{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:FU23WKB3N4CIN7KQDCI4GZFNHN","short_pith_number":"pith:FU23WKB3","canonical_record":{"source":{"id":"1906.00460","kind":"arxiv","version":17},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2019-06-02T17:57:08Z","cross_cats_sorted":["cs.CV","cs.NA","math.NA","stat.ML"],"title_canon_sha256":"d3117f85090c11965eb324ff510cc64d9d45af639334de22706fbb5b42815f31","abstract_canon_sha256":"7a21486eac7426bdcaec90a2dc9d73f02ba165fbefb4d2d30400f2c9cf0b3c04"},"schema_version":"1.0"},"canonical_sha256":"2d35bb283b6f0486fd501891c364ad3b423cd9c8cc4116b3b575ba283647922a","source":{"kind":"arxiv","id":"1906.00460","version":17},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.00460","created_at":"2026-07-05T03:13:19Z"},{"alias_kind":"arxiv_version","alias_value":"1906.00460v17","created_at":"2026-07-05T03:13:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00460","created_at":"2026-07-05T03:13:19Z"},{"alias_kind":"pith_short_12","alias_value":"FU23WKB3N4CI","created_at":"2026-07-05T03:13:19Z"},{"alias_kind":"pith_short_16","alias_value":"FU23WKB3N4CIN7KQ","created_at":"2026-07-05T03:13:19Z"},{"alias_kind":"pith_short_8","alias_value":"FU23WKB3","created_at":"2026-07-05T03:13:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:FU23WKB3N4CIN7KQDCI4GZFNHN","target":"record","payload":{"canonical_record":{"source":{"id":"1906.00460","kind":"arxiv","version":17},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2019-06-02T17:57:08Z","cross_cats_sorted":["cs.CV","cs.NA","math.NA","stat.ML"],"title_canon_sha256":"d3117f85090c11965eb324ff510cc64d9d45af639334de22706fbb5b42815f31","abstract_canon_sha256":"7a21486eac7426bdcaec90a2dc9d73f02ba165fbefb4d2d30400f2c9cf0b3c04"},"schema_version":"1.0"},"canonical_sha256":"2d35bb283b6f0486fd501891c364ad3b423cd9c8cc4116b3b575ba283647922a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:13:19.865345Z","signature_b64":"b1Qj5EpEQqo4gPYM4gtbEVaQ2xDrl+Ir6lsgeB9Tqd9ogpfzUcjLwR9PQy9ZrI6EpGSEhUzy9XPuXeEqXaiACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d35bb283b6f0486fd501891c364ad3b423cd9c8cc4116b3b575ba283647922a","last_reissued_at":"2026-07-05T03:13:19.864890Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:13:19.864890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.00460","source_version":17,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:13:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eQD9e01ljD/bP1FTn7B4bUIrtt+/aWLSl3+YowsuVlwQ3/g6IHsUQIR4+8K9v36BSuAJuXBFUPkERpuFQoKPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:52:25.285465Z"},"content_sha256":"ff376777fe5a6b18f9f29d39130e3a220f7dcebf4a9b1b22fc8aa0d1aa0951e8","schema_version":"1.0","event_id":"sha256:ff376777fe5a6b18f9f29d39130e3a220f7dcebf4a9b1b22fc8aa0d1aa0951e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:FU23WKB3N4CIN7KQDCI4GZFNHN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On The Radon-Nikodym Spectral Approach With Optimal Clustering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CV","cs.NA","math.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Vladislav Gennadievich Malyshkin","submitted_at":"2019-06-02T17:57:08Z","abstract_excerpt":"Problems of interpolation, classification, and clustering are considered. In the tenets of Radon--Nikodym approach $\\langle f(\\mathbf{x})\\psi^2 \\rangle / \\langle\\psi^2\\rangle$, where the $\\psi(\\mathbf{x})$ is a linear function on input attributes, all the answers are obtained from a generalized eigenproblem $|f|\\psi^{[i]}\\rangle = \\lambda^{[i]} |\\psi^{[i]}\\rangle$. The solution to the interpolation problem is a regular Radon-Nikodym derivative. The solution to the classification problem requires prior and posterior probabilities that are obtained using the Lebesgue quadrature[1] technique. Whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00460","kind":"arxiv","version":17},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1906.00460/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:13:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yZasPcndfu3aZJxxXNBlHWO/u+e9oguNlLL6jQlUmcwRTbuGX3J06RHnSIKnbHl6MJT3cuzFpp/TqWE03UWKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T18:52:25.286018Z"},"content_sha256":"0423a107a9029685fd7f6fa2fc1c058fe1e4d3af3924f0dc574527a19f3af523","schema_version":"1.0","event_id":"sha256:0423a107a9029685fd7f6fa2fc1c058fe1e4d3af3924f0dc574527a19f3af523"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FU23WKB3N4CIN7KQDCI4GZFNHN/bundle.json","state_url":"https://pith