{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QSZJNXQ7FILDR6AYFLR6OUWIXM","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":"9b8ff995de2734a6ac102d97a311f385128c26589b69f5a955176c49294504a6","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-04T17:02:03Z","title_canon_sha256":"35d061ab1dda59c67f9fd44856e991a82931a49c7108061cac66160c5d223e74"},"schema_version":"1.0","source":{"id":"2606.06395","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06395","created_at":"2026-06-05T01:15:44Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06395v1","created_at":"2026-06-05T01:15:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06395","created_at":"2026-06-05T01:15:44Z"},{"alias_kind":"pith_short_12","alias_value":"QSZJNXQ7FILD","created_at":"2026-06-05T01:15:44Z"},{"alias_kind":"pith_short_16","alias_value":"QSZJNXQ7FILDR6AY","created_at":"2026-06-05T01:15:44Z"},{"alias_kind":"pith_short_8","alias_value":"QSZJNXQ7","created_at":"2026-06-05T01:15:44Z"}],"graph_snapshots":[{"event_id":"sha256:f5b2b8c80b0bc896a79ece130b7f9b0c64e2c2747d97330379d3e2d7c7c5ff49","target":"graph","created_at":"2026-06-05T01:15:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.06395/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The probability simplex is one of the most standard statistical manifolds, and information geometry initiated by S. Amari and H. Nagaoka studies the statistical submanifold theory of the probability simplex. On the other hand, H. Furuhata defined doubly totally-umbilical submanifolds in the geometry of statistical manifolds. We give the complete classification of doubly totally-umbilical submanifolds in the probability simplex.","authors_text":"Ryu Ueno","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-04T17:02:03Z","title":"Doubly Totally-Umbilical Statistical Submanifolds in the Probability Simplex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06395","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":"sha256:506f7372f4ecdb9076f998bce4ea48c4660828475b69111c3cdf74de787fde2e","target":"record","created_at":"2026-06-05T01:15:44Z","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":"9b8ff995de2734a6ac102d97a311f385128c26589b69f5a955176c49294504a6","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-04T17:02:03Z","title_canon_sha256":"35d061ab1dda59c67f9fd44856e991a82931a49c7108061cac66160c5d223e74"},"schema_version":"1.0","source":{"id":"2606.06395","kind":"arxiv","version":1}},"canonical_sha256":"84b296de1f2a1638f8182ae3e752c8bb2701f9a5d6c2710ab7989e36b966adde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84b296de1f2a1638f8182ae3e752c8bb2701f9a5d6c2710ab7989e36b966adde","first_computed_at":"2026-06-05T01:15:44.318030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:44.318030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AD33vTJWdQeICbohBduKPZHm8cy8uqyIEtPG5GJrIqpHud3hep27NPWrum0XUWqP4B8JLVk2KrgnZlm3nowgDQ==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:44.318642Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06395","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:506f7372f4ecdb9076f998bce4ea48c4660828475b69111c3cdf74de787fde2e","sha256:f5b2b8c80b0bc896a79ece130b7f9b0c64e2c2747d97330379d3e2d7c7c5ff49"],"state_sha256":"a2b2ebcdaa5a78647dcd192d27eb44fdd533d11063c02d885a8c725d40babdba"}