{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N6LD3NT4BDVC6QUMQCHURKMXJX","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":"b3f68baf491e70561625bca94562c63b97ecc9ada2ded527c90422f617f952c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-19T06:40:51Z","title_canon_sha256":"7c0eb1b216ce959acaf8f1986040ae89788100802895c6a20a293e84c21f2593"},"schema_version":"1.0","source":{"id":"1108.3905","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3905","created_at":"2026-05-18T04:08:14Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3905v2","created_at":"2026-05-18T04:08:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3905","created_at":"2026-05-18T04:08:14Z"},{"alias_kind":"pith_short_12","alias_value":"N6LD3NT4BDVC","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N6LD3NT4BDVC6QUM","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N6LD3NT4","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:f056a650f1342be6e0a42286c729f8aa6c8d73e44451298f47c36afdac4d6165","target":"graph","created_at":"2026-05-18T04:08:14Z","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":"We provide conditions under which an isometric immersion of a (warped) product of manifolds into a space form must be a (warped) product of isometric immersions.","authors_text":"M. Dajczer, T. Vlachos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-19T06:40:51Z","title":"Isometric immersions of warped products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3905","kind":"arxiv","version":2},"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":"sha256:8418af26a1b6c79a11ee1ad0ae30296a6debbcc5135549ba821229a151bc8766","target":"record","created_at":"2026-05-18T04:08:14Z","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":"b3f68baf491e70561625bca94562c63b97ecc9ada2ded527c90422f617f952c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-19T06:40:51Z","title_canon_sha256":"7c0eb1b216ce959acaf8f1986040ae89788100802895c6a20a293e84c21f2593"},"schema_version":"1.0","source":{"id":"1108.3905","kind":"arxiv","version":2}},"canonical_sha256":"6f963db67c08ea2f428c808f48a9974de7605948721058c0480935c1bb6b3e62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f963db67c08ea2f428c808f48a9974de7605948721058c0480935c1bb6b3e62","first_computed_at":"2026-05-18T04:08:14.388138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:14.388138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9cf+kaK0IBIlYUKjb+IH6yTf/8xW/ElWqFPNZ5/QeNeRIyNZQW8r/XdsWCiBUN6ikVbKWLZ0ltsv4QVIhgAICA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:14.388706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3905","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8418af26a1b6c79a11ee1ad0ae30296a6debbcc5135549ba821229a151bc8766","sha256:f056a650f1342be6e0a42286c729f8aa6c8d73e44451298f47c36afdac4d6165"],"state_sha256":"79f9b042d5324f0290db92a264647a5b817d8dd395ce58de0d2a37b1ba016dab"}