{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:W6MLCT27ENY5CP6M6Y3HENRKK2","short_pith_number":"pith:W6MLCT27","schema_version":"1.0","canonical_sha256":"b798b14f5f2371d13fccf63672362a56ade7abedf0b74cb72eeed1ae5bedbd88","source":{"kind":"arxiv","id":"2607.06348","version":1},"attestation_state":"computed","paper":{"title":"Physics-Informed Neural Embeddings of PDE Solution Families","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"David N. Spergel, Leonid Sarieddine, Pavlos Protopapas, Pedro Taranc\\'on-\\'Alvarez, Raul Jimenez, Svitlana Mayboroda","submitted_at":"2026-07-07T14:45:42Z","abstract_excerpt":"We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations. The method uses a multihead Physics-Informed Neural Network in which a shared body learns a latent manifold representing the solution space, while linear heads reconstruct individual solutions associated with different initial conditions. A head-orthogonalization penalty removes degeneracies in the latent representation and stabilizes the principal-component spectrum across training realizations. Because the initial condition is built into the network out"},"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":"2607.06348","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-07T14:45:42Z","cross_cats_sorted":["cs.NA","math.NA","physics.comp-ph"],"title_canon_sha256":"ba1ab3b7048d70f4566e9371b767589683835170b78d3c394161f8ea88052a95","abstract_canon_sha256":"13ce0f6ed546c4563fc210b326882128136e0f858e22f9b732ca88fce8a9525e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:19:22.240215Z","signature_b64":"jcpdpapHBG6LThiC+IeRGSVNX5SyaUp4sOCcJZX5DPF+myJNFxcrvqe9n71u78ekFJGME5MuNBWG2uHyxgJtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b798b14f5f2371d13fccf63672362a56ade7abedf0b74cb72eeed1ae5bedbd88","last_reissued_at":"2026-07-08T01:19:22.239789Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:19:22.239789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Physics-Informed Neural Embeddings of PDE Solution Families","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"David N. Spergel, Leonid Sarieddine, Pavlos Protopapas, Pedro Taranc\\'on-\\'Alvarez, Raul Jimenez, Svitlana Mayboroda","submitted_at":"2026-07-07T14:45:42Z","abstract_excerpt":"We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations. The method uses a multihead Physics-Informed Neural Network in which a shared body learns a latent manifold representing the solution space, while linear heads reconstruct individual solutions associated with different initial conditions. A head-orthogonalization penalty removes degeneracies in the latent representation and stabilizes the principal-component spectrum across training realizations. Because the initial condition is built into the network out"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06348","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/2607.06348/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":"2607.06348","created_at":"2026-07-08T01:19:22.239859+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.06348v1","created_at":"2026-07-08T01:19:22.239859+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06348","created_at":"2026-07-08T01:19:22.239859+00:00"},{"alias_kind":"pith_short_12","alias_value":"W6MLCT27ENY5","created_at":"2026-07-08T01:19:22.239859+00:00"},{"alias_kind":"pith_short_16","alias_value":"W6MLCT27ENY5CP6M","created_at":"2026-07-08T01:19:22.239859+00:00"},{"alias_kind":"pith_short_8","alias_value":"W6MLCT27","created_at":"2026-07-08T01:19:22.239859+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/W6MLCT27ENY5CP6M6Y3HENRKK2","json":"https://pith.science/pith/W6MLCT27ENY5CP6M6Y3HENRKK2.json","graph_json":"https://pith.science/api/pith-number/W6MLCT27ENY5CP6M6Y3HENRKK2/graph.json","events_json":"https://pith.science/api/pith-number/W6MLCT27ENY5CP6M6Y3HENRKK2/events.json","paper":"https://pith.science/paper/W6MLCT27"},"agent_actions":{"view_html":"https://pith.science/pith/W6MLCT27ENY5CP6M6Y3HENRKK2","download_json":"https://pith.science/pith/W6MLCT27ENY5CP6M6Y3HENRKK2.json","view_paper":"https://pith.science/paper/W6MLCT27","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.06348&json=true","fetch_graph":"https://pith.science/api/pith-number/W6MLCT27ENY5CP6M6Y3HENRKK2/graph.json","fetch_events":"https://pith.science/api/pith-number/W6MLCT27ENY5CP6M6Y3HENRKK2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W6MLCT27ENY5CP6M6Y3HENRKK2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W6MLCT27ENY5CP6M6Y3HENRKK2/action/storage_attestation","attest_author":"https://pith.science/pith/W6MLCT27ENY5CP6M6Y3HENRKK2/action/author_attestation","sign_citation":"https://pith.science/pith/W6MLCT27ENY5CP6M6Y3HENRKK2/action/citation_signature","submit_replication":"https://pith.science/pith/W6MLCT27ENY5CP6M6Y3HENRKK2/action/replication_record"}},"created_at":"2026-07-08T01:19:22.239859+00:00","updated_at":"2026-07-08T01:19:22.239859+00:00"}