{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LAD46BUVFUVWP7HD3V3ZS72AF4","short_pith_number":"pith:LAD46BUV","schema_version":"1.0","canonical_sha256":"5807cf06952d2b67fce3dd77997f402f2d023dd8c33dcf0a750fe4d28bf45fe8","source":{"kind":"arxiv","id":"1607.05099","version":1},"attestation_state":"computed","paper":{"title":"Geometric construction of bases of $H_2(\\overline\\Omega, \\partial\\Omega, \\mathbb{Z})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ana Alonso Rodr\\'iguez, Enrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna","submitted_at":"2016-07-18T14:27:19Z","abstract_excerpt":"We present an efficient algorithm for the construction of a basis of $H_2(\\overline{\\Omega},\\partial\\Omega;\\mathbb Z)$ via the Poincar\\'e--Lefschetz duality theorem. Denoting by $g$ the first Betti number of $\\overline \\Omega$ the idea is to find, first $g$ different $1$-boundaries of $\\overline{\\Omega}$ with supports contained in $\\partial\\Omega$ whose homology classes in $\\mathbb R^3 \\setminus \\Omega$ form a basis of $H_1(\\mathbb R^3 \\setminus \\Omega;\\mathbb Z)$, and then to construct in $\\overline{\\Omega}$ a homological Seifert surface of each one of these $1$-boundaries. The Poincar\\'e--Le"},"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":"1607.05099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-07-18T14:27:19Z","cross_cats_sorted":[],"title_canon_sha256":"f9e01171454a0f8a97557ba22597c78eeadac3d611560b3b2586d341c2b8cd6f","abstract_canon_sha256":"0c9b0a2eff70285b51314c4dcf1fd9587f16694990d52dfe58f6a9f0b02a703a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:55.921791Z","signature_b64":"bj3FityrKAi6wT/ieM/nIp+j9Hafe/s7NDnBCxax74Oedvo9T7EDM96BC1p1yLb+3yn9IPPap9ZeUqbm1Cr3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5807cf06952d2b67fce3dd77997f402f2d023dd8c33dcf0a750fe4d28bf45fe8","last_reissued_at":"2026-05-18T01:10:55.921350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:55.921350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric construction of bases of $H_2(\\overline\\Omega, \\partial\\Omega, \\mathbb{Z})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ana Alonso Rodr\\'iguez, Enrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna","submitted_at":"2016-07-18T14:27:19Z","abstract_excerpt":"We present an efficient algorithm for the construction of a basis of $H_2(\\overline{\\Omega},\\partial\\Omega;\\mathbb Z)$ via the Poincar\\'e--Lefschetz duality theorem. Denoting by $g$ the first Betti number of $\\overline \\Omega$ the idea is to find, first $g$ different $1$-boundaries of $\\overline{\\Omega}$ with supports contained in $\\partial\\Omega$ whose homology classes in $\\mathbb R^3 \\setminus \\Omega$ form a basis of $H_1(\\mathbb R^3 \\setminus \\Omega;\\mathbb Z)$, and then to construct in $\\overline{\\Omega}$ a homological Seifert surface of each one of these $1$-boundaries. The Poincar\\'e--Le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05099","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":"1607.05099","created_at":"2026-05-18T01:10:55.921417+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.05099v1","created_at":"2026-05-18T01:10:55.921417+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05099","created_at":"2026-05-18T01:10:55.921417+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAD46BUVFUVW","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAD46BUVFUVWP7HD","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAD46BUV","created_at":"2026-05-18T12:30:29.479603+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/LAD46BUVFUVWP7HD3V3ZS72AF4","json":"https://pith.science/pith/LAD46BUVFUVWP7HD3V3ZS72AF4.json","graph_json":"https://pith.science/api/pith-number/LAD46BUVFUVWP7HD3V3ZS72AF4/graph.json","events_json":"https://pith.science/api/pith-number/LAD46BUVFUVWP7HD3V3ZS72AF4/events.json","paper":"https://pith.science/paper/LAD46BUV"},"agent_actions":{"view_html":"https://pith.science/pith/LAD46BUVFUVWP7HD3V3ZS72AF4","download_json":"https://pith.science/pith/LAD46BUVFUVWP7HD3V3ZS72AF4.json","view_paper":"https://pith.science/paper/LAD46BUV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.05099&json=true","fetch_graph":"https://pith.science/api/pith-number/LAD46BUVFUVWP7HD3V3ZS72AF4/graph.json","fetch_events":"https://pith.science/api/pith-number/LAD46BUVFUVWP7HD3V3ZS72AF4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAD46BUVFUVWP7HD3V3ZS72AF4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAD46BUVFUVWP7HD3V3ZS72AF4/action/storage_attestation","attest_author":"https://pith.science/pith/LAD46BUVFUVWP7HD3V3ZS72AF4/action/author_attestation","sign_citation":"https://pith.science/pith/LAD46BUVFUVWP7HD3V3ZS72AF4/action/citation_signature","submit_replication":"https://pith.science/pith/LAD46BUVFUVWP7HD3V3ZS72AF4/action/replication_record"}},"created_at":"2026-05-18T01:10:55.921417+00:00","updated_at":"2026-05-18T01:10:55.921417+00:00"}