{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:VRCNXOSC6OSICLL7JKM3O3K6WV","short_pith_number":"pith:VRCNXOSC","schema_version":"1.0","canonical_sha256":"ac44dbba42f3a4812d7f4a99b76d5eb5528a161e20b38ac0a6c38eee756dc148","source":{"kind":"arxiv","id":"1003.3029","version":2},"attestation_state":"computed","paper":{"title":"Embedding 3-manifolds with boundary into closed 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Dmitry Tonkonog","submitted_at":"2010-03-15T20:56:52Z","abstract_excerpt":"We prove that there is an algorithm which determines whether or not a given 2-polyhedron can be embedded into some integral homology 3-sphere.\n  This is a corollary of the following main result. Let $M$ be a compact connected orientable 3-manifold with boundary. Denote $G=\\Z$, $G=\\Z/p\\Z$ or $G=\\Q$. If $H_1(M;G)\\cong G^k$ and $\\bd M$ is a surface of genus $g$, then the minimal group $H_1(Q;G)$ for closed 3-manifolds $Q$ containing $M$ is isomorphic to $G^{k-g}$.\n  Another corollary is that for a graph $L$ the minimal number $\\rk H_1(Q;\\Z)$ for closed orientable 3-manifolds $Q$ containing $L\\tim"},"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":"1003.3029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-15T20:56:52Z","cross_cats_sorted":[],"title_canon_sha256":"730cdf13afa9b89fbe3abcb994aae92ff7d1451830db18084243403b9920128f","abstract_canon_sha256":"6cdeda76712553f8e3da7284fd5e297311b4c3ae48bc32444ff01eb1695ed278"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:05.335527Z","signature_b64":"78ZIbXHwhQVGX83ParJ/1YUhQl2l1Leq+vuQ0vt89c2aib4gZz2jmGbfv4x8hJdj4ppAllYrWv8xDhGm/NOOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac44dbba42f3a4812d7f4a99b76d5eb5528a161e20b38ac0a6c38eee756dc148","last_reissued_at":"2026-05-18T01:13:05.334990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:05.334990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embedding 3-manifolds with boundary into closed 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Dmitry Tonkonog","submitted_at":"2010-03-15T20:56:52Z","abstract_excerpt":"We prove that there is an algorithm which determines whether or not a given 2-polyhedron can be embedded into some integral homology 3-sphere.\n  This is a corollary of the following main result. Let $M$ be a compact connected orientable 3-manifold with boundary. Denote $G=\\Z$, $G=\\Z/p\\Z$ or $G=\\Q$. If $H_1(M;G)\\cong G^k$ and $\\bd M$ is a surface of genus $g$, then the minimal group $H_1(Q;G)$ for closed 3-manifolds $Q$ containing $M$ is isomorphic to $G^{k-g}$.\n  Another corollary is that for a graph $L$ the minimal number $\\rk H_1(Q;\\Z)$ for closed orientable 3-manifolds $Q$ containing $L\\tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3029","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":"1003.3029","created_at":"2026-05-18T01:13:05.335068+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.3029v2","created_at":"2026-05-18T01:13:05.335068+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3029","created_at":"2026-05-18T01:13:05.335068+00:00"},{"alias_kind":"pith_short_12","alias_value":"VRCNXOSC6OSI","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"VRCNXOSC6OSICLL7","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"VRCNXOSC","created_at":"2026-05-18T12:26:15.391820+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/VRCNXOSC6OSICLL7JKM3O3K6WV","json":"https://pith.science/pith/VRCNXOSC6OSICLL7JKM3O3K6WV.json","graph_json":"https://pith.science/api/pith-number/VRCNXOSC6OSICLL7JKM3O3K6WV/graph.json","events_json":"https://pith.science/api/pith-number/VRCNXOSC6OSICLL7JKM3O3K6WV/events.json","paper":"https://pith.science/paper/VRCNXOSC"},"agent_actions":{"view_html":"https://pith.science/pith/VRCNXOSC6OSICLL7JKM3O3K6WV","download_json":"https://pith.science/pith/VRCNXOSC6OSICLL7JKM3O3K6WV.json","view_paper":"https://pith.science/paper/VRCNXOSC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.3029&json=true","fetch_graph":"https://pith.science/api/pith-number/VRCNXOSC6OSICLL7JKM3O3K6WV/graph.json","fetch_events":"https://pith.science/api/pith-number/VRCNXOSC6OSICLL7JKM3O3K6WV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VRCNXOSC6OSICLL7JKM3O3K6WV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VRCNXOSC6OSICLL7JKM3O3K6WV/action/storage_attestation","attest_author":"https://pith.science/pith/VRCNXOSC6OSICLL7JKM3O3K6WV/action/author_attestation","sign_citation":"https://pith.science/pith/VRCNXOSC6OSICLL7JKM3O3K6WV/action/citation_signature","submit_replication":"https://pith.science/pith/VRCNXOSC6OSICLL7JKM3O3K6WV/action/replication_record"}},"created_at":"2026-05-18T01:13:05.335068+00:00","updated_at":"2026-05-18T01:13:05.335068+00:00"}