{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YYECHOOMS2ON477AAJBWIEQQNM","short_pith_number":"pith:YYECHOOM","schema_version":"1.0","canonical_sha256":"c60823b9cc969cde7fe002436412106b29d18069b8ef4d42a31829b01d7d4381","source":{"kind":"arxiv","id":"1401.0403","version":5},"attestation_state":"computed","paper":{"title":"Torus manifolds and non-negative curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Michael Wiemeler","submitted_at":"2014-01-02T09:56:41Z","abstract_excerpt":"A torus manifold $M$ is a $2n$-dimensional orientable manifold with an effective action of an $n$-dimensional torus such that $M^T\\neq \\emptyset$. In this paper we discuss the classification of torus manifolds which admit an invariant metric of non-negative curvature. If $M$ is a simply connected torus manifold which admits such a metric, then $M$ is diffeomorphic to a quotient of a free linear torus action on a product of spheres. We also classify rationally elliptic torus manifolds $M$ with $H^{\\text{odd}}(M;\\mathbb{Z})=0$ up homeomorphism."},"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":"1401.0403","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-02T09:56:41Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"43868cebf0fa23f9e13bc576e9e6b82f90792a865e05fcdf24c0af16d930bf0a","abstract_canon_sha256":"1824ecda28e0daa8540cfee57157aace6d7d73977a67197d19734f6be3d03109"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:54.923605Z","signature_b64":"xW7gY6WIvGIGeU9bioDAnjTmRSO3631CU+8OGE5GJabd7gJXx2TpMTTFNMUH/gdZOI4XlEbMzBFSR0b4fAMyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c60823b9cc969cde7fe002436412106b29d18069b8ef4d42a31829b01d7d4381","last_reissued_at":"2026-05-18T01:27:54.922929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:54.922929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Torus manifolds and non-negative curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Michael Wiemeler","submitted_at":"2014-01-02T09:56:41Z","abstract_excerpt":"A torus manifold $M$ is a $2n$-dimensional orientable manifold with an effective action of an $n$-dimensional torus such that $M^T\\neq \\emptyset$. In this paper we discuss the classification of torus manifolds which admit an invariant metric of non-negative curvature. If $M$ is a simply connected torus manifold which admits such a metric, then $M$ is diffeomorphic to a quotient of a free linear torus action on a product of spheres. We also classify rationally elliptic torus manifolds $M$ with $H^{\\text{odd}}(M;\\mathbb{Z})=0$ up homeomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0403","kind":"arxiv","version":5},"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":"1401.0403","created_at":"2026-05-18T01:27:54.923029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.0403v5","created_at":"2026-05-18T01:27:54.923029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0403","created_at":"2026-05-18T01:27:54.923029+00:00"},{"alias_kind":"pith_short_12","alias_value":"YYECHOOMS2ON","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"YYECHOOMS2ON477A","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"YYECHOOM","created_at":"2026-05-18T12:28:59.999130+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/YYECHOOMS2ON477AAJBWIEQQNM","json":"https://pith.science/pith/YYECHOOMS2ON477AAJBWIEQQNM.json","graph_json":"https://pith.science/api/pith-number/YYECHOOMS2ON477AAJBWIEQQNM/graph.json","events_json":"https://pith.science/api/pith-number/YYECHOOMS2ON477AAJBWIEQQNM/events.json","paper":"https://pith.science/paper/YYECHOOM"},"agent_actions":{"view_html":"https://pith.science/pith/YYECHOOMS2ON477AAJBWIEQQNM","download_json":"https://pith.science/pith/YYECHOOMS2ON477AAJBWIEQQNM.json","view_paper":"https://pith.science/paper/YYECHOOM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.0403&json=true","fetch_graph":"https://pith.science/api/pith-number/YYECHOOMS2ON477AAJBWIEQQNM/graph.json","fetch_events":"https://pith.science/api/pith-number/YYECHOOMS2ON477AAJBWIEQQNM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YYECHOOMS2ON477AAJBWIEQQNM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YYECHOOMS2ON477AAJBWIEQQNM/action/storage_attestation","attest_author":"https://pith.science/pith/YYECHOOMS2ON477AAJBWIEQQNM/action/author_attestation","sign_citation":"https://pith.science/pith/YYECHOOMS2ON477AAJBWIEQQNM/action/citation_signature","submit_replication":"https://pith.science/pith/YYECHOOMS2ON477AAJBWIEQQNM/action/replication_record"}},"created_at":"2026-05-18T01:27:54.923029+00:00","updated_at":"2026-05-18T01:27:54.923029+00:00"}