{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LULAI3PB2CBC2TVZDFDSLXD2TW","short_pith_number":"pith:LULAI3PB","canonical_record":{"source":{"id":"2606.20920","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T20:19:44Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f456e04940ac0866550730697661a3eda7c2fe65eee114d72e71e8bb8a8328af","abstract_canon_sha256":"5b00e1c343cdf22538b8be247911fe2a9c912f162a53dbb32cae1d4e72f75d4f"},"schema_version":"1.0"},"canonical_sha256":"5d16046de1d0822d4eb9194725dc7a9db9300796216fcb09cf218449c4d65ad0","source":{"kind":"arxiv","id":"2606.20920","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20920","created_at":"2026-06-23T01:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20920v1","created_at":"2026-06-23T01:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20920","created_at":"2026-06-23T01:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"LULAI3PB2CBC","created_at":"2026-06-23T01:12:22Z"},{"alias_kind":"pith_short_16","alias_value":"LULAI3PB2CBC2TVZ","created_at":"2026-06-23T01:12:22Z"},{"alias_kind":"pith_short_8","alias_value":"LULAI3PB","created_at":"2026-06-23T01:12:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LULAI3PB2CBC2TVZDFDSLXD2TW","target":"record","payload":{"canonical_record":{"source":{"id":"2606.20920","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T20:19:44Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f456e04940ac0866550730697661a3eda7c2fe65eee114d72e71e8bb8a8328af","abstract_canon_sha256":"5b00e1c343cdf22538b8be247911fe2a9c912f162a53dbb32cae1d4e72f75d4f"},"schema_version":"1.0"},"canonical_sha256":"5d16046de1d0822d4eb9194725dc7a9db9300796216fcb09cf218449c4d65ad0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:22.050201Z","signature_b64":"6Q+0jk5OqFPC1YbVnFVmVKYfY1fTkxMRvWWbOv9slYituJhE3LOhri88/Do9igyLiN6ygtwFaOVxa90uxH+pCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d16046de1d0822d4eb9194725dc7a9db9300796216fcb09cf218449c4d65ad0","last_reissued_at":"2026-06-23T01:12:22.049689Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:22.049689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.20920","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T01:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fXdgz7jaViH8z4oQeOD5pGi8tdTJc/F4HbJPjiYFLLviRUU3nP5AJA4BhbslDi4tVoBFFLTr/5rOlAz6NKDTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:12:33.562600Z"},"content_sha256":"6d7f272abe94f206076c0aa92e23011f982acac5a66fb2984447f86e4fa9776f","schema_version":"1.0","event_id":"sha256:6d7f272abe94f206076c0aa92e23011f982acac5a66fb2984447f86e4fa9776f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LULAI3PB2CBC2TVZDFDSLXD2TW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\Omega$: Operator-based Mixture Ensemble for Generative Assimilation","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cs.LG","authors_text":"Nan Chen, Pouria Behnoudfar","submitted_at":"2026-06-18T20:19:44Z","abstract_excerpt":"Characterizing non-Gaussian posterior distributions in partially observed high-dimensional nonlinear systems remains a fundamental challenge in data assimilation. Ensemble Kalman filters rely on Gaussian approximations that can be inaccurate for strongly non-Gaussian posteriors, whereas particle filters suffer from severe scalability limitations. Recent score-based generative approaches improve posterior characterization but typically require supervised training with ground-truth posterior samples, which are unavailable in most practical applications. We introduce $\\Omega$ (Operator-based Mixt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20920","kind":"arxiv","version":1},"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/2606.20920/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":"2026-06-23T01:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e1lrZ1LoeNoFst59Y24KeXjYTN/HYdx+p93kivHnHEKLb4lP7p236tm3b0X3mBlahyQc2g7gbjtAhK4XBNsVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:12:33.562967Z"},"content_sha256":"9bd1253b08e70c1c7f889c4bbc552cf925a834765396d6f25a7c137cd3519f79","schema_version":"1.0","event_id":"sha256:9bd1253b08e70c1c7f889c4bbc552cf925a834765396d6f25a7c137cd3519f79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LULAI3PB2CBC2TVZDFDSLXD2TW/bundle.json","state_url":"https