{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6IXEKTOVJZ6C6SMPAUOVSFHR6N","short_pith_number":"pith:6IXEKTOV","canonical_record":{"source":{"id":"2409.09811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-15T18:20:15Z","cross_cats_sorted":["cs.NA","math.NA","physics.flu-dyn"],"title_canon_sha256":"8d50118e030a21c7f24bb1096ac8b90b2a26d35f9a776809fe1893880be64c3a","abstract_canon_sha256":"af01cdcfe51f529a6ebbcf86516009cea93a68e88a9b34e7895e8acdb3953642"},"schema_version":"1.0"},"canonical_sha256":"f22e454dd54e7c2f498f051d5914f1f35e1a6a2d6f1bbf63a9963237b6483beb","source":{"kind":"arxiv","id":"2409.09811","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.09811","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"2409.09811v1","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.09811","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"6IXEKTOVJZ6C","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_16","alias_value":"6IXEKTOVJZ6C6SMP","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_8","alias_value":"6IXEKTOV","created_at":"2026-07-05T09:07:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6IXEKTOVJZ6C6SMPAUOVSFHR6N","target":"record","payload":{"canonical_record":{"source":{"id":"2409.09811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-15T18:20:15Z","cross_cats_sorted":["cs.NA","math.NA","physics.flu-dyn"],"title_canon_sha256":"8d50118e030a21c7f24bb1096ac8b90b2a26d35f9a776809fe1893880be64c3a","abstract_canon_sha256":"af01cdcfe51f529a6ebbcf86516009cea93a68e88a9b34e7895e8acdb3953642"},"schema_version":"1.0"},"canonical_sha256":"f22e454dd54e7c2f498f051d5914f1f35e1a6a2d6f1bbf63a9963237b6483beb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:07:32.512416Z","signature_b64":"iPGkEVyDzJ746hSvsuxqXpZoKUpjl2kAyuMPTQHlfXPXKuRkD0KgCcHVKRGSdw2ibawf7GRdxJYW3cRv6Rz7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f22e454dd54e7c2f498f051d5914f1f35e1a6a2d6f1bbf63a9963237b6483beb","last_reissued_at":"2026-07-05T09:07:32.511945Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:07:32.511945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.09811","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":"2026-07-05T09:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpeH997KvmMFuwXyGHkkaBSDdJsUIGEB1MDQfc522AnQd3J417cnRj8c4ofHpmmEsjA+uEkwk4bGa7bEXu2cAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:09:32.609110Z"},"content_sha256":"ffe8970ab311a0d38fd1ad492b46f4fff11b340cb431998ac3b25d77b4c5a8b3","schema_version":"1.0","event_id":"sha256:ffe8970ab311a0d38fd1ad492b46f4fff11b340cb431998ac3b25d77b4c5a8b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6IXEKTOVJZ6C6SMPAUOVSFHR6N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","physics.flu-dyn"],"primary_cat":"cs.LG","authors_text":"Griffin Pinney, Hayden Schaeffer, Jingmin Sun, Xinjie He, Yuxuan Liu, Zecheng Zhang","submitted_at":"2024-09-15T18:20:15Z","abstract_excerpt":"We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inpu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.09811","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/2409.09811/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":"2026-07-05T09:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D+rr3GWdFnacmisXtUiFfLkyxvJn6P3mQBOElU34eBGGj7XM4gQHXHdELIJTCM9+gv68yIeDVElLTG8/WUSwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:09:32.610080Z"},"content_sha256":"76b8da1cfe804d749b6bc98e6e2baeb5c850661430777acb6bf5a67cbb2ea99b","schema_version":"1.0","event_id":"sha256:76b8da1cfe804d749b6bc98e6e2baeb5c850661430777acb6bf5a67cbb2ea99b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6IXEKTOVJZ6C6SMPAUOVSFHR6N/bundle.json","state_url":"https://pith.science