{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JSVFKJDXN2BJAD2HYOA7QRB7TD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"81e2d9330323427969658f590af6c78c7b9390b1c683ef75abdc5d1c5147b463","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-28T14:20:46Z","title_canon_sha256":"77c9a0b2f02d14a782b6c0548a9258cba25f65ab12490ebf2b5d658e1e8069ed"},"schema_version":"1.0","source":{"id":"1508.07223","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07223","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07223v1","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07223","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"JSVFKJDXN2BJ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JSVFKJDXN2BJAD2H","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JSVFKJDX","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:189ba9d100dcb470b1d053ca887a0e3164447b087ceb90cfd3683fc812d09577","target":"graph","created_at":"2026-05-18T01:34:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we give a definition of coherent tangent bundles of space form type, which is a generalized notion of space forms. Then, we classify their realizations in the sphere as a wave front, which is a generalization of a theorem of O'Neill and Stiel: any isometric immersion of the n-sphere into the (n+1)-sphere of the same sectional curvature is totally geodesic.","authors_text":"Atsufumi Honda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-28T14:20:46Z","title":"Isometric immersions with singularities between space forms of the same positive curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07223","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aa87835aac6833830cb63e3ad584a7af073b51dfc3b76fa8abe18437a8f85a6f","target":"record","created_at":"2026-05-18T01:34:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"81e2d9330323427969658f590af6c78c7b9390b1c683ef75abdc5d1c5147b463","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-28T14:20:46Z","title_canon_sha256":"77c9a0b2f02d14a782b6c0548a9258cba25f65ab12490ebf2b5d658e1e8069ed"},"schema_version":"1.0","source":{"id":"1508.07223","kind":"arxiv","version":1}},"canonical_sha256":"4caa5524776e82900f47c381f8443f98eb37bcfe498f4e6efcb6f4fdd01dc6e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4caa5524776e82900f47c381f8443f98eb37bcfe498f4e6efcb6f4fdd01dc6e6","first_computed_at":"2026-05-18T01:34:36.565598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:36.565598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cWLD3oO3boqgvORD37cJjisBxqgAyf2vVh4FUTq+RKDdhK6AHtjXsD+k01mfNQShgg4Q3LE9rS7XgNOzm/2HAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:36.566279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07223","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa87835aac6833830cb63e3ad584a7af073b51dfc3b76fa8abe18437a8f85a6f","sha256:189ba9d100dcb470b1d053ca887a0e3164447b087ceb90cfd3683fc812d09577"],"state_sha256":"e54b6dec9da11fad6618f388c1e31a2e179940fd6bfa05a8e7ec6bd464ff65d9"}