{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KS7DYYXWPNJLJB7TWJEOFCUNPU","short_pith_number":"pith:KS7DYYXW","schema_version":"1.0","canonical_sha256":"54be3c62f67b52b487f3b248e28a8d7d3c597047f63763c327aa4bb01376c9bf","source":{"kind":"arxiv","id":"1803.05521","version":3},"attestation_state":"computed","paper":{"title":"Sequential and exact formulae for the subdifferential of nonconvex integral functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Abderrahim Hantoute, Pedro P\\'erez-Aros, Rafael Correa","submitted_at":"2018-03-14T21:52:16Z","abstract_excerpt":"This work concerns the study of the subdifferential of the integral functional\n  $$\n  E_f(x)=\\int_{T} f(t,x)d\\mu(t),\n  $$ where $f$ is a (not necessarily convex) normal integrand, $({T},\\mathcal{A},\\mu)$ is a $\\sigma$-finite measure space, while the decision variables vary in a separable Asplund space.\n  First, using techniques of variational analysis we establish sequential approximate formulae for the Fr\\'echet subdifferential of $E_f$. Secondly, we introduce a Lipschitz-like condition, which allows us to give an upper-estimation for the limiting subdifferential of $E_{f}$ even when this fun"},"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":"1803.05521","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-14T21:52:16Z","cross_cats_sorted":[],"title_canon_sha256":"c384a814a0e43825ed99de2a812d49755728eb0533785a19b954e1b4566b23be","abstract_canon_sha256":"e927d369605f296f9ad5f04bcd64cd4511dd3220ba50e48f1947ae617bba18d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:51.560192Z","signature_b64":"bCC9oaT0qBmuN2x78x1D/aOJqJzFC7a/XUQHnZJaaitNizZy0t6M/j51U6l5wYvFFn8A065tJ0P0oeodSWIyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54be3c62f67b52b487f3b248e28a8d7d3c597047f63763c327aa4bb01376c9bf","last_reissued_at":"2026-05-17T23:53:51.559469Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:51.559469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sequential and exact formulae for the subdifferential of nonconvex integral functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Abderrahim Hantoute, Pedro P\\'erez-Aros, Rafael Correa","submitted_at":"2018-03-14T21:52:16Z","abstract_excerpt":"This work concerns the study of the subdifferential of the integral functional\n  $$\n  E_f(x)=\\int_{T} f(t,x)d\\mu(t),\n  $$ where $f$ is a (not necessarily convex) normal integrand, $({T},\\mathcal{A},\\mu)$ is a $\\sigma$-finite measure space, while the decision variables vary in a separable Asplund space.\n  First, using techniques of variational analysis we establish sequential approximate formulae for the Fr\\'echet subdifferential of $E_f$. Secondly, we introduce a Lipschitz-like condition, which allows us to give an upper-estimation for the limiting subdifferential of $E_{f}$ even when this fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05521","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":"1803.05521","created_at":"2026-05-17T23:53:51.559580+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.05521v3","created_at":"2026-05-17T23:53:51.559580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05521","created_at":"2026-05-17T23:53:51.559580+00:00"},{"alias_kind":"pith_short_12","alias_value":"KS7DYYXWPNJL","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"KS7DYYXWPNJLJB7T","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"KS7DYYXW","created_at":"2026-05-18T12:32:33.847187+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/KS7DYYXWPNJLJB7TWJEOFCUNPU","json":"https://pith.science/pith/KS7DYYXWPNJLJB7TWJEOFCUNPU.json","graph_json":"https://pith.science/api/pith-number/KS7DYYXWPNJLJB7TWJEOFCUNPU/graph.json","events_json":"https://pith.science/api/pith-number/KS7DYYXWPNJLJB7TWJEOFCUNPU/events.json","paper":"https://pith.science/paper/KS7DYYXW"},"agent_actions":{"view_html":"https://pith.science/pith/KS7DYYXWPNJLJB7TWJEOFCUNPU","download_json":"https://pith.science/pith/KS7DYYXWPNJLJB7TWJEOFCUNPU.json","view_paper":"https://pith.science/paper/KS7DYYXW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.05521&json=true","fetch_graph":"https://pith.science/api/pith-number/KS7DYYXWPNJLJB7TWJEOFCUNPU/graph.json","fetch_events":"https://pith.science/api/pith-number/KS7DYYXWPNJLJB7TWJEOFCUNPU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KS7DYYXWPNJLJB7TWJEOFCUNPU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KS7DYYXWPNJLJB7TWJEOFCUNPU/action/storage_attestation","attest_author":"https://pith.science/pith/KS7DYYXWPNJLJB7TWJEOFCUNPU/action/author_attestation","sign_citation":"https://pith.science/pith/KS7DYYXWPNJLJB7TWJEOFCUNPU/action/citation_signature","submit_replication":"https://pith.science/pith/KS7DYYXWPNJLJB7TWJEOFCUNPU/action/replication_record"}},"created_at":"2026-05-17T23:53:51.559580+00:00","updated_at":"2026-05-17T23:53:51.559580+00:00"}