{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:BKLGZAXB3TBUFLNTAHECOZYWN2","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":"b3c97520462cf54b61d5cc49d5db64b7bea655bf59e90c30b0911cfcb4e64c27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-17T23:53:34Z","title_canon_sha256":"e2b072a271564b7511294abeaffd2f8082e7aa29660852859d954def1237ca3a"},"schema_version":"1.0","source":{"id":"2409.11609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.11609","created_at":"2026-07-05T09:08:34Z"},{"alias_kind":"arxiv_version","alias_value":"2409.11609v1","created_at":"2026-07-05T09:08:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.11609","created_at":"2026-07-05T09:08:34Z"},{"alias_kind":"pith_short_12","alias_value":"BKLGZAXB3TBU","created_at":"2026-07-05T09:08:34Z"},{"alias_kind":"pith_short_16","alias_value":"BKLGZAXB3TBUFLNT","created_at":"2026-07-05T09:08:34Z"},{"alias_kind":"pith_short_8","alias_value":"BKLGZAXB","created_at":"2026-07-05T09:08:34Z"}],"graph_snapshots":[{"event_id":"sha256:faabf807a34c0c17ec8293cc5570f9681b1fd73a975688e877ac3ec841096f41","target":"graph","created_at":"2026-07-05T09:08:34Z","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/2409.11609/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-dependent partial differential equations, the equation itself provides an additional modality to identify the system. The utilization of symbolic expressions along side time-series samples allows for the development of multimodal predictive neural networks. A key challenge with current approaches is that the symbolic information, i.e. the equations, must be manually preprocessed (simplified, rearranged, etc.) to match an","authors_text":"Derek Jollie, Hayden Schaeffer, Jingmin Sun, Zecheng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-17T23:53:34Z","title":"Time-Series Forecasting, Knowledge Distillation, and Refinement within a Multimodal PDE Foundation Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.11609","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:ae9802eaac0b768bf351ae7bfda07152f045e102adaf2fa242102070978a6e2c","target":"record","created_at":"2026-07-05T09:08:34Z","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":"b3c97520462cf54b61d5cc49d5db64b7bea655bf59e90c30b0911cfcb4e64c27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-17T23:53:34Z","title_canon_sha256":"e2b072a271564b7511294abeaffd2f8082e7aa29660852859d954def1237ca3a"},"schema_version":"1.0","source":{"id":"2409.11609","kind":"arxiv","version":1}},"canonical_sha256":"0a966c82e1dcc342adb301c82767166e98403aa82b6b86c776e936a813a06352","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a966c82e1dcc342adb301c82767166e98403aa82b6b86c776e936a813a06352","first_computed_at":"2026-07-05T09:08:34.433546Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:08:34.433546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CMGWvRu0FkXAt9wIeMLQElaeU6+pImNEDnvyp7iNOx7/o7os7vU5FND8xy7mvVMC6L/h03olVIgYuuQrTMz9Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:08:34.434035Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.11609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae9802eaac0b768bf351ae7bfda07152f045e102adaf2fa242102070978a6e2c","sha256:faabf807a34c0c17ec8293cc5570f9681b1fd73a975688e877ac3ec841096f41"],"state_sha256":"f8d5c1e67341bee05372b1932933751c921307ba20d131e27cb128782f14779a"}