{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SG5HBXO2D62CVCGJOIOVLOQ5F4","short_pith_number":"pith:SG5HBXO2","schema_version":"1.0","canonical_sha256":"91ba70ddda1fb42a88c9721d55ba1d2f33354358e5c82bc87c4c169b3749aceb","source":{"kind":"arxiv","id":"1504.06703","version":1},"attestation_state":"computed","paper":{"title":"Complements of tori in $\\#_{2k}S^2 \\times S^2$ that admit a hyperbolic structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hemanth Saratchandran","submitted_at":"2015-04-25T09:17:07Z","abstract_excerpt":"We construct examples of codimension two hyperbolic link complements in closed smooth 4-manifolds with homeomorphism type $\\#_{2k}S^2 \\times S^2$. All our examples are based on a construction of J. Ratcliffe and S. Tschantz, who constructed 1171 non-compact finite volume hyperbolic 4-manifolds of minimal volume. We then give necessary conditions for a closed smooth simply connected 4-manifold to contain a codimension two link complement that admits a hyperbolic structure."},"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":"1504.06703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-04-25T09:17:07Z","cross_cats_sorted":[],"title_canon_sha256":"73577a5bb5bbdb12a26af63ddc28746583f162c9564b037da72a4c6a322b66c2","abstract_canon_sha256":"b515d9f6eda75ef573bb5764f0d3897d593c3fb584a2bd98a520bddf88f6e51c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:44.590202Z","signature_b64":"mA7w13by+3lobW3ckaeOtRLM8OvC4N1R0pIL7JJJk9KhdWWxIwtl9kJ3DJI2X0xAduw+/U4KMnzYUie941KbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91ba70ddda1fb42a88c9721d55ba1d2f33354358e5c82bc87c4c169b3749aceb","last_reissued_at":"2026-05-18T02:17:44.589637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:44.589637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complements of tori in $\\#_{2k}S^2 \\times S^2$ that admit a hyperbolic structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hemanth Saratchandran","submitted_at":"2015-04-25T09:17:07Z","abstract_excerpt":"We construct examples of codimension two hyperbolic link complements in closed smooth 4-manifolds with homeomorphism type $\\#_{2k}S^2 \\times S^2$. All our examples are based on a construction of J. Ratcliffe and S. Tschantz, who constructed 1171 non-compact finite volume hyperbolic 4-manifolds of minimal volume. We then give necessary conditions for a closed smooth simply connected 4-manifold to contain a codimension two link complement that admits a hyperbolic structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06703","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":"1504.06703","created_at":"2026-05-18T02:17:44.589747+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06703v1","created_at":"2026-05-18T02:17:44.589747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06703","created_at":"2026-05-18T02:17:44.589747+00:00"},{"alias_kind":"pith_short_12","alias_value":"SG5HBXO2D62C","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SG5HBXO2D62CVCGJ","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SG5HBXO2","created_at":"2026-05-18T12:29:42.218222+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/SG5HBXO2D62CVCGJOIOVLOQ5F4","json":"https://pith.science/pith/SG5HBXO2D62CVCGJOIOVLOQ5F4.json","graph_json":"https://pith.science/api/pith-number/SG5HBXO2D62CVCGJOIOVLOQ5F4/graph.json","events_json":"https://pith.science/api/pith-number/SG5HBXO2D62CVCGJOIOVLOQ5F4/events.json","paper":"https://pith.science/paper/SG5HBXO2"},"agent_actions":{"view_html":"https://pith.science/pith/SG5HBXO2D62CVCGJOIOVLOQ5F4","download_json":"https://pith.science/pith/SG5HBXO2D62CVCGJOIOVLOQ5F4.json","view_paper":"https://pith.science/paper/SG5HBXO2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06703&json=true","fetch_graph":"https://pith.science/api/pith-number/SG5HBXO2D62CVCGJOIOVLOQ5F4/graph.json","fetch_events":"https://pith.science/api/pith-number/SG5HBXO2D62CVCGJOIOVLOQ5F4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SG5HBXO2D62CVCGJOIOVLOQ5F4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SG5HBXO2D62CVCGJOIOVLOQ5F4/action/storage_attestation","attest_author":"https://pith.science/pith/SG5HBXO2D62CVCGJOIOVLOQ5F4/action/author_attestation","sign_citation":"https://pith.science/pith/SG5HBXO2D62CVCGJOIOVLOQ5F4/action/citation_signature","submit_replication":"https://pith.science/pith/SG5HBXO2D62CVCGJOIOVLOQ5F4/action/replication_record"}},"created_at":"2026-05-18T02:17:44.589747+00:00","updated_at":"2026-05-18T02:17:44.589747+00:00"}