{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:4Q5UTWNOH336T5BCXGL7PD4ET3","short_pith_number":"pith:4Q5UTWNO","schema_version":"1.0","canonical_sha256":"e43b49d9ae3ef7e9f422b997f78f849ecdb164ac9598654cddaae70843a84461","source":{"kind":"arxiv","id":"0912.4874","version":4},"attestation_state":"computed","paper":{"title":"Codimension two souls and cancellation phenomena","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"Igor Belegradek, Reinhard Schultz, Slawomir Kwasik","submitted_at":"2009-12-24T14:59:25Z","abstract_excerpt":"For each nonnegative integer we find an open (4m+9)-dimensional simply-connected manifold admitting complete nonnegatively curved metrics whose souls are non-diffeomorphic, homeomorphic, and have codimension 2. We give a diffeomorphism classification of the pairs (N, soul) when N is a nontrivial complex line bundle over the product of 7-sphere and complex projective plane: up to diffeomorphism there are precisely three such pairs, distinguished by their non-diffeomorphic souls."},"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":"0912.4874","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-12-24T14:59:25Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"2d13cb20c7f984ae57221e20155d5aeec7e74fbd16250488973affd0fbd5353f","abstract_canon_sha256":"cd68449990000796e722f68cb1a2e9096bf90a1786c23f0b7fefc57c18e42226"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:11.269787Z","signature_b64":"auZ1fW4J9z6jvjQhcoUc+zNLiX6e8fL3xrf4JTx+SZppGYI+1UjcSzN93Wt4g+J8Si+cBo0pImIoo4ObdYhWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e43b49d9ae3ef7e9f422b997f78f849ecdb164ac9598654cddaae70843a84461","last_reissued_at":"2026-05-18T02:26:11.269125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:11.269125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Codimension two souls and cancellation phenomena","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"Igor Belegradek, Reinhard Schultz, Slawomir Kwasik","submitted_at":"2009-12-24T14:59:25Z","abstract_excerpt":"For each nonnegative integer we find an open (4m+9)-dimensional simply-connected manifold admitting complete nonnegatively curved metrics whose souls are non-diffeomorphic, homeomorphic, and have codimension 2. We give a diffeomorphism classification of the pairs (N, soul) when N is a nontrivial complex line bundle over the product of 7-sphere and complex projective plane: up to diffeomorphism there are precisely three such pairs, distinguished by their non-diffeomorphic souls."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4874","kind":"arxiv","version":4},"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":"0912.4874","created_at":"2026-05-18T02:26:11.269229+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.4874v4","created_at":"2026-05-18T02:26:11.269229+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4874","created_at":"2026-05-18T02:26:11.269229+00:00"},{"alias_kind":"pith_short_12","alias_value":"4Q5UTWNOH336","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"4Q5UTWNOH336T5BC","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"4Q5UTWNO","created_at":"2026-05-18T12:25:58.837520+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/4Q5UTWNOH336T5BCXGL7PD4ET3","json":"https://pith.science/pith/4Q5UTWNOH336T5BCXGL7PD4ET3.json","graph_json":"https://pith.science/api/pith-number/4Q5UTWNOH336T5BCXGL7PD4ET3/graph.json","events_json":"https://pith.science/api/pith-number/4Q5UTWNOH336T5BCXGL7PD4ET3/events.json","paper":"https://pith.science/paper/4Q5UTWNO"},"agent_actions":{"view_html":"https://pith.science/pith/4Q5UTWNOH336T5BCXGL7PD4ET3","download_json":"https://pith.science/pith/4Q5UTWNOH336T5BCXGL7PD4ET3.json","view_paper":"https://pith.science/paper/4Q5UTWNO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.4874&json=true","fetch_graph":"https://pith.science/api/pith-number/4Q5UTWNOH336T5BCXGL7PD4ET3/graph.json","fetch_events":"https://pith.science/api/pith-number/4Q5UTWNOH336T5BCXGL7PD4ET3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4Q5UTWNOH336T5BCXGL7PD4ET3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4Q5UTWNOH336T5BCXGL7PD4ET3/action/storage_attestation","attest_author":"https://pith.science/pith/4Q5UTWNOH336T5BCXGL7PD4ET3/action/author_attestation","sign_citation":"https://pith.science/pith/4Q5UTWNOH336T5BCXGL7PD4ET3/action/citation_signature","submit_replication":"https://pith.science/pith/4Q5UTWNOH336T5BCXGL7PD4ET3/action/replication_record"}},"created_at":"2026-05-18T02:26:11.269229+00:00","updated_at":"2026-05-18T02:26:11.269229+00:00"}