{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GKUQOHWYJ5WVBSTHKKQS5KD4YA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2260d14a0bb8fa4a01013aadfc18181183536f8ce6b3cdc5eb423958f5575a1e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-03T20:38:42Z","title_canon_sha256":"7b2ec7a2bbd46f9ee05a4ef1c5eaec0700490432b784c2d296831e6ff9f8e067"},"schema_version":"1.0","source":{"id":"1212.0532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0532","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0532v2","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0532","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"GKUQOHWYJ5WV","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GKUQOHWYJ5WVBSTH","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GKUQOHWY","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:5ac9920273cab8d9ebe6831283db38bb5f23cc363659619bdbd9a1c4b301da7c","target":"graph","created_at":"2026-05-18T03:01:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential. From the sufficient condition we derive that any subdifferential operator is monotone absorbing, hence maximal monotone when the function is convex.","authors_text":"Florence Jules, Marc Lassonde","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-03T20:38:42Z","title":"Subdifferential Test for Optimality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0532","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:23e2b85ef1da2533042df1987d4278ea43193cc91564263f0ff7d3051783aa8e","target":"record","created_at":"2026-05-18T03:01:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2260d14a0bb8fa4a01013aadfc18181183536f8ce6b3cdc5eb423958f5575a1e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-03T20:38:42Z","title_canon_sha256":"7b2ec7a2bbd46f9ee05a4ef1c5eaec0700490432b784c2d296831e6ff9f8e067"},"schema_version":"1.0","source":{"id":"1212.0532","kind":"arxiv","version":2}},"canonical_sha256":"32a9071ed84f6d50ca6752a12ea87cc03623d14f1a4702f4c03afde847814f17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32a9071ed84f6d50ca6752a12ea87cc03623d14f1a4702f4c03afde847814f17","first_computed_at":"2026-05-18T03:01:25.405665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:25.405665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DMYyWHXcDYWrB3vWF+iEcrTi1qDLnHAJ4ONHt+3ElpZOcVMx6YAQIdIH/c2aHSKVtvG4tdRzxu7Rz6delqQ9Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:25.406597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23e2b85ef1da2533042df1987d4278ea43193cc91564263f0ff7d3051783aa8e","sha256:5ac9920273cab8d9ebe6831283db38bb5f23cc363659619bdbd9a1c4b301da7c"],"state_sha256":"e3bb7c8c47fee20299c545edab7b800102db057b1c1a59eb2dfc90a772cd440b"}