{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2SBO3R22ISUI2CB5GLFSRF7OY3","short_pith_number":"pith:2SBO3R22","schema_version":"1.0","canonical_sha256":"d482edc75a44a88d083d32cb2897eec6d4fa330c49cc1cda1b163206991a3f2a","source":{"kind":"arxiv","id":"1001.0338","version":3},"attestation_state":"computed","paper":{"title":"Optimal Homologous Cycles, Total Unimodularity, and Linear Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DS","math.OC"],"primary_cat":"math.AT","authors_text":"Anil N. Hirani, Bala Krishnamoorthy, Tamal K. Dey","submitted_at":"2010-01-02T23:30:11Z","abstract_excerpt":"Given a simplicial complex with weights on its simplices, and a nontrivial cycle on it, we are interested in finding the cycle with minimal weight which is homologous to the given one. Assuming that the homology is defined with integer coefficients, we show the following : For a finite simplicial complex $K$ of dimension greater than $p$, the boundary matrix $[\\partial_{p+1}]$ is totally unimodular if and only if $H_p(L, L_0)$ is torsion-free, for all pure subcomplexes $L_0, L$ in $K$ of dimensions $p$ and $p+1$ respectively, where $L_0$ is a subset of $L$. Because of the total unimodularity o"},"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":"1001.0338","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-01-02T23:30:11Z","cross_cats_sorted":["cs.CG","cs.DS","math.OC"],"title_canon_sha256":"0ba040fbf008554f48e4a00c4c5b195c4007d80033b6f39e7ecccac5855cfbee","abstract_canon_sha256":"397a77540a1766b03003139ba7143c36477cab251a8aa01de727c9cd16fe0afa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:36.890166Z","signature_b64":"E+X2ffEiw74ph1CBJLHZ4qrQ5bJwFocpDNhVm5ceOW4kOdVEQtSEFkt8NW1L0dca+Pedly8wpXttLFpurctBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d482edc75a44a88d083d32cb2897eec6d4fa330c49cc1cda1b163206991a3f2a","last_reissued_at":"2026-05-18T04:30:36.889490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:36.889490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Homologous Cycles, Total Unimodularity, and Linear Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DS","math.OC"],"primary_cat":"math.AT","authors_text":"Anil N. Hirani, Bala Krishnamoorthy, Tamal K. Dey","submitted_at":"2010-01-02T23:30:11Z","abstract_excerpt":"Given a simplicial complex with weights on its simplices, and a nontrivial cycle on it, we are interested in finding the cycle with minimal weight which is homologous to the given one. Assuming that the homology is defined with integer coefficients, we show the following : For a finite simplicial complex $K$ of dimension greater than $p$, the boundary matrix $[\\partial_{p+1}]$ is totally unimodular if and only if $H_p(L, L_0)$ is torsion-free, for all pure subcomplexes $L_0, L$ in $K$ of dimensions $p$ and $p+1$ respectively, where $L_0$ is a subset of $L$. Because of the total unimodularity o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0338","kind":"arxiv","version":3},"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":"1001.0338","created_at":"2026-05-18T04:30:36.889589+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.0338v3","created_at":"2026-05-18T04:30:36.889589+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0338","created_at":"2026-05-18T04:30:36.889589+00:00"},{"alias_kind":"pith_short_12","alias_value":"2SBO3R22ISUI","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2SBO3R22ISUI2CB5","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2SBO3R22","created_at":"2026-05-18T12:26:03.138858+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/2SBO3R22ISUI2CB5GLFSRF7OY3","json":"https://pith.science/pith/2SBO3R22ISUI2CB5GLFSRF7OY3.json","graph_json":"https://pith.science/api/pith-number/2SBO3R22ISUI2CB5GLFSRF7OY3/graph.json","events_json":"https://pith.science/api/pith-number/2SBO3R22ISUI2CB5GLFSRF7OY3/events.json","paper":"https://pith.science/paper/2SBO3R22"},"agent_actions":{"view_html":"https://pith.science/pith/2SBO3R22ISUI2CB5GLFSRF7OY3","download_json":"https://pith.science/pith/2SBO3R22ISUI2CB5GLFSRF7OY3.json","view_paper":"https://pith.science/paper/2SBO3R22","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.0338&json=true","fetch_graph":"https://pith.science/api/pith-number/2SBO3R22ISUI2CB5GLFSRF7OY3/graph.json","fetch_events":"https://pith.science/api/pith-number/2SBO3R22ISUI2CB5GLFSRF7OY3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2SBO3R22ISUI2CB5GLFSRF7OY3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2SBO3R22ISUI2CB5GLFSRF7OY3/action/storage_attestation","attest_author":"https://pith.science/pith/2SBO3R22ISUI2CB5GLFSRF7OY3/action/author_attestation","sign_citation":"https://pith.science/pith/2SBO3R22ISUI2CB5GLFSRF7OY3/action/citation_signature","submit_replication":"https://pith.science/pith/2SBO3R22ISUI2CB5GLFSRF7OY3/action/replication_record"}},"created_at":"2026-05-18T04:30:36.889589+00:00","updated_at":"2026-05-18T04:30:36.889589+00:00"}