{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IKADU5PUB76TZP4DD3O4ZJEX4H","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":"0b1fa38070eef21e97ae66464fe351b1508bdfc41c71346dece83aef3d97c8ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-27T17:06:43Z","title_canon_sha256":"413cc86164ce37613abe5ba3580b560f507163e16ce93598fdf5f4af9f346822"},"schema_version":"1.0","source":{"id":"1608.07726","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07726","created_at":"2026-05-18T01:03:37Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07726v1","created_at":"2026-05-18T01:03:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07726","created_at":"2026-05-18T01:03:37Z"},{"alias_kind":"pith_short_12","alias_value":"IKADU5PUB76T","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IKADU5PUB76TZP4D","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IKADU5PU","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:a6be3a1275ac6a8a496d2407206b86009e775dffec4e074ae8c6054d8234e006","target":"graph","created_at":"2026-05-18T01:03:37Z","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":"In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new calculus results on intersection rules for normal cones to convex sets and on infimal convolutions of support functions.","authors_text":"Boris Mordukhovich, Nguyen Mau Nam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-27T17:06:43Z","title":"Extremality of Convex Sets with Some Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07726","kind":"arxiv","version":1},"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":"sha256:8d0310b669f9dcb5f154e82ce7dc75633a2a3fa8943ebcbd21adffbc4f817998","target":"record","created_at":"2026-05-18T01:03:37Z","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":"0b1fa38070eef21e97ae66464fe351b1508bdfc41c71346dece83aef3d97c8ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-27T17:06:43Z","title_canon_sha256":"413cc86164ce37613abe5ba3580b560f507163e16ce93598fdf5f4af9f346822"},"schema_version":"1.0","source":{"id":"1608.07726","kind":"arxiv","version":1}},"canonical_sha256":"42803a75f40ffd3cbf831eddcca497e1e5caee04515608f8767c22ad8e3db572","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42803a75f40ffd3cbf831eddcca497e1e5caee04515608f8767c22ad8e3db572","first_computed_at":"2026-05-18T01:03:37.566807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:37.566807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VZbsRWmYVNDzSBWXJ6L3Y94vdRVZjV5+XpG+enTpmkMAGuK1Cba7FLw0Ap+ygp516V2LTSWh7O4NF8gScoCTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:37.567415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07726","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d0310b669f9dcb5f154e82ce7dc75633a2a3fa8943ebcbd21adffbc4f817998","sha256:a6be3a1275ac6a8a496d2407206b86009e775dffec4e074ae8c6054d8234e006"],"state_sha256":"5f8ebe45c3b3c16afebf155ecd169c08715abc11e5b0c39ab0abf0a999f6a8b2"}