://pith.science/pith/LULAI3PB2CBC2TVZDFDSLXD2TW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LULAI3PB2CBC2TVZDFDSLXD2TW/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":"2026-07-04T18:12:33Z","links":{"resolver":"https://pith.science/pith/LULAI3PB2CBC2TVZDFDSLXD2TW","bundle":"https://pith.science/pith/LULAI3PB2CBC2TVZDFDSLXD2TW/bundle.json","state":"https://pith.science/pith/LULAI3PB2CBC2TVZDFDSLXD2TW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LULAI3PB2CBC2TVZDFDSLXD2TW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LULAI3PB2CBC2TVZDFDSLXD2TW","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":"5b00e1c343cdf22538b8be247911fe2a9c912f162a53dbb32cae1d4e72f75d4f","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T20:19:44Z","title_canon_sha256":"f456e04940ac0866550730697661a3eda7c2fe65eee114d72e71e8bb8a8328af"},"schema_version":"1.0","source":{"id":"2606.20920","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20920","created_at":"2026-06-23T01:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20920v1","created_at":"2026-06-23T01:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20920","created_at":"2026-06-23T01:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"LULAI3PB2CBC","created_at":"2026-06-23T01:12:22Z"},{"alias_kind":"pith_short_16","alias_value":"LULAI3PB2CBC2TVZ","created_at":"2026-06-23T01:12:22Z"},{"alias_kind":"pith_short_8","alias_value":"LULAI3PB","created_at":"2026-06-23T01:12:22Z"}],"graph_snapshots":[{"event_id":"sha256:9bd1253b08e70c1c7f889c4bbc552cf925a834765396d6f25a7c137cd3519f79","target":"graph","created_at":"2026-06-23T01:12:22Z","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/2606.20920/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Characterizing non-Gaussian posterior distributions in partially observed high-dimensional nonlinear systems remains a fundamental challenge in data assimilation. Ensemble Kalman filters rely on Gaussian approximations that can be inaccurate for strongly non-Gaussian posteriors, whereas particle filters suffer from severe scalability limitations. Recent score-based generative approaches improve posterior characterization but typically require supervised training with ground-truth posterior samples, which are unavailable in most practical applications. We introduce $\\Omega$ (Operator-based Mixt","authors_text":"Nan Chen, Pouria Behnoudfar","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T20:19:44Z","title":"$\\Omega$: Operator-based Mixture Ensemble for Generative Assimilation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20920","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":"sha256:6d7f272abe94f206076c0aa92e23011f982acac5a66fb2984447f86e4fa9776f","target":"record","created_at":"2026-06-23T01:12:22Z","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":"5b00e1c343cdf22538b8be247911fe2a9c912f162a53dbb32cae1d4e72f75d4f","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T20:19:44Z","title_canon_sha256":"f456e04940ac0866550730697661a3eda7c2fe65eee114d72e71e8bb8a8328af"},"schema_version":"1.0","source":{"id":"2606.20920","kind":"arxiv","version":1}},"canonical_sha256":"5d16046de1d0822d4eb9194725dc7a9db9300796216fcb09cf218449c4d65ad0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d16046de1d0822d4eb9194725dc7a9db9300796216fcb09cf218449c4d65ad0","first_computed_at":"2026-06-23T01:12:22.049689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T01:12:22.049689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Q+0jk5OqFPC1YbVnFVmVKYfY1fTkxMRvWWbOv9slYituJhE3LOhri88/Do9igyLiN6ygtwFaOVxa90uxH+pCQ==","signature_status":"signed_v1","signed_at":"2026-06-23T01:12:22.050201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.20920","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d7f272abe94f206076c0aa92e23011f982acac5a66fb2984447f86e4fa9776f","sha256:9bd1253b08e70c1c7f889c4bbc552cf925a834765396d6f25a7c137cd3519f79"],"state_sha256":"9aca247e3982912abbf46632644d8cac4ad29567b6936845e5254813f163257b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O2GQmZ1aGBXrd4OdYHNq25NJ8ZZIQASJTbZ5G5HMV3Pr18yq3AwLzNszM3tfxxkZnt1aJO+Njy9jbjbXNlzaAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T18:12:33.565179Z","bundle_sha256":"14c5780a8417264354d1e3a7e3b854ba8359d78148882662b0a6b04ee15de0cd"}}