.science/pith/FU23WKB3N4CIN7KQDCI4GZFNHN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FU23WKB3N4CIN7KQDCI4GZFNHN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-19T18:52:25Z","links":{"resolver":"https://pith.science/pith/FU23WKB3N4CIN7KQDCI4GZFNHN","bundle":"https://pith.science/pith/FU23WKB3N4CIN7KQDCI4GZFNHN/bundle.json","state":"https://pith.science/pith/FU23WKB3N4CIN7KQDCI4GZFNHN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FU23WKB3N4CIN7KQDCI4GZFNHN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FU23WKB3N4CIN7KQDCI4GZFNHN","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":"7a21486eac7426bdcaec90a2dc9d73f02ba165fbefb4d2d30400f2c9cf0b3c04","cross_cats_sorted":["cs.CV","cs.NA","math.NA","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2019-06-02T17:57:08Z","title_canon_sha256":"d3117f85090c11965eb324ff510cc64d9d45af639334de22706fbb5b42815f31"},"schema_version":"1.0","source":{"id":"1906.00460","kind":"arxiv","version":17}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.00460","created_at":"2026-07-05T03:13:19Z"},{"alias_kind":"arxiv_version","alias_value":"1906.00460v17","created_at":"2026-07-05T03:13:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00460","created_at":"2026-07-05T03:13:19Z"},{"alias_kind":"pith_short_12","alias_value":"FU23WKB3N4CI","created_at":"2026-07-05T03:13:19Z"},{"alias_kind":"pith_short_16","alias_value":"FU23WKB3N4CIN7KQ","created_at":"2026-07-05T03:13:19Z"},{"alias_kind":"pith_short_8","alias_value":"FU23WKB3","created_at":"2026-07-05T03:13:19Z"}],"graph_snapshots":[{"event_id":"sha256:0423a107a9029685fd7f6fa2fc1c058fe1e4d3af3924f0dc574527a19f3af523","target":"graph","created_at":"2026-07-05T03:13:19Z","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/1906.00460/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Problems of interpolation, classification, and clustering are considered. In the tenets of Radon--Nikodym approach $\\langle f(\\mathbf{x})\\psi^2 \\rangle / \\langle\\psi^2\\rangle$, where the $\\psi(\\mathbf{x})$ is a linear function on input attributes, all the answers are obtained from a generalized eigenproblem $|f|\\psi^{[i]}\\rangle = \\lambda^{[i]} |\\psi^{[i]}\\rangle$. The solution to the interpolation problem is a regular Radon-Nikodym derivative. The solution to the classification problem requires prior and posterior probabilities that are obtained using the Lebesgue quadrature[1] technique. Whe","authors_text":"Vladislav Gennadievich Malyshkin","cross_cats":["cs.CV","cs.NA","math.NA","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2019-06-02T17:57:08Z","title":"On The Radon-Nikodym Spectral Approach With Optimal Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00460","kind":"arxiv","version":17},"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:ff376777fe5a6b18f9f29d39130e3a220f7dcebf4a9b1b22fc8aa0d1aa0951e8","target":"record","created_at":"2026-07-05T03:13:19Z","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":"7a21486eac7426bdcaec90a2dc9d73f02ba165fbefb4d2d30400f2c9cf0b3c04","cross_cats_sorted":["cs.CV","cs.NA","math.NA","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2019-06-02T17:57:08Z","title_canon_sha256":"d3117f85090c11965eb324ff510cc64d9d45af639334de22706fbb5b42815f31"},"schema_version":"1.0","source":{"id":"1906.00460","kind":"arxiv","version":17}},"canonical_sha256":"2d35bb283b6f0486fd501891c364ad3b423cd9c8cc4116b3b575ba283647922a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d35bb283b6f0486fd501891c364ad3b423cd9c8cc4116b3b575ba283647922a","first_computed_at":"2026-07-05T03:13:19.864890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:13:19.864890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b1Qj5EpEQqo4gPYM4gtbEVaQ2xDrl+Ir6lsgeB9Tqd9ogpfzUcjLwR9PQy9ZrI6EpGSEhUzy9XPuXeEqXaiACw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:13:19.865345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.00460","source_kind":"arxiv","source_version":17}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff376777fe5a6b18f9f29d39130e3a220f7dcebf4a9b1b22fc8aa0d1aa0951e8","sha256:0423a107a9029685fd7f6fa2fc1c058fe1e4d3af3924f0dc574527a19f3af523"],"state_sha256":"bdc4bacecd39e45771ac8e27e9deb09fbe9d3135f62ca11cb1a81e64d763d16f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gqUvn1lEd6D6jq/G3+iIEb30DHfwQoXFgLmrpF3MZw7/lfzZaZFxv2IsR35iE77dmS8d3uFoU6JXeGwK/xQ0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T18:52:25.291854Z","bundle_sha256":"62aecaae3a27bd141849248841314ecd6adbeee4deb5d92cc5c6963393a79b94"}}