{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CUS7ZET6XBXEQJ34ZBODTINXBL","short_pith_number":"pith:CUS7ZET6","schema_version":"1.0","canonical_sha256":"1525fc927eb86e48277cc85c39a1b70addd248f57c8fb4140876412aeba47d59","source":{"kind":"arxiv","id":"2606.06720","version":1},"attestation_state":"computed","paper":{"title":"A Spectral-Based Method for Network-Formation PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Claudia Wytrzens, Pedro Aceves-Sanchez, Pierre Degond, Sara Merino-Aceituno","submitted_at":"2026-06-04T21:10:54Z","abstract_excerpt":"We propose and study a simple and scalable Fourier-based spectral method for a continuum model of network formation under periodic boundary conditions. The model provides the evolution of the pressure $p$ and the conductivity $m$ over time. The evolution of $p$ is given by an anisotropic Poisson equation, while the equation for $m$ contains three terms corresponding to a diffusion and an activation term of the network -- that depends on the gradient of the pressure -- as well as a relaxation term that acts as a decaying term. This system arises as a formal $L^2$-gradient flow of a non-convex e"},"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":"2606.06720","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-04T21:10:54Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e930af09b28265824afeb73ef0de19abe72866a9b314989e188e72b4ec1da46f","abstract_canon_sha256":"7560781982927accf2c4b417fa554aaed166613ecccaba3528e8ec9e3c4dae16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:04:24.486060Z","signature_b64":"D79IHXrsl0RKekAdkg5xBQwQTiKyfkSXc/awQpHN9cF8vQb/LlhI0BFC8hfkjZXeGO27oCUaqKwYdFCAIi49BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1525fc927eb86e48277cc85c39a1b70addd248f57c8fb4140876412aeba47d59","last_reissued_at":"2026-06-08T01:04:24.483239Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:04:24.483239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Spectral-Based Method for Network-Formation PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Claudia Wytrzens, Pedro Aceves-Sanchez, Pierre Degond, Sara Merino-Aceituno","submitted_at":"2026-06-04T21:10:54Z","abstract_excerpt":"We propose and study a simple and scalable Fourier-based spectral method for a continuum model of network formation under periodic boundary conditions. The model provides the evolution of the pressure $p$ and the conductivity $m$ over time. The evolution of $p$ is given by an anisotropic Poisson equation, while the equation for $m$ contains three terms corresponding to a diffusion and an activation term of the network -- that depends on the gradient of the pressure -- as well as a relaxation term that acts as a decaying term. This system arises as a formal $L^2$-gradient flow of a non-convex e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06720","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/2606.06720/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":"2606.06720","created_at":"2026-06-08T01:04:24.485332+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.06720v1","created_at":"2026-06-08T01:04:24.485332+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06720","created_at":"2026-06-08T01:04:24.485332+00:00"},{"alias_kind":"pith_short_12","alias_value":"CUS7ZET6XBXE","created_at":"2026-06-08T01:04:24.485332+00:00"},{"alias_kind":"pith_short_16","alias_value":"CUS7ZET6XBXEQJ34","created_at":"2026-06-08T01:04:24.485332+00:00"},{"alias_kind":"pith_short_8","alias_value":"CUS7ZET6","created_at":"2026-06-08T01:04:24.485332+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/CUS7ZET6XBXEQJ34ZBODTINXBL","json":"https://pith.science/pith/CUS7ZET6XBXEQJ34ZBODTINXBL.json","graph_json":"https://pith.science/api/pith-number/CUS7ZET6XBXEQJ34ZBODTINXBL/graph.json","events_json":"https://pith.science/api/pith-number/CUS7ZET6XBXEQJ34ZBODTINXBL/events.json","paper":"https://pith.science/paper/CUS7ZET6"},"agent_actions":{"view_html":"https://pith.science/pith/CUS7ZET6XBXEQJ34ZBODTINXBL","download_json":"https://pith.science/pith/CUS7ZET6XBXEQJ34ZBODTINXBL.json","view_paper":"https://pith.science/paper/CUS7ZET6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.06720&json=true","fetch_graph":"https://pith.science/api/pith-number/CUS7ZET6XBXEQJ34ZBODTINXBL/graph.json","fetch_events":"https://pith.science/api/pith-number/CUS7ZET6XBXEQJ34ZBODTINXBL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CUS7ZET6XBXEQJ34ZBODTINXBL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CUS7ZET6XBXEQJ34ZBODTINXBL/action/storage_attestation","attest_author":"https://pith.science/pith/CUS7ZET6XBXEQJ34ZBODTINXBL/action/author_attestation","sign_citation":"https://pith.science/pith/CUS7ZET6XBXEQJ34ZBODTINXBL/action/citation_signature","submit_replication":"https://pith.science/pith/CUS7ZET6XBXEQJ34ZBODTINXBL/action/replication_record"}},"created_at":"2026-06-08T01:04:24.485332+00:00","updated_at":"2026-06-08T01:04:24.485332+00:00"}