{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:AOBC7JMGQJUTRWBYWU7ORVTYXK","short_pith_number":"pith:AOBC7JMG","schema_version":"1.0","canonical_sha256":"03822fa586826938d838b53ee8d678ba833fb23fdacd01e6c4a81eb63d25e4ba","source":{"kind":"arxiv","id":"2607.21352","version":1},"attestation_state":"computed","paper":{"title":"Double screening in the training dynamics of variational physics-informed neural networks for heterogeneous coupled parabolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Ouattara Kouma, Gossrin Jean-Marc Bomisso","submitted_at":"2026-07-23T14:16:44Z","abstract_excerpt":"We analyze the training dynamics of variational physics-informed neural networks applied to linear coupled parabolic convection--diffusion--reaction systems, called heterogeneous when only a subset of the components undergoes convective transport. In the neural tangent kernel regime, the gradient flow on the space-time variational residuals reduces to a linear differential system whose operator is a Gram matrix built from the space-time symbol of the system operator and the matrix tangent kernel. The main result is a double screening theorem. Under dominant convection, the Schur complement of "},"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":"2607.21352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-23T14:16:44Z","cross_cats_sorted":[],"title_canon_sha256":"700f1b4eb318cc6f7fc18cf98dec3c78e71f47cf62f9e002dbfe5b8332948597","abstract_canon_sha256":"f05332a7e91d0ea87d22d6cf8dbe2c91e495b2f333a0c9c269abcdf075de6eee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T01:24:27.164183Z","signature_b64":"ipd7WwI5ITB2gyhEqWFdHiAp+hGnnUgNJYabkPk5CCTD2lvTIjr64dYSVYs9cjkOqOazl2BzDatxthgdn55nAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03822fa586826938d838b53ee8d678ba833fb23fdacd01e6c4a81eb63d25e4ba","last_reissued_at":"2026-07-24T01:24:27.163277Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T01:24:27.163277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Double screening in the training dynamics of variational physics-informed neural networks for heterogeneous coupled parabolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Ouattara Kouma, Gossrin Jean-Marc Bomisso","submitted_at":"2026-07-23T14:16:44Z","abstract_excerpt":"We analyze the training dynamics of variational physics-informed neural networks applied to linear coupled parabolic convection--diffusion--reaction systems, called heterogeneous when only a subset of the components undergoes convective transport. In the neural tangent kernel regime, the gradient flow on the space-time variational residuals reduces to a linear differential system whose operator is a Gram matrix built from the space-time symbol of the system operator and the matrix tangent kernel. The main result is a double screening theorem. Under dominant convection, the Schur complement of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21352","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/2607.21352/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":"2607.21352","created_at":"2026-07-24T01:24:27.163739+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.21352v1","created_at":"2026-07-24T01:24:27.163739+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21352","created_at":"2026-07-24T01:24:27.163739+00:00"},{"alias_kind":"pith_short_12","alias_value":"AOBC7JMGQJUT","created_at":"2026-07-24T01:24:27.163739+00:00"},{"alias_kind":"pith_short_16","alias_value":"AOBC7JMGQJUTRWBY","created_at":"2026-07-24T01:24:27.163739+00:00"},{"alias_kind":"pith_short_8","alias_value":"AOBC7JMG","created_at":"2026-07-24T01:24:27.163739+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/AOBC7JMGQJUTRWBYWU7ORVTYXK","json":"https://pith.science/pith/AOBC7JMGQJUTRWBYWU7ORVTYXK.json","graph_json":"https://pith.science/api/pith-number/AOBC7JMGQJUTRWBYWU7ORVTYXK/graph.json","events_json":"https://pith.science/api/pith-number/AOBC7JMGQJUTRWBYWU7ORVTYXK/events.json","paper":"https://pith.science/paper/AOBC7JMG"},"agent_actions":{"view_html":"https://pith.science/pith/AOBC7JMGQJUTRWBYWU7ORVTYXK","download_json":"https://pith.science/pith/AOBC7JMGQJUTRWBYWU7ORVTYXK.json","view_paper":"https://pith.science/paper/AOBC7JMG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.21352&json=true","fetch_graph":"https://pith.science/api/pith-number/AOBC7JMGQJUTRWBYWU7ORVTYXK/graph.json","fetch_events":"https://pith.science/api/pith-number/AOBC7JMGQJUTRWBYWU7ORVTYXK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AOBC7JMGQJUTRWBYWU7ORVTYXK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AOBC7JMGQJUTRWBYWU7ORVTYXK/action/storage_attestation","attest_author":"https://pith.science/pith/AOBC7JMGQJUTRWBYWU7ORVTYXK/action/author_attestation","sign_citation":"https://pith.science/pith/AOBC7JMGQJUTRWBYWU7ORVTYXK/action/citation_signature","submit_replication":"https://pith.science/pith/AOBC7JMGQJUTRWBYWU7ORVTYXK/action/replication_record"}},"created_at":"2026-07-24T01:24:27.163739+00:00","updated_at":"2026-07-24T01:24:27.163739+00:00"}