct we obtain an \"effective\" method, based on the program \"Normaliz\", to determine whether a given clutter satisfies the max-flow min-cut property. Let C be a clutter and let I be its edge ideal. We prove that C has the max-flow min-cut property if and only if I is normally torsion free, that is, I^i=I^{"},"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":"math/0511307","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2005-11-11T17:18:56Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4df5980d5e124096b3e8e3e55fe8059619a474932b761b2737811b1727b7de1d","abstract_canon_sha256":"ac331f40737ff8a06dc2dcfa8aad6be6f83e51dd77ccef316ad973d291c4b534"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:03.634810Z","signature_b64":"p7mrXbEqAglOr2I1KtmWM0qufBnNXQo+susrPgw9kKdDF6m4caN8tbp7FIuUBeD+cXZg3TIMX+i0TXzmY7q9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27b70128f5dc1eddaaa166d8f85d658895cdb6ec293dfb3079a287a05f97415f","last_reissued_at":"2026-05-18T04:25:03.634085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:03.634085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on Rees algebras and the MFMC property","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"C. E. Valencia, I. Gitler, R. H. Villarreal","submitted_at":"2005-11-11T17:18:56Z","abstract_excerpt":"We study irreducible representations of Rees cones and characterize the max-flow min-cut property of clutters in terms of the normality of Rees algebras and the integrality of certain polyhedra. Then we present some applications to combinatorial optimization and commutative algebra. As a byproduct we obtain an \"effective\" method, based on the program \"Normaliz\", to determine whether a given clutter satisfies the max-flow min-cut property. Let C be a clutter and let I be its edge ideal. We prove that C has the max-flow min-cut property if and only if I is normally torsion free, that is, I^i=I^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511307","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":""},"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":"math/0511307","created_at":"2026-05-18T04:25:03.634188+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0511307v2","created_at":"2026-05-18T04:25:03.634188+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0511307","created_at":"2026-05-18T04:25:03.634188+00:00"},{"alias_kind":"pith_short_12","alias_value":"E63QCKHV3QPN","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"E63QCKHV3QPN3KVB","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"E63QCKHV","created_at":"2026-05-18T12:25:53.335082+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/E63QCKHV3QPN3KVBM3MPQXLFRC","json":"https://pith.science/pith/E63QCKHV3QPN3KVBM3MPQXLFRC.json","graph_json":"https://pith.science/api/pith-number/E63QCKHV3QPN3KVBM3MPQXLFRC/graph.json","events_json":"https://pith.science/api/pith-number/E63QCKHV3QPN3KVBM3MPQXLFRC/events.json","paper":"https://pith.science/paper/E63QCKHV"},"agent_actions":{"view_html":"https://pith.science/pith/E63QCKHV3QPN3KVBM3MPQXLFRC","download_json":"https://pith.science/pith/E63QCKHV3QPN3KVBM3MPQXLFRC.json","view_paper":"https://pith.science/paper/E63QCKHV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0511307&json=true","fetch_graph":"https://pith.science/api/pith-number/E63QCKHV3QPN3KVBM3MPQXLFRC/graph.json","fetch_events":"https://pith.science/api/pith-number/E63QCKHV3QPN3KVBM3MPQXLFRC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E63QCKHV3QPN3KVBM3MPQXLFRC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E63QCKHV3QPN3KVBM3MPQXLFRC/action/storage_attestation","attest_author":"https://pith.science/pith/E63QCKHV3QPN3KVBM3MPQXLFRC/action/author_attestation","sign_citation":"https://pith.science/pith/E63QCKHV3QPN3KVBM3MPQXLFRC/action/citation_signature","submit_replication":"https://pith.science/pith/E63QCKHV3QPN3KVBM3MPQXLFRC/action/replication_record"}},"created_at":"2026-05-18T04:25:03.634188+00:00","updated_at":"2026-05-18T04:25:03.634188+00:00"}