{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:OSTHV6KAQA3EWOCCSLPBLZM2WU","short_pith_number":"pith:OSTHV6KA","schema_version":"1.0","canonical_sha256":"74a67af94080364b384292de15e59ab5360ceb89eb665d5faeaa8dffa4cc3ae4","source":{"kind":"arxiv","id":"1408.2759","version":3},"attestation_state":"computed","paper":{"title":"Systems of Integro-PDEs with Interconnected Obstacles and Multi-Modes Switching Problem Driven by L\\'evy Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sa\\\"id Hamad\\`ene, Xuzhe Zhao","submitted_at":"2014-08-12T16:04:05Z","abstract_excerpt":"In this paper we show existence and uniqueness of the solution in viscosity sense for a system of nonlinear $m$ variational integral-partial differential equations with interconnected obstacles whose coefficients $(f_i)_{i=1,\\cdots, m}$ depend on $(u_j)_{j=1,\\cdots,m}$. From the probabilistic point of view, this system is related to optimal stochastic switching problem when the noise is driven by a L\\'evy process. The switching costs depend on $(t,x)$. As a by-product of the main result we obtain that the value function of the switching problem is continuous and unique solution of its associat"},"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":"1408.2759","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-12T16:04:05Z","cross_cats_sorted":[],"title_canon_sha256":"c869e94fec31f37dd55de143c621ae547b7b25234aab91c7dbb46cef9576917c","abstract_canon_sha256":"dc3f7674c3732f449429b68c5c9134254f0bb982bc249f88a35262b47a62c692"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:16.568022Z","signature_b64":"d+BbprsQjuO/dOQ7EKN+K2PUjrOjQBEdZ69GItkhnwzpeUuBEM6kqIamoznUtfkNZDzhhz0d2F9gM+iLcG5bDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74a67af94080364b384292de15e59ab5360ceb89eb665d5faeaa8dffa4cc3ae4","last_reissued_at":"2026-05-18T01:35:16.567306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:16.567306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Systems of Integro-PDEs with Interconnected Obstacles and Multi-Modes Switching Problem Driven by L\\'evy Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sa\\\"id Hamad\\`ene, Xuzhe Zhao","submitted_at":"2014-08-12T16:04:05Z","abstract_excerpt":"In this paper we show existence and uniqueness of the solution in viscosity sense for a system of nonlinear $m$ variational integral-partial differential equations with interconnected obstacles whose coefficients $(f_i)_{i=1,\\cdots, m}$ depend on $(u_j)_{j=1,\\cdots,m}$. From the probabilistic point of view, this system is related to optimal stochastic switching problem when the noise is driven by a L\\'evy process. The switching costs depend on $(t,x)$. As a by-product of the main result we obtain that the value function of the switching problem is continuous and unique solution of its associat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2759","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1408.2759","created_at":"2026-05-18T01:35:16.567426+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.2759v3","created_at":"2026-05-18T01:35:16.567426+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2759","created_at":"2026-05-18T01:35:16.567426+00:00"},{"alias_kind":"pith_short_12","alias_value":"OSTHV6KAQA3E","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OSTHV6KAQA3EWOCC","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OSTHV6KA","created_at":"2026-05-18T12:28:43.426989+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/OSTHV6KAQA3EWOCCSLPBLZM2WU","json":"https://pith.science/pith/OSTHV6KAQA3EWOCCSLPBLZM2WU.json","graph_json":"https://pith.science/api/pith-number/OSTHV6KAQA3EWOCCSLPBLZM2WU/graph.json","events_json":"https://pith.science/api/pith-number/OSTHV6KAQA3EWOCCSLPBLZM2WU/events.json","paper":"https://pith.science/paper/OSTHV6KA"},"agent_actions":{"view_html":"https://pith.science/pith/OSTHV6KAQA3EWOCCSLPBLZM2WU","download_json":"https://pith.science/pith/OSTHV6KAQA3EWOCCSLPBLZM2WU.json","view_paper":"https://pith.science/paper/OSTHV6KA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.2759&json=true","fetch_graph":"https://pith.science/api/pith-number/OSTHV6KAQA3EWOCCSLPBLZM2WU/graph.json","fetch_events":"https://pith.science/api/pith-number/OSTHV6KAQA3EWOCCSLPBLZM2WU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OSTHV6KAQA3EWOCCSLPBLZM2WU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OSTHV6KAQA3EWOCCSLPBLZM2WU/action/storage_attestation","attest_author":"https://pith.science/pith/OSTHV6KAQA3EWOCCSLPBLZM2WU/action/author_attestation","sign_citation":"https://pith.science/pith/OSTHV6KAQA3EWOCCSLPBLZM2WU/action/citation_signature","submit_replication":"https://pith.science/pith/OSTHV6KAQA3EWOCCSLPBLZM2WU/action/replication_record"}},"created_at":"2026-05-18T01:35:16.567426+00:00","updated_at":"2026-05-18T01:35:16.567426+00:00"}