{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QJFYUEW4JX3GSSGFK7X36GKH5Y","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":"1869c5a97c1456900c1951b493c5fa2f81b69cc2650c1c3ac85919da77cc93f9","cross_cats_sorted":["cs.LG","math.CT","math.DG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-05-06T16:27:06Z","title_canon_sha256":"a53e5c484f37104c91e3b14d5a915dfd05be92c2c11fd15f0ec19b539e455ce4"},"schema_version":"1.0","source":{"id":"2505.03862","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.03862","created_at":"2026-07-05T10:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"2505.03862v1","created_at":"2026-07-05T10:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.03862","created_at":"2026-07-05T10:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"QJFYUEW4JX3G","created_at":"2026-07-05T10:59:32Z"},{"alias_kind":"pith_short_16","alias_value":"QJFYUEW4JX3GSSGF","created_at":"2026-07-05T10:59:32Z"},{"alias_kind":"pith_short_8","alias_value":"QJFYUEW4","created_at":"2026-07-05T10:59:32Z"}],"graph_snapshots":[{"event_id":"sha256:6ff39e955087410fa019352a6e901af0b9b97ac123023e4dba1d1bc3006f3197","target":"graph","created_at":"2026-07-05T10:59:32Z","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/2505.03862/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present and discuss applications of the category of probabilistic morphisms, initially developed in \\cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall be, along with many other topics, considered in depth in the forthcoming book \\cite{LMPT2024}.","authors_text":"Frederic Protin, H\\`a Quang Minh, H\\^ong V\\^an L\\^e, Wilderich Tuschmann","cross_cats":["cs.LG","math.CT","math.DG","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-05-06T16:27:06Z","title":"Categorical and geometric methods in statistical, manifold, and machine learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.03862","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:dae3b1852ccd45a798f6227f6dafe60e5844b9709bb66255e03afcbc25266bc7","target":"record","created_at":"2026-07-05T10:59:32Z","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":"1869c5a97c1456900c1951b493c5fa2f81b69cc2650c1c3ac85919da77cc93f9","cross_cats_sorted":["cs.LG","math.CT","math.DG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-05-06T16:27:06Z","title_canon_sha256":"a53e5c484f37104c91e3b14d5a915dfd05be92c2c11fd15f0ec19b539e455ce4"},"schema_version":"1.0","source":{"id":"2505.03862","kind":"arxiv","version":1}},"canonical_sha256":"824b8a12dc4df66948c557efbf1947ee0d04c00326f4421049b7d2ed99448c34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"824b8a12dc4df66948c557efbf1947ee0d04c00326f4421049b7d2ed99448c34","first_computed_at":"2026-07-05T10:59:32.775844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:59:32.775844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0hOV4AAmyuowj4uvdLFcAmW5W0ApdECuidgLCreYdfSdzxQy3X48Dqc9YLCDAXOKjXNac7BWAWTK6uPOtBV3Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:59:32.776366Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.03862","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dae3b1852ccd45a798f6227f6dafe60e5844b9709bb66255e03afcbc25266bc7","sha256:6ff39e955087410fa019352a6e901af0b9b97ac123023e4dba1d1bc3006f3197"],"state_sha256":"6b326120ca516ea9957e0265948fa82d92baa142ec81013f26ebc21c281b95aa"}