{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FAF225OOJQN2IJNI64VBFFWJU6","short_pith_number":"pith:FAF225OO","canonical_record":{"source":{"id":"2601.23262","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-30T18:30:24Z","cross_cats_sorted":[],"title_canon_sha256":"87e9309c73968ee7f33c0671434033454e566d091ae01ee414ad182a4d6bd83e","abstract_canon_sha256":"ebeb1333149ccb1d9966b3de4804e1f5fd235c93898780de82337e1ace3d00a9"},"schema_version":"1.0"},"canonical_sha256":"280bad75ce4c1ba425a8f72a1296c9a7b92846d4f7351f1d25f3d3a8cba022d6","source":{"kind":"arxiv","id":"2601.23262","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.23262","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2601.23262v2","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.23262","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"FAF225OOJQN2","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"FAF225OOJQN2IJNI","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"FAF225OO","created_at":"2026-05-28T02:04:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FAF225OOJQN2IJNI64VBFFWJU6","target":"record","payload":{"canonical_record":{"source":{"id":"2601.23262","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-30T18:30:24Z","cross_cats_sorted":[],"title_canon_sha256":"87e9309c73968ee7f33c0671434033454e566d091ae01ee414ad182a4d6bd83e","abstract_canon_sha256":"ebeb1333149ccb1d9966b3de4804e1f5fd235c93898780de82337e1ace3d00a9"},"schema_version":"1.0"},"canonical_sha256":"280bad75ce4c1ba425a8f72a1296c9a7b92846d4f7351f1d25f3d3a8cba022d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:04:45.629987Z","signature_b64":"P2Xpm4kB3mEL1cpPyrHVD6rksC9QUXwNPYf6hnu07oR8buuNSVMGKjvcaXKXsT4oyoN4m94osFAV0xwV5/GYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"280bad75ce4c1ba425a8f72a1296c9a7b92846d4f7351f1d25f3d3a8cba022d6","last_reissued_at":"2026-05-28T02:04:45.629501Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:04:45.629501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.23262","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":"2026-05-28T02:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ekufQMI1THnrthuyWTTJGuLcGCWcAQlhkfJh2zfMPFlUmOwRHmA7tG+GFk62nBje5MXj/gRf6/e0fGL0UyVBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T19:23:12.528625Z"},"content_sha256":"f5883e5593d0323b7c2e0230d1c7edbd31cf17cd2268597641abe1d5af17229d","schema_version":"1.0","event_id":"sha256:f5883e5593d0323b7c2e0230d1c7edbd31cf17cd2268597641abe1d5af17229d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FAF225OOJQN2IJNI64VBFFWJU6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Particle-Guided Diffusion Models for Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Andrew Millard, Fredrik Lindsten, Zheng Zhao","submitted_at":"2026-01-30T18:30:24Z","abstract_excerpt":"We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples remain physically admissible. We embed this sampling procedure within a new Sequential Monte Carlo (SMC) framework, yielding a scalable generative PDE solver. Across multiple benchmark PDE systems as well as multiphysics and interacting PDE systems, our method produces solution fields with lower numerical error than existing state-of-the-art generative method"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.23262","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.23262/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":"2026-05-28T02:04:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jIv/cyxRSURdiwDtjoebTKmmO6i36q/hoUANKqGw+JHBubueGWkA7EjyNEAjwD4HvlO2TGF2WGRjcwl7nw06BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T19:23:12.529395Z"},"content_sha256":"e9318fa98a39c4b358709843ed3dd409e145c2f9c78c0d2d4a3db4cfe2af45a0","schema_version":"1.0","event_id":"sha256:e9318fa98a39c4b358709843ed3dd409e145c2f9c78c0d2d4a3db4cfe2af45a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FAF225OOJQN2IJNI64VBFFWJU6/bundle.json","state_url":"https://pith.science/pith/FAF225OOJQN2IJNI64VBFFWJU6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FAF225OOJQN2IJNI64VBFFWJU6/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":"2026-05-29T19:23:12Z","links":{"resolver":"https://pith.science/pith/FAF225OOJQN2IJNI64VBFFWJU6","bundle":"https://pith.science/pith/FAF225OOJQN2IJNI64VBFFWJU6/bundle.json","state":"https://pith.science/pith/FAF225OOJQN2IJNI64VBFFWJU6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FAF225OOJQN2IJNI64VBFFWJU6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FAF225OOJQN2IJNI64VBFFWJU6","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":"ebeb1333149ccb1d9966b3de4804e1f5fd235c93898780de82337e1ace3d00a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-30T18:30:24Z","title_canon_sha256":"87e9309c73968ee7f33c0671434033454e566d091ae01ee414ad182a4d6bd83e"},"schema_version":"1.0","source":{"id":"2601.23262","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.23262","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"2601.23262v2","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.23262","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"FAF225OOJQN2","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_16","alias_value":"FAF225OOJQN2IJNI","created_at":"2026-05-28T02:04:45Z"},{"alias_kind":"pith_short_8","alias_value":"FAF225OO","created_at":"2026-05-28T02:04:45Z"}],"graph_snapshots":[{"event_id":"sha256:e9318fa98a39c4b358709843ed3dd409e145c2f9c78c0d2d4a3db4cfe2af45a0","target":"graph","created_at":"2026-05-28T02:04:45Z","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/2601.23262/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples remain physically admissible. We embed this sampling procedure within a new Sequential Monte Carlo (SMC) framework, yielding a scalable generative PDE solver. Across multiple benchmark PDE systems as well as multiphysics and interacting PDE systems, our method produces solution fields with lower numerical error than existing state-of-the-art generative method","authors_text":"Andrew Millard, Fredrik Lindsten, Zheng Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-30T18:30:24Z","title":"Particle-Guided Diffusion Models for Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.23262","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:f5883e5593d0323b7c2e0230d1c7edbd31cf17cd2268597641abe1d5af17229d","target":"record","created_at":"2026-05-28T02:04:45Z","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":"ebeb1333149ccb1d9966b3de4804e1f5fd235c93898780de82337e1ace3d00a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-30T18:30:24Z","title_canon_sha256":"87e9309c73968ee7f33c0671434033454e566d091ae01ee414ad182a4d6bd83e"},"schema_version":"1.0","source":{"id":"2601.23262","kind":"arxiv","version":2}},"canonical_sha256":"280bad75ce4c1ba425a8f72a1296c9a7b92846d4f7351f1d25f3d3a8cba022d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"280bad75ce4c1ba425a8f72a1296c9a7b92846d4f7351f1d25f3d3a8cba022d6","first_computed_at":"2026-05-28T02:04:45.629501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T02:04:45.629501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P2Xpm4kB3mEL1cpPyrHVD6rksC9QUXwNPYf6hnu07oR8buuNSVMGKjvcaXKXsT4oyoN4m94osFAV0xwV5/GYBg==","signature_status":"signed_v1","signed_at":"2026-05-28T02:04:45.629987Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.23262","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5883e5593d0323b7c2e0230d1c7edbd31cf17cd2268597641abe1d5af17229d","sha256:e9318fa98a39c4b358709843ed3dd409e145c2f9c78c0d2d4a3db4cfe2af45a0"],"state_sha256":"85d378ffc5da9dccaae195510e5c4064845b72176bc1040bb3e57b8037dce2d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d87kdFfOQK841CIrjn0BTsAkHqriAJCyeLtwVaVP2f2PzGCVtjxKED5/wFsdozR/v8ZihBybP4uBkldH54eKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T19:23:12.532510Z","bundle_sha256":"6c0b50ede394946410641d7c298f43b10e271ab454967a5e370cf44a8256e030"}}