{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:HBDVSDBPRBVXVVVINOLHZU5DF2","short_pith_number":"pith:HBDVSDBP","canonical_record":{"source":{"id":"1911.10850","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-11-25T11:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"340b65890dd3026b2037a88e44ef7d627f05ec56fc84e8d168b4810a55f53e2f","abstract_canon_sha256":"60d0c462d2d470df19bb582c82af8af18d42d58415ac724f7facdac5097aba0c"},"schema_version":"1.0"},"canonical_sha256":"3847590c2f886b7ad6a86b967cd3a32ea77b98d15b013f8da41e8b037d919ff9","source":{"kind":"arxiv","id":"1911.10850","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.10850","created_at":"2026-07-05T01:21:17Z"},{"alias_kind":"arxiv_version","alias_value":"1911.10850v3","created_at":"2026-07-05T01:21:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.10850","created_at":"2026-07-05T01:21:17Z"},{"alias_kind":"pith_short_12","alias_value":"HBDVSDBPRBVX","created_at":"2026-07-05T01:21:17Z"},{"alias_kind":"pith_short_16","alias_value":"HBDVSDBPRBVXVVVI","created_at":"2026-07-05T01:21:17Z"},{"alias_kind":"pith_short_8","alias_value":"HBDVSDBP","created_at":"2026-07-05T01:21:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:HBDVSDBPRBVXVVVINOLHZU5DF2","target":"record","payload":{"canonical_record":{"source":{"id":"1911.10850","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-11-25T11:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"340b65890dd3026b2037a88e44ef7d627f05ec56fc84e8d168b4810a55f53e2f","abstract_canon_sha256":"60d0c462d2d470df19bb582c82af8af18d42d58415ac724f7facdac5097aba0c"},"schema_version":"1.0"},"canonical_sha256":"3847590c2f886b7ad6a86b967cd3a32ea77b98d15b013f8da41e8b037d919ff9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:21:17.218765Z","signature_b64":"uo9dPDWEXY1hILiriu3n68UyA053GOXyD4o06xyZ2Piuh3WC7sONA1DFg5HYkS+Eln9broCv4g0OsIqJwtTUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3847590c2f886b7ad6a86b967cd3a32ea77b98d15b013f8da41e8b037d919ff9","last_reissued_at":"2026-07-05T01:21:17.218359Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:21:17.218359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.10850","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:21:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RNpSpdF8pxdUqOJ8stAXKV2Y5hnlnpk5viRJT/vxnVONTwpCDFAW5nwlOyhzhpQ3KQ4RRCoDWo8cobQrmuNgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:01:37.992113Z"},"content_sha256":"dedac0a4feaae331a7982bbbb100d3db4f99dd3fe719d5ed5ac6127eb6fe7bf7","schema_version":"1.0","event_id":"sha256:dedac0a4feaae331a7982bbbb100d3db4f99dd3fe719d5ed5ac6127eb6fe7bf7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:HBDVSDBPRBVXVVVINOLHZU5DF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New extremal principles with applications to stochastic and semi-infinite programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Boris S. Mordukhovich, Pedro P\\'erez-Aros","submitted_at":"2019-11-25T11:54:40Z","abstract_excerpt":"This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact forms. The obtained principles are instrumental to derive via variational approaches integral representations and upper estimates of regular and limiting normals cones to essential intersections of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.10850","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.10850/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:21:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oQwBNNlN1LXyLI/aOTWP+t2IuzTGwXO+jdedOqAkuiGlIbeiM7x6Mx2OQmEsxeEDJUZH1zT7Cl65svtlO0UdBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:01:37.992614Z"},"content_sha256":"7e332978b98d850046227995ec825601818f930f186826813d3b6a599aa86077","schema_version":"1.0","event_id":"sha256:7e332978b98d850046227995ec825601818f930f186826813d3b6a599aa86077"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HBDVSDBPRBVXVVVINOLHZU5DF2/bundle.json","