{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:AUA6T5DHKYQ4UX3T6UMFVJNT5Y","short_pith_number":"pith:AUA6T5DH","schema_version":"1.0","canonical_sha256":"0501e9f4675621ca5f73f5185aa5b3ee195cb329c12bcd60351a6869ab902ca8","source":{"kind":"arxiv","id":"2411.13126","version":1},"attestation_state":"computed","paper":{"title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erwin Topp (IM / UFRJ), Guy Barles (IDP), Olivier Ley (IRMAR)","submitted_at":"2024-11-20T08:37:16Z","abstract_excerpt":"In this article, we consider nonlocal Hamilton-Jacobi Equations on networks with Kirchhoff type conditions for the interior vertices and Dirichlet boundary conditions for the boundary ones: our aim is to provide general existence and comparison results in the case when the integro-differential operators are of order strictly less than 1. The main originality of these results is to allow these nonlocal terms to have contributions on several different edges of the network. The existence of Lipschitz continuous solutions is proved in two ways: either by using the vanishing viscosity method or by "},"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":"2411.13126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-20T08:37:16Z","cross_cats_sorted":[],"title_canon_sha256":"cf21c25744302fe6c4b6ca0698df2193e3cf6bdc580309c56e64f3d141b6c08e","abstract_canon_sha256":"6c923bd8cf75dcbffc220647274d58403882a703854915f28e90967f5c96402c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:05.486157Z","signature_b64":"xwCu7Li9mm5JdbN8jmvkNpjzE9pY1zm4YRvDNJCzX2Cd/qLqIvd347v6m5BOCQZhbl5jCw17ADGt/aFHhQu/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0501e9f4675621ca5f73f5185aa5b3ee195cb329c12bcd60351a6869ab902ca8","last_reissued_at":"2026-07-05T09:38:05.485702Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:05.485702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlocal Hamilton-Jacobi Equations on a network with Kirchhoff type conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erwin Topp (IM / UFRJ), Guy Barles (IDP), Olivier Ley (IRMAR)","submitted_at":"2024-11-20T08:37:16Z","abstract_excerpt":"In this article, we consider nonlocal Hamilton-Jacobi Equations on networks with Kirchhoff type conditions for the interior vertices and Dirichlet boundary conditions for the boundary ones: our aim is to provide general existence and comparison results in the case when the integro-differential operators are of order strictly less than 1. The main originality of these results is to allow these nonlocal terms to have contributions on several different edges of the network. The existence of Lipschitz continuous solutions is proved in two ways: either by using the vanishing viscosity method or by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13126","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/2411.13126/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":"2411.13126","created_at":"2026-07-05T09:38:05.485758+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.13126v1","created_at":"2026-07-05T09:38:05.485758+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13126","created_at":"2026-07-05T09:38:05.485758+00:00"},{"alias_kind":"pith_short_12","alias_value":"AUA6T5DHKYQ4","created_at":"2026-07-05T09:38:05.485758+00:00"},{"alias_kind":"pith_short_16","alias_value":"AUA6T5DHKYQ4UX3T","created_at":"2026-07-05T09:38:05.485758+00:00"},{"alias_kind":"pith_short_8","alias_value":"AUA6T5DH","created_at":"2026-07-05T09:38:05.485758+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.18057","citing_title":"Stochastic scattering control of spider diffusion governed by an optimal diffraction probability measure selected from its own local-time","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AUA6T5DHKYQ4UX3T6UMFVJNT5Y","json":"https://pith.science/pith/AUA6T5DHKYQ4UX3T6UMFVJNT5Y.json","graph_json":"https://pith.science/api/pith-number/AUA6T5DHKYQ4UX3T6UMFVJNT5Y/graph.json","events_json":"https://pith.science/api/pith-number/AUA6T5DHKYQ4UX3T6UMFVJNT5Y/events.json","paper":"https://pith.science/paper/AUA6T5DH"},"agent_actions":{"view_html":"https://pith.science/pith/AUA6T5DHKYQ4UX3T6UMFVJNT5Y","download_json":"https://pith.science/pith/AUA6T5DHKYQ4UX3T6UMFVJNT5Y.json","view_paper":"https://pith.science/paper/AUA6T5DH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.13126&json=true","fetch_graph":"https://pith.science/api/pith-number/AUA6T5DHKYQ4UX3T6UMFVJNT5Y/graph.json","fetch_events":"https://pith.science/api/pith-number/AUA6T5DHKYQ4UX3T6UMFVJNT5Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AUA6T5DHKYQ4UX3T6UMFVJNT5Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AUA6T5DHKYQ4UX3T6UMFVJNT5Y/action/storage_attestation","attest_author":"https://pith.science/pith/AUA6T5DHKYQ4UX3T6UMFVJNT5Y/action/author_attestation","sign_citation":"https://pith.science/pith/AUA6T5DHKYQ4UX3T6UMFVJNT5Y/action/citation_signature","submit_replication":"https://pith.science/pith/AUA6T5DHKYQ4UX3T6UMFVJNT5Y/action/replication_record"}},"created_at":"2026-07-05T09:38:05.485758+00:00","updated_at":"2026-07-05T09:38:05.485758+00:00"}