{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HCE46NV6EUZUKGE3HFCZB2L2U5","short_pith_number":"pith:HCE46NV6","canonical_record":{"source":{"id":"2509.10356","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-12T15:45:10Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"5b04456affcfa2f77e49080a892bea5794e42185fa7cd8848673cbdbcc99afa2","abstract_canon_sha256":"322d6008e0e02535b82a41c886a00f7096a7967ee0890ecf7e52d1b75714039b"},"schema_version":"1.0"},"canonical_sha256":"3889cf36be253345189b394590e97aa76c081254adfd6469d3d136a8f86b6219","source":{"kind":"arxiv","id":"2509.10356","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.10356","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"2509.10356v2","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.10356","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"HCE46NV6EUZU","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"HCE46NV6EUZUKGE3","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"HCE46NV6","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HCE46NV6EUZUKGE3HFCZB2L2U5","target":"record","payload":{"canonical_record":{"source":{"id":"2509.10356","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-12T15:45:10Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"5b04456affcfa2f77e49080a892bea5794e42185fa7cd8848673cbdbcc99afa2","abstract_canon_sha256":"322d6008e0e02535b82a41c886a00f7096a7967ee0890ecf7e52d1b75714039b"},"schema_version":"1.0"},"canonical_sha256":"3889cf36be253345189b394590e97aa76c081254adfd6469d3d136a8f86b6219","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:17.552019Z","signature_b64":"HyyxIJXdTYX6GizjHwE6MzN/AOGhaH868voJx8sR1ki3Jiy+MJYoMRm5Ij9efD7H8q1QNUKhk4ll2mjH7jmZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3889cf36be253345189b394590e97aa76c081254adfd6469d3d136a8f86b6219","last_reissued_at":"2026-05-17T23:39:17.551266Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:17.551266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.10356","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vmtUPw/jVJA17GfI6DfZgvW7dadfn/AbTCEsc7qz5s6lH3avLGP1mowS2Mq736mmvMHUR50v1+Lzr69oHc56DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T16:52:49.609623Z"},"content_sha256":"438b98da787d6b9fc71b3aaf380f0100583a8ae19023bbcea3c115e266927a3c","schema_version":"1.0","event_id":"sha256:438b98da787d6b9fc71b3aaf380f0100583a8ae19023bbcea3c115e266927a3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HCE46NV6EUZUKGE3HFCZB2L2U5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constrained Variational Inference via Safe Particle Flow","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Jorge Cort\\'es, Nikolay Atanasov, Yinzhuang Yi","submitted_at":"2025-09-12T15:45:10Z","abstract_excerpt":"We propose a control barrier function (CBF) formulation for enforcing equality and inequality constraints in variational inference. The key idea is to define a barrier functional on the space of probability density functions that encode the desired constraints imposed on the variational density. By leveraging the Liouville equation, we establish a connection between the time derivative of the variational density and the particle drift, which enables the systematic construction of corresponding CBFs associated to the particle drift. Enforcing these CBFs gives rise to the safe particle flow and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.10356","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USO7w3hBq6eJqxbw5JZ+ueI/vr9NZJWKQxnuEFgDdCSKXa85u2YWvjW7wvOo6WW4P5sUdFSVOkwhJs1Ej+UiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T16:52:49.610067Z"},"content_sha256":"72b71f4978d3b62ded6b1359c11c54801d5e255668d3f0d41be6e61a75538d0a","schema_version":"1.0","event_id":"sha256:72b71f4978d3b62ded6b1359c11c54801d5e255668d3f0d41be6e61a75538d0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCE46NV6EUZUKGE3HFCZB2L2U5/bundle.json","state_url":"https://pith.science/pith/HCE46NV6EUZUKGE3HFCZB2L2U5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCE46NV6EUZUKGE3HFCZB2L2U5/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":"2026-05-21T16:52:49Z","links":{"resolver":"https://pith.science/pith/HCE46NV6EUZUKGE3HFCZB2L2U5","bundle":"https://pith.science/pith/HCE46NV6EUZUKGE3HFCZB2L2U5/bundle.json","state":"https://pith.science/pith/HCE46NV6EUZUKGE3HFCZB2L2U5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCE46NV6EUZUKGE3HFCZB2L2U5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HCE46NV6EUZUKGE3HFCZB2L2U5","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":"322d6008e0e02535b82a41c886a00f7096a7967ee0890ecf7e52d1b75714039b","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-12T15:45:10Z","title_canon_sha256":"5b04456affcfa2f77e49080a892bea5794e42185fa7cd8848673cbdbcc99afa2"},"schema_version":"1.0","source":{"id":"2509.10356","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.10356","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"2509.10356v2","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.10356","created_at":"2026-05-17T23:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"HCE46NV6EUZU","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"HCE46NV6EUZUKGE3","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"HCE46NV6","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:72b71f4978d3b62ded6b1359c11c54801d5e255668d3f0d41be6e61a75538d0a","target":"graph","created_at":"2026-05-17T23:39:17Z","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 propose a control barrier function (CBF) formulation for enforcing equality and inequality constraints in variational inference. The key idea is to define a barrier functional on the space of probability density functions that encode the desired constraints imposed on the variational density. By leveraging the Liouville equation, we establish a connection between the time derivative of the variational density and the particle drift, which enables the systematic construction of corresponding CBFs associated to the particle drift. Enforcing these CBFs gives rise to the safe particle flow and ","authors_text":"Jorge Cort\\'es, Nikolay Atanasov, Yinzhuang Yi","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-12T15:45:10Z","title":"Constrained Variational Inference via Safe Particle Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.10356","kind":"arxiv","version":2},"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":"sha256:438b98da787d6b9fc71b3aaf380f0100583a8ae19023bbcea3c115e266927a3c","target":"record","created_at":"2026-05-17T23:39:17Z","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":"322d6008e0e02535b82a41c886a00f7096a7967ee0890ecf7e52d1b75714039b","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-12T15:45:10Z","title_canon_sha256":"5b04456affcfa2f77e49080a892bea5794e42185fa7cd8848673cbdbcc99afa2"},"schema_version":"1.0","source":{"id":"2509.10356","kind":"arxiv","version":2}},"canonical_sha256":"3889cf36be253345189b394590e97aa76c081254adfd6469d3d136a8f86b6219","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3889cf36be253345189b394590e97aa76c081254adfd6469d3d136a8f86b6219","first_computed_at":"2026-05-17T23:39:17.551266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:17.551266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HyyxIJXdTYX6GizjHwE6MzN/AOGhaH868voJx8sR1ki3Jiy+MJYoMRm5Ij9efD7H8q1QNUKhk4ll2mjH7jmZDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:17.552019Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.10356","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:438b98da787d6b9fc71b3aaf380f0100583a8ae19023bbcea3c115e266927a3c","sha256:72b71f4978d3b62ded6b1359c11c54801d5e255668d3f0d41be6e61a75538d0a"],"state_sha256":"f126e0e0be7c312cba367ca32a22ce6a6ccf3d589553e32ccdf8399ee65b1397"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A+6YUZ4lPJgIp2dblI+jlmj8agIHaF+b8BvR31wzFjcEvINRunVp8WEXE+0+CYMxXJmTPZHbY8QsVe2PypXrBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T16:52:49.613061Z","bundle_sha256":"8f2f55aed560e1a73024c4bef68a1d6abd17ca30a814387bf1c66d25a306f436"}}