{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:INNBXSWR7QGG44P2QDLBAM254D","short_pith_number":"pith:INNBXSWR","schema_version":"1.0","canonical_sha256":"435a1bcad1fc0c6e71fa80d610335de0cb378beb97c0ab6c729bcf16de2d0888","source":{"kind":"arxiv","id":"2606.20467","version":1},"attestation_state":"computed","paper":{"title":"Agentic Symbolic Search: Characterizing PDEs Beyond Hand-crafted Expressions, Meshes, and Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Liu Yang, Zongmin Yu","submitted_at":"2026-06-18T16:46:42Z","abstract_excerpt":"Mathematicians understand a PDE solution through mathematical structures rather than tables of computed values. Historically, this has been the product of mathematical analysis, carried out by hand for each problem individually. Neither numerical simulation nor neural networks produce those structures directly. We propose Agentic Symbolic Search (ASYS), a prior-guided framework in which an agent translates PDE theory, public problem constraints, and accumulated search experience into testable differentiable symbolic programs. The mathematical forms are refined under evolutionary search, while "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.20467","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T16:46:42Z","cross_cats_sorted":["cs.NA","math.NA","physics.comp-ph"],"title_canon_sha256":"0e6a27ad9a4273c89ed4af44ef7a140cf663f20226f6a5102649b296f7740506","abstract_canon_sha256":"040f5319a24871c8708095acbff0ae0cf5fced1a75aac6766d570c3c36e1585f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:13:13.095977Z","signature_b64":"tzqEn8U3u+wT7EZM6UFXcWBhBNg6/uVFGWowE8Jjee5nJcWm5GfqezRdPcSL9BzXPY8hJvys6LtC/+12nlDCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"435a1bcad1fc0c6e71fa80d610335de0cb378beb97c0ab6c729bcf16de2d0888","last_reissued_at":"2026-06-19T16:13:13.095503Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:13:13.095503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Agentic Symbolic Search: Characterizing PDEs Beyond Hand-crafted Expressions, Meshes, and Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Liu Yang, Zongmin Yu","submitted_at":"2026-06-18T16:46:42Z","abstract_excerpt":"Mathematicians understand a PDE solution through mathematical structures rather than tables of computed values. Historically, this has been the product of mathematical analysis, carried out by hand for each problem individually. Neither numerical simulation nor neural networks produce those structures directly. We propose Agentic Symbolic Search (ASYS), a prior-guided framework in which an agent translates PDE theory, public problem constraints, and accumulated search experience into testable differentiable symbolic programs. The mathematical forms are refined under evolutionary search, while "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20467","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/2606.20467/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.20467","created_at":"2026-06-19T16:13:13.095566+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.20467v1","created_at":"2026-06-19T16:13:13.095566+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20467","created_at":"2026-06-19T16:13:13.095566+00:00"},{"alias_kind":"pith_short_12","alias_value":"INNBXSWR7QGG","created_at":"2026-06-19T16:13:13.095566+00:00"},{"alias_kind":"pith_short_16","alias_value":"INNBXSWR7QGG44P2","created_at":"2026-06-19T16:13:13.095566+00:00"},{"alias_kind":"pith_short_8","alias_value":"INNBXSWR","created_at":"2026-06-19T16:13:13.095566+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/INNBXSWR7QGG44P2QDLBAM254D","json":"https://pith.science/pith/INNBXSWR7QGG44P2QDLBAM254D.json","graph_json":"https://pith.science/api/pith-number/INNBXSWR7QGG44P2QDLBAM254D/graph.json","events_json":"https://pith.science/api/pith-number/INNBXSWR7QGG44P2QDLBAM254D/events.json","paper":"https://pith.science/paper/INNBXSWR"},"agent_actions":{"view_html":"https://pith.science/pith/INNBXSWR7QGG44P2QDLBAM254D","download_json":"https://pith.science/pith/INNBXSWR7QGG44P2QDLBAM254D.json","view_paper":"https://pith.science/paper/INNBXSWR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.20467&json=true","fetch_graph":"https://pith.science/api/pith-number/INNBXSWR7QGG44P2QDLBAM254D/graph.json","fetch_events":"https://pith.science/api/pith-number/INNBXSWR7QGG44P2QDLBAM254D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/INNBXSWR7QGG44P2QDLBAM254D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/INNBXSWR7QGG44P2QDLBAM254D/action/storage_attestation","attest_author":"https://pith.science/pith/INNBXSWR7QGG44P2QDLBAM254D/action/author_attestation","sign_citation":"https://pith.science/pith/INNBXSWR7QGG44P2QDLBAM254D/action/citation_signature","submit_replication":"https://pith.science/pith/INNBXSWR7QGG44P2QDLBAM254D/action/replication_record"}},"created_at":"2026-06-19T16:13:13.095566+00:00","updated_at":"2026-06-19T16:13:13.095566+00:00"}