/pith/6IXEKTOVJZ6C6SMPAUOVSFHR6N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6IXEKTOVJZ6C6SMPAUOVSFHR6N/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":"2026-08-04T15:09:32Z","links":{"resolver":"https://pith.science/pith/6IXEKTOVJZ6C6SMPAUOVSFHR6N","bundle":"https://pith.science/pith/6IXEKTOVJZ6C6SMPAUOVSFHR6N/bundle.json","state":"https://pith.science/pith/6IXEKTOVJZ6C6SMPAUOVSFHR6N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6IXEKTOVJZ6C6SMPAUOVSFHR6N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6IXEKTOVJZ6C6SMPAUOVSFHR6N","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":"af01cdcfe51f529a6ebbcf86516009cea93a68e88a9b34e7895e8acdb3953642","cross_cats_sorted":["cs.NA","math.NA","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-15T18:20:15Z","title_canon_sha256":"8d50118e030a21c7f24bb1096ac8b90b2a26d35f9a776809fe1893880be64c3a"},"schema_version":"1.0","source":{"id":"2409.09811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.09811","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"2409.09811v1","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.09811","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"6IXEKTOVJZ6C","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_16","alias_value":"6IXEKTOVJZ6C6SMP","created_at":"2026-07-05T09:07:32Z"},{"alias_kind":"pith_short_8","alias_value":"6IXEKTOV","created_at":"2026-07-05T09:07:32Z"}],"graph_snapshots":[{"event_id":"sha256:76b8da1cfe804d749b6bc98e6e2baeb5c850661430777acb6bf5a67cbb2ea99b","target":"graph","created_at":"2026-07-05T09:07:32Z","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/2409.09811/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inpu","authors_text":"Griffin Pinney, Hayden Schaeffer, Jingmin Sun, Xinjie He, Yuxuan Liu, Zecheng Zhang","cross_cats":["cs.NA","math.NA","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-15T18:20:15Z","title":"PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.09811","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:ffe8970ab311a0d38fd1ad492b46f4fff11b340cb431998ac3b25d77b4c5a8b3","target":"record","created_at":"2026-07-05T09:07:32Z","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":"af01cdcfe51f529a6ebbcf86516009cea93a68e88a9b34e7895e8acdb3953642","cross_cats_sorted":["cs.NA","math.NA","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-15T18:20:15Z","title_canon_sha256":"8d50118e030a21c7f24bb1096ac8b90b2a26d35f9a776809fe1893880be64c3a"},"schema_version":"1.0","source":{"id":"2409.09811","kind":"arxiv","version":1}},"canonical_sha256":"f22e454dd54e7c2f498f051d5914f1f35e1a6a2d6f1bbf63a9963237b6483beb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f22e454dd54e7c2f498f051d5914f1f35e1a6a2d6f1bbf63a9963237b6483beb","first_computed_at":"2026-07-05T09:07:32.511945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:07:32.511945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iPGkEVyDzJ746hSvsuxqXpZoKUpjl2kAyuMPTQHlfXPXKuRkD0KgCcHVKRGSdw2ibawf7GRdxJYW3cRv6Rz7DA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:07:32.512416Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.09811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffe8970ab311a0d38fd1ad492b46f4fff11b340cb431998ac3b25d77b4c5a8b3","sha256:76b8da1cfe804d749b6bc98e6e2baeb5c850661430777acb6bf5a67cbb2ea99b"],"state_sha256":"729f2efd0d3f0bdbdac71f9eca0688bea72b4cc3b27b989216caeb4d9548008a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GOgJujNua8R3YUG9u3H5T+J3c8y9CSxwkGpNBz9fdE4ZmGR1NJdDBTws7EvVu/ZUBmC+jzRXGduZwaogQkVaAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T15:09:32.693883Z","bundle_sha256":"35ba85d795519cfe90e0917a3bbbb66b61667f8dfe61cf9ac6a21ff3cfdd3d03"}}