{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6PB4CAUC7TGG5O4BWBNWJLMAU7","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":"8a7fc0fcd6fbef89743434414bd8c3e1f629bd15e6c57c8ef4103dd9cc0aa3e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-27T15:39:01Z","title_canon_sha256":"04786cedd564174314f44b56c8d48298c9ebaf728cc94af7a44ce34d21801e9f"},"schema_version":"1.0","source":{"id":"1607.08153","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08153","created_at":"2026-05-18T01:10:20Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08153v1","created_at":"2026-05-18T01:10:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08153","created_at":"2026-05-18T01:10:20Z"},{"alias_kind":"pith_short_12","alias_value":"6PB4CAUC7TGG","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6PB4CAUC7TGG5O4B","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6PB4CAUC","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:b677dce48a0123c510816a8e279b5e0a2ebf6930860d2fd5bd8b71b5ca14d82c","target":"graph","created_at":"2026-05-18T01:10:20Z","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 show that every spherical 2-Dupin submanifold that is not a hypersurface is conformally congruent to the standard embedding of the real, complex, quaternionic or octonionic projective plane. We also classify 2-CPC, 2-umbilical and weakly 2-umbilical submanifolds in space forms.","authors_text":"Antonio J. Di Scala, Guilherme Machado de Freitas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-27T15:39:01Z","title":"Spherical 2-Dupin submanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08153","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":"sha256:110d69ea18234ec525d606536c4324d5a478beb8ef1164600a988d3de60a176e","target":"record","created_at":"2026-05-18T01:10:20Z","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":"8a7fc0fcd6fbef89743434414bd8c3e1f629bd15e6c57c8ef4103dd9cc0aa3e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-27T15:39:01Z","title_canon_sha256":"04786cedd564174314f44b56c8d48298c9ebaf728cc94af7a44ce34d21801e9f"},"schema_version":"1.0","source":{"id":"1607.08153","kind":"arxiv","version":1}},"canonical_sha256":"f3c3c10282fccc6ebb81b05b64ad80a7e682280035907d7de2e90ba2670c0967","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3c3c10282fccc6ebb81b05b64ad80a7e682280035907d7de2e90ba2670c0967","first_computed_at":"2026-05-18T01:10:20.899269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:20.899269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WAzz8FMTTO9Y068R6GQ9KPfZCl1MDk7JOiR9poCBsoDkT1Ic+KOwO1MNscmdFXwQs5Og7grISGcPA+rYzEg3CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:20.900001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08153","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:110d69ea18234ec525d606536c4324d5a478beb8ef1164600a988d3de60a176e","sha256:b677dce48a0123c510816a8e279b5e0a2ebf6930860d2fd5bd8b71b5ca14d82c"],"state_sha256":"d9bbcec9f6435cc48c66d7b1952bcca78b3c8cd5925e753e99361f00a6af1959"}