{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:72LQH5WLHR24OPHENT7VV66NTP","short_pith_number":"pith:72LQH5WL","schema_version":"1.0","canonical_sha256":"fe9703f6cb3c75c73ce46cff5afbcd9bec9bdd4abc97428976facc6097a4177f","source":{"kind":"arxiv","id":"math/0502293","version":2},"attestation_state":"computed","paper":{"title":"Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Dubravko Ivansic, John G. Ratcliffe, Steven T. Tschantz","submitted_at":"2005-02-14T17:30:47Z","abstract_excerpt":"Many noncompact hyperbolic 3-manifolds are topologically complements of links in the 3-sphere. Generalizing to dimension 4, we construct a dozen examples of noncompact hyperbolic 4-manifolds, all of which are topologically complements of varying numbers of tori and Klein bottles in the 4-sphere. Finite covers of some of those manifolds are then shown to be complements of tori and Klein bottles in other simply-connected closed 4-manifolds. All the examples are based on a construction of Ratcliffe and Tschantz, who produced 1171 noncompact hyperbolic 4-manifolds of minimal volume. Our examples a"},"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":"math/0502293","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2005-02-14T17:30:47Z","cross_cats_sorted":[],"title_canon_sha256":"def1a933b90e0823f57f812597f4b4603e14cea04cf72395a316c7b8bd2362f1","abstract_canon_sha256":"2b1c254d3d85528825bb10e68b14283fc6052d2f4e57e89aabd1c80eec440499"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:32.097009Z","signature_b64":"3zCEghP243Q7CRPgQCa1tUSv6RRmCKjfPqW4I3LI++r4w8dTKVOFOR6DK+En1uKhU07l7EvfKZeor9FU1sK9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe9703f6cb3c75c73ce46cff5afbcd9bec9bdd4abc97428976facc6097a4177f","last_reissued_at":"2026-05-18T02:41:32.096540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:32.096540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Dubravko Ivansic, John G. Ratcliffe, Steven T. Tschantz","submitted_at":"2005-02-14T17:30:47Z","abstract_excerpt":"Many noncompact hyperbolic 3-manifolds are topologically complements of links in the 3-sphere. Generalizing to dimension 4, we construct a dozen examples of noncompact hyperbolic 4-manifolds, all of which are topologically complements of varying numbers of tori and Klein bottles in the 4-sphere. Finite covers of some of those manifolds are then shown to be complements of tori and Klein bottles in other simply-connected closed 4-manifolds. All the examples are based on a construction of Ratcliffe and Tschantz, who produced 1171 noncompact hyperbolic 4-manifolds of minimal volume. Our examples a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502293","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":"math/0502293","created_at":"2026-05-18T02:41:32.096607+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0502293v2","created_at":"2026-05-18T02:41:32.096607+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502293","created_at":"2026-05-18T02:41:32.096607+00:00"},{"alias_kind":"pith_short_12","alias_value":"72LQH5WLHR24","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"72LQH5WLHR24OPHE","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"72LQH5WL","created_at":"2026-05-18T12:25:53.335082+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/72LQH5WLHR24OPHENT7VV66NTP","json":"https://pith.science/pith/72LQH5WLHR24OPHENT7VV66NTP.json","graph_json":"https://pith.science/api/pith-number/72LQH5WLHR24OPHENT7VV66NTP/graph.json","events_json":"https://pith.science/api/pith-number/72LQH5WLHR24OPHENT7VV66NTP/events.json","paper":"https://pith.science/paper/72LQH5WL"},"agent_actions":{"view_html":"https://pith.science/pith/72LQH5WLHR24OPHENT7VV66NTP","download_json":"https://pith.science/pith/72LQH5WLHR24OPHENT7VV66NTP.json","view_paper":"https://pith.science/paper/72LQH5WL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0502293&json=true","fetch_graph":"https://pith.science/api/pith-number/72LQH5WLHR24OPHENT7VV66NTP/graph.json","fetch_events":"https://pith.science/api/pith-number/72LQH5WLHR24OPHENT7VV66NTP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/72LQH5WLHR24OPHENT7VV66NTP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/72LQH5WLHR24OPHENT7VV66NTP/action/storage_attestation","attest_author":"https://pith.science/pith/72LQH5WLHR24OPHENT7VV66NTP/action/author_attestation","sign_citation":"https://pith.science/pith/72LQH5WLHR24OPHENT7VV66NTP/action/citation_signature","submit_replication":"https://pith.science/pith/72LQH5WLHR24OPHENT7VV66NTP/action/replication_record"}},"created_at":"2026-05-18T02:41:32.096607+00:00","updated_at":"2026-05-18T02:41:32.096607+00:00"}