{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TVYRBC5QWPD27VCEOATLJP7YEP","short_pith_number":"pith:TVYRBC5Q","schema_version":"1.0","canonical_sha256":"9d71108bb0b3c7afd4447026b4bff823fcbf473e378a3c54e5d0d699dbcd3910","source":{"kind":"arxiv","id":"1506.03535","version":2},"attestation_state":"computed","paper":{"title":"An Isometrical ${\\Bbb C\\Bbb P}^{n}$-Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongwei Sun, Xiaole Su, Yusheng Wang","submitted_at":"2015-06-11T03:11:53Z","abstract_excerpt":"Let $M^n\\ (n\\geq3)$ be a complete Riemannian manifold with $\\sec_M\\geq 1$, and let $M_i^{n_i}$ ($i=1,2$) be two comlplete totally geodesic submanifolds in $M$. We prove that if $n_1+n_2=n-2$ and if the distance $|M_1M_2|\\geq\\frac{\\pi}{2}$, then $M_i$ is isometric to $\\Bbb S^{n_i}/\\Bbb Z_h$, ${\\Bbb C\\Bbb P}^{\\frac {n_i}2}$ or ${\\Bbb C\\Bbb P}^{\\frac {n_i}2}/\\Bbb Z_2$ with the canonical metric when $n_i>0$, and thus $M$ is isometric to $\\Bbb S^n/\\Bbb Z_h$, ${\\Bbb C\\Bbb P}^{\\frac n2}$ or ${\\Bbb C\\Bbb P}^{\\frac n2}/\\Bbb Z_2$ except possibly when $n=3$ and $M_1$ (or $M_2$) $\\stackrel{\\rm iso}{\\cong}"},"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":"1506.03535","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-11T03:11:53Z","cross_cats_sorted":[],"title_canon_sha256":"552d981ffc6053c50fc7eebb9acdeba76712a25daa1dfb6d55073bb4a7e53f6a","abstract_canon_sha256":"250cd2787152e92cd9eb256b9657a013615bcdd7c6f33c9008bdc3818cb61b88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:36.206888Z","signature_b64":"VYYbyGOz/KwYV4OiFloNT8iIAO4zAxmd67JfYLMAsxBMa8DWJvILTK63ma6+oEciu/rN/fOCv+F8P0V7FkjFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d71108bb0b3c7afd4447026b4bff823fcbf473e378a3c54e5d0d699dbcd3910","last_reissued_at":"2026-05-18T01:15:36.206175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:36.206175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Isometrical ${\\Bbb C\\Bbb P}^{n}$-Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongwei Sun, Xiaole Su, Yusheng Wang","submitted_at":"2015-06-11T03:11:53Z","abstract_excerpt":"Let $M^n\\ (n\\geq3)$ be a complete Riemannian manifold with $\\sec_M\\geq 1$, and let $M_i^{n_i}$ ($i=1,2$) be two comlplete totally geodesic submanifolds in $M$. We prove that if $n_1+n_2=n-2$ and if the distance $|M_1M_2|\\geq\\frac{\\pi}{2}$, then $M_i$ is isometric to $\\Bbb S^{n_i}/\\Bbb Z_h$, ${\\Bbb C\\Bbb P}^{\\frac {n_i}2}$ or ${\\Bbb C\\Bbb P}^{\\frac {n_i}2}/\\Bbb Z_2$ with the canonical metric when $n_i>0$, and thus $M$ is isometric to $\\Bbb S^n/\\Bbb Z_h$, ${\\Bbb C\\Bbb P}^{\\frac n2}$ or ${\\Bbb C\\Bbb P}^{\\frac n2}/\\Bbb Z_2$ except possibly when $n=3$ and $M_1$ (or $M_2$) $\\stackrel{\\rm iso}{\\cong}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03535","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":"1506.03535","created_at":"2026-05-18T01:15:36.206278+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.03535v2","created_at":"2026-05-18T01:15:36.206278+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03535","created_at":"2026-05-18T01:15:36.206278+00:00"},{"alias_kind":"pith_short_12","alias_value":"TVYRBC5QWPD2","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TVYRBC5QWPD27VCE","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TVYRBC5Q","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/TVYRBC5QWPD27VCEOATLJP7YEP","json":"https://pith.science/pith/TVYRBC5QWPD27VCEOATLJP7YEP.json","graph_json":"https://pith.science/api/pith-number/TVYRBC5QWPD27VCEOATLJP7YEP/graph.json","events_json":"https://pith.science/api/pith-number/TVYRBC5QWPD27VCEOATLJP7YEP/events.json","paper":"https://pith.science/paper/TVYRBC5Q"},"agent_actions":{"view_html":"https://pith.science/pith/TVYRBC5QWPD27VCEOATLJP7YEP","download_json":"https://pith.science/pith/TVYRBC5QWPD27VCEOATLJP7YEP.json","view_paper":"https://pith.science/paper/TVYRBC5Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.03535&json=true","fetch_graph":"https://pith.science/api/pith-number/TVYRBC5QWPD27VCEOATLJP7YEP/graph.json","fetch_events":"https://pith.science/api/pith-number/TVYRBC5QWPD27VCEOATLJP7YEP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TVYRBC5QWPD27VCEOATLJP7YEP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TVYRBC5QWPD27VCEOATLJP7YEP/action/storage_attestation","attest_author":"https://pith.science/pith/TVYRBC5QWPD27VCEOATLJP7YEP/action/author_attestation","sign_citation":"https://pith.science/pith/TVYRBC5QWPD27VCEOATLJP7YEP/action/citation_signature","submit_replication":"https://pith.science/pith/TVYRBC5QWPD27VCEOATLJP7YEP/action/replication_record"}},"created_at":"2026-05-18T01:15:36.206278+00:00","updated_at":"2026-05-18T01:15:36.206278+00:00"}