{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FJMJ7R37NUM2VG2WJIKRC23ZON","short_pith_number":"pith:FJMJ7R37","schema_version":"1.0","canonical_sha256":"2a589fc77f6d19aa9b564a15116b79736a9db5209670ab9abd5717037ecb0d18","source":{"kind":"arxiv","id":"1207.1326","version":1},"attestation_state":"computed","paper":{"title":"Embeddings of homology equivalent manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"A. Skopenkov, D. Goncalves","submitted_at":"2012-07-05T18:55:37Z","abstract_excerpt":"We prove a theorem on equivariant maps implying the following two corollaries:\n  (1) Let N and M be compact orientable n-manifolds with boundaries such that M\\subset N, the inclusion M\\to N induces an isomorphism in integral cohomology, both M and N have (n-d-1)-dimensional spines and m > max {n+2, (3n+1-d)/2} . Then the restriction-induced map E^m(N)\\to E^m(M) is bijective. Here E^m(X) is the set of embeddings X\\to R^m up to isotopy (in the PL or smooth category).\n  (2) For a 3-manifold N with boundary whose integral homology groups are trivial and such that N\\not\\cong D^3 (or for its special"},"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":"1207.1326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-07-05T18:55:37Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f67885f932b55aa108636e65e8abee66fe92f3e56aba157d253d7edd5d145304","abstract_canon_sha256":"e58d256aa2268ab9861eec259984a1db34e7d69e2c2cfa08201363c81764758e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:46.322066Z","signature_b64":"d5Xi5/2vZouGGi6FSRyEoNxGjDxecr8TM/L4yCijwlyhYx6o8wPcBHVPIJ5FzbSiJwaf6rcVAO5HQ3R66UARCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a589fc77f6d19aa9b564a15116b79736a9db5209670ab9abd5717037ecb0d18","last_reissued_at":"2026-05-18T03:51:46.321154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:46.321154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embeddings of homology equivalent manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"A. Skopenkov, D. Goncalves","submitted_at":"2012-07-05T18:55:37Z","abstract_excerpt":"We prove a theorem on equivariant maps implying the following two corollaries:\n  (1) Let N and M be compact orientable n-manifolds with boundaries such that M\\subset N, the inclusion M\\to N induces an isomorphism in integral cohomology, both M and N have (n-d-1)-dimensional spines and m > max {n+2, (3n+1-d)/2} . Then the restriction-induced map E^m(N)\\to E^m(M) is bijective. Here E^m(X) is the set of embeddings X\\to R^m up to isotopy (in the PL or smooth category).\n  (2) For a 3-manifold N with boundary whose integral homology groups are trivial and such that N\\not\\cong D^3 (or for its special"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1326","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":"1207.1326","created_at":"2026-05-18T03:51:46.321304+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.1326v1","created_at":"2026-05-18T03:51:46.321304+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1326","created_at":"2026-05-18T03:51:46.321304+00:00"},{"alias_kind":"pith_short_12","alias_value":"FJMJ7R37NUM2","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FJMJ7R37NUM2VG2W","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FJMJ7R37","created_at":"2026-05-18T12:27:06.952714+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/FJMJ7R37NUM2VG2WJIKRC23ZON","json":"https://pith.science/pith/FJMJ7R37NUM2VG2WJIKRC23ZON.json","graph_json":"https://pith.science/api/pith-number/FJMJ7R37NUM2VG2WJIKRC23ZON/graph.json","events_json":"https://pith.science/api/pith-number/FJMJ7R37NUM2VG2WJIKRC23ZON/events.json","paper":"https://pith.science/paper/FJMJ7R37"},"agent_actions":{"view_html":"https://pith.science/pith/FJMJ7R37NUM2VG2WJIKRC23ZON","download_json":"https://pith.science/pith/FJMJ7R37NUM2VG2WJIKRC23ZON.json","view_paper":"https://pith.science/paper/FJMJ7R37","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.1326&json=true","fetch_graph":"https://pith.science/api/pith-number/FJMJ7R37NUM2VG2WJIKRC23ZON/graph.json","fetch_events":"https://pith.science/api/pith-number/FJMJ7R37NUM2VG2WJIKRC23ZON/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FJMJ7R37NUM2VG2WJIKRC23ZON/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FJMJ7R37NUM2VG2WJIKRC23ZON/action/storage_attestation","attest_author":"https://pith.science/pith/FJMJ7R37NUM2VG2WJIKRC23ZON/action/author_attestation","sign_citation":"https://pith.science/pith/FJMJ7R37NUM2VG2WJIKRC23ZON/action/citation_signature","submit_replication":"https://pith.science/pith/FJMJ7R37NUM2VG2WJIKRC23ZON/action/replication_record"}},"created_at":"2026-05-18T03:51:46.321304+00:00","updated_at":"2026-05-18T03:51:46.321304+00:00"}