{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:5J4XM6UGQZMCVQ2UEGZTYW4NUQ","short_pith_number":"pith:5J4XM6UG","canonical_record":{"source":{"id":"2309.15139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-09-26T15:38:57Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"56df84da27fc34c83cd248c75cc6501f33f5ebb81579af51ac54d105a016cedb","abstract_canon_sha256":"82bc4b719aa74d57c4be921745bd55e9ee53b2fd3a43c247ab19f67232083f5a"},"schema_version":"1.0"},"canonical_sha256":"ea79767a8686582ac35421b33c5b8da4176831d14c10038bb1728da10768fe94","source":{"kind":"arxiv","id":"2309.15139","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.15139","created_at":"2026-07-05T06:54:41Z"},{"alias_kind":"arxiv_version","alias_value":"2309.15139v1","created_at":"2026-07-05T06:54:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.15139","created_at":"2026-07-05T06:54:41Z"},{"alias_kind":"pith_short_12","alias_value":"5J4XM6UGQZMC","created_at":"2026-07-05T06:54:41Z"},{"alias_kind":"pith_short_16","alias_value":"5J4XM6UGQZMCVQ2U","created_at":"2026-07-05T06:54:41Z"},{"alias_kind":"pith_short_8","alias_value":"5J4XM6UG","created_at":"2026-07-05T06:54:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:5J4XM6UGQZMCVQ2UEGZTYW4NUQ","target":"record","payload":{"canonical_record":{"source":{"id":"2309.15139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-09-26T15:38:57Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"56df84da27fc34c83cd248c75cc6501f33f5ebb81579af51ac54d105a016cedb","abstract_canon_sha256":"82bc4b719aa74d57c4be921745bd55e9ee53b2fd3a43c247ab19f67232083f5a"},"schema_version":"1.0"},"canonical_sha256":"ea79767a8686582ac35421b33c5b8da4176831d14c10038bb1728da10768fe94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:54:41.779090Z","signature_b64":"lGw3r3BO9nf1d+3m2OpNx1GHn7Iak7/jn4O8wRY7z2shQ8umpX+HN69UGMGMlOpoMzFYOKbCvbYisagKpNqqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea79767a8686582ac35421b33c5b8da4176831d14c10038bb1728da10768fe94","last_reissued_at":"2026-07-05T06:54:41.778673Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:54:41.778673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.15139","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":"2026-07-05T06:54:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iGNDgHhh/PAHxxBR6j8IXwtp0Qu1KnFcGB6cVFxf5CxJbWRV+i0fSrVRwmEkWJlR2e4e34zW3+9h0TpPACvSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T22:34:53.509236Z"},"content_sha256":"9ec4c91f0dd7fcf71e8c900dcb8f61ba7cb8cd2df9733d4ee3cbf2ee9c2b1c44","schema_version":"1.0","event_id":"sha256:9ec4c91f0dd7fcf71e8c900dcb8f61ba7cb8cd2df9733d4ee3cbf2ee9c2b1c44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:5J4XM6UGQZMCVQ2UEGZTYW4NUQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Faguo Wu, Feng Liu, Xiao Zhang","submitted_at":"2023-09-26T15:38:57Z","abstract_excerpt":"The normalization constraint on probability density poses a significant challenge for solving the Fokker-Planck equation. Normalizing Flow, an invertible generative model leverages the change of variables formula to ensure probability density conservation and enable the learning of complex data distributions. In this paper, we introduce Physics-Informed Normalizing Flows (PINF), a novel extension of continuous normalizing flows, incorporating diffusion through the method of characteristics. Our method, which is mesh-free and causality-free, can efficiently solve high dimensional time-dependent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.15139","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/2309.15139/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":"2026-07-05T06:54:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yuuEmEK/IryqQSpNfzn108LTeopBc8fj3Wdk5CdyG4huX4+skpHaTTGjNNg75AaY0q0Rdl0zAuqPwYP9ZOXgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T22:34:53.509739Z"},"content_sha256":"bc7a34599a0ae3808493a9db8c0093db09b22d8ac90e6de7fa1bad449b5fa930","schema_version":"1.0","event_id":"sha256:bc7a34599a0ae3808493a9db8c0093db09b22d8ac90e6de7fa1bad449b5fa930"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5J4XM6UGQZMCVQ2UEGZTYW4NUQ/bundle.json","state_url":"https://pith.science/pith/5J4XM6UGQZMCVQ2UEGZTYW4NUQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5J4XM6UGQZMCVQ2UEGZTYW4NUQ/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":"2026-08-05T22:34:53Z","links":{"resolver":"https://pith.science/pith/5J4XM6UGQZMCVQ2UEGZTYW4NUQ","bundle":"https://pith.science/pith/5J4XM6UGQZMCVQ2UEGZTYW4NUQ/bundle.json","state":"https://pith.science/pith/5J4XM6UGQZMCVQ2UEGZTYW4NUQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5J4XM6UGQZMCVQ2UEGZTYW4NUQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5J4XM6UGQZMCVQ2UEGZTYW4NUQ","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":"82bc4b719aa74d57c4be921745bd55e9ee53b2fd3a43c247ab19f67232083f5a","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-09-26T15:38:57Z","title_canon_sha256":"56df84da27fc34c83cd248c75cc6501f33f5ebb81579af51ac54d105a016cedb"},"schema_version":"1.0","source":{"id":"2309.15139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.15139","created_at":"2026-07-05T06:54:41Z"},{"alias_kind":"arxiv_version","alias_value":"2309.15139v1","created_at":"2026-07-05T06:54:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.15139","created_at":"2026-07-05T06:54:41Z"},{"alias_kind":"pith_short_12","alias_value":"5J4XM6UGQZMC","created_at":"2026-07-05T06:54:41Z"},{"alias_kind":"pith_short_16","alias_value":"5J4XM6UGQZMCVQ2U","created_at":"2026-07-05T06:54:41Z"},{"alias_kind":"pith_short_8","alias_value":"5J4XM6UG","created_at":"2026-07-05T06:54:41Z"}],"graph_snapshots":[{"event_id":"sha256:bc7a34599a0ae3808493a9db8c0093db09b22d8ac90e6de7fa1bad449b5fa930","target":"graph","created_at":"2026-07-05T06:54:41Z","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/2309.15139/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The normalization constraint on probability density poses a significant challenge for solving the Fokker-Planck equation. Normalizing Flow, an invertible generative model leverages the change of variables formula to ensure probability density conservation and enable the learning of complex data distributions. In this paper, we introduce Physics-Informed Normalizing Flows (PINF), a novel extension of continuous normalizing flows, incorporating diffusion through the method of characteristics. Our method, which is mesh-free and causality-free, can efficiently solve high dimensional time-dependent","authors_text":"Faguo Wu, Feng Liu, Xiao Zhang","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-09-26T15:38:57Z","title":"PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.15139","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":"sha256:9ec4c91f0dd7fcf71e8c900dcb8f61ba7cb8cd2df9733d4ee3cbf2ee9c2b1c44","target":"record","created_at":"2026-07-05T06:54:41Z","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":"82bc4b719aa74d57c4be921745bd55e9ee53b2fd3a43c247ab19f67232083f5a","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-09-26T15:38:57Z","title_canon_sha256":"56df84da27fc34c83cd248c75cc6501f33f5ebb81579af51ac54d105a016cedb"},"schema_version":"1.0","source":{"id":"2309.15139","kind":"arxiv","version":1}},"canonical_sha256":"ea79767a8686582ac35421b33c5b8da4176831d14c10038bb1728da10768fe94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea79767a8686582ac35421b33c5b8da4176831d14c10038bb1728da10768fe94","first_computed_at":"2026-07-05T06:54:41.778673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:54:41.778673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lGw3r3BO9nf1d+3m2OpNx1GHn7Iak7/jn4O8wRY7z2shQ8umpX+HN69UGMGMlOpoMzFYOKbCvbYisagKpNqqBw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:54:41.779090Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.15139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ec4c91f0dd7fcf71e8c900dcb8f61ba7cb8cd2df9733d4ee3cbf2ee9c2b1c44","sha256:bc7a34599a0ae3808493a9db8c0093db09b22d8ac90e6de7fa1bad449b5fa930"],"state_sha256":"a68dcba49886dd4cfdbc38db2da7c28b7900c5852e7ae7f1fb7c600752f969cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lNWkIiz3HB8N+oSQveNfnSIAIuUQ78xF0Mbhqba4NixSqK2j5dkIrgPdsTiuc0GE739j3YwKuRgZSRA14LtHCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T22:34:53.513906Z","bundle_sha256":"72be502eb82cb1ac124b71f0f004fcfb47b40857450af25112ff3ea336ad5e61"}}