state_url":"https://pith.science/pith/HBDVSDBPRBVXVVVINOLHZU5DF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HBDVSDBPRBVXVVVINOLHZU5DF2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T02:01:37Z","links":{"resolver":"https://pith.science/pith/HBDVSDBPRBVXVVVINOLHZU5DF2","bundle":"https://pith.science/pith/HBDVSDBPRBVXVVVINOLHZU5DF2/bundle.json","state":"https://pith.science/pith/HBDVSDBPRBVXVVVINOLHZU5DF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HBDVSDBPRBVXVVVINOLHZU5DF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HBDVSDBPRBVXVVVINOLHZU5DF2","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":"60d0c462d2d470df19bb582c82af8af18d42d58415ac724f7facdac5097aba0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-11-25T11:54:40Z","title_canon_sha256":"340b65890dd3026b2037a88e44ef7d627f05ec56fc84e8d168b4810a55f53e2f"},"schema_version":"1.0","source":{"id":"1911.10850","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.10850","created_at":"2026-07-05T01:21:17Z"},{"alias_kind":"arxiv_version","alias_value":"1911.10850v3","created_at":"2026-07-05T01:21:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.10850","created_at":"2026-07-05T01:21:17Z"},{"alias_kind":"pith_short_12","alias_value":"HBDVSDBPRBVX","created_at":"2026-07-05T01:21:17Z"},{"alias_kind":"pith_short_16","alias_value":"HBDVSDBPRBVXVVVI","created_at":"2026-07-05T01:21:17Z"},{"alias_kind":"pith_short_8","alias_value":"HBDVSDBP","created_at":"2026-07-05T01:21:17Z"}],"graph_snapshots":[{"event_id":"sha256:7e332978b98d850046227995ec825601818f930f186826813d3b6a599aa86077","target":"graph","created_at":"2026-07-05T01:21:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.10850/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact forms. The obtained principles are instrumental to derive via variational approaches integral representations and upper estimates of regular and limiting normals cones to essential intersections of","authors_text":"Boris S. Mordukhovich, Pedro P\\'erez-Aros","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-11-25T11:54:40Z","title":"New extremal principles with applications to stochastic and semi-infinite programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.10850","kind":"arxiv","version":3},"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:dedac0a4feaae331a7982bbbb100d3db4f99dd3fe719d5ed5ac6127eb6fe7bf7","target":"record","created_at":"2026-07-05T01:21:17Z","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":"60d0c462d2d470df19bb582c82af8af18d42d58415ac724f7facdac5097aba0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-11-25T11:54:40Z","title_canon_sha256":"340b65890dd3026b2037a88e44ef7d627f05ec56fc84e8d168b4810a55f53e2f"},"schema_version":"1.0","source":{"id":"1911.10850","kind":"arxiv","version":3}},"canonical_sha256":"3847590c2f886b7ad6a86b967cd3a32ea77b98d15b013f8da41e8b037d919ff9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3847590c2f886b7ad6a86b967cd3a32ea77b98d15b013f8da41e8b037d919ff9","first_computed_at":"2026-07-05T01:21:17.218359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:21:17.218359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uo9dPDWEXY1hILiriu3n68UyA053GOXyD4o06xyZ2Piuh3WC7sONA1DFg5HYkS+Eln9broCv4g0OsIqJwtTUDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:21:17.218765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.10850","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dedac0a4feaae331a7982bbbb100d3db4f99dd3fe719d5ed5ac6127eb6fe7bf7","sha256:7e332978b98d850046227995ec825601818f930f186826813d3b6a599aa86077"],"state_sha256":"0540e7bf3bc6819b4cf7d25360db1695df74aec2d57ee658f42cd413e5e17184"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTR1c4z/9Nd6gnDn9dLXTHTNsQ2CEsvgsbpR0x6KC6s/C8f6hRv6gvQZgyWiVNiMH+QIBjPHOJjBQoaA1s7vCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T02:01:37.996238Z","bundle_sha256":"bb52f597c041486117fd57eec52c4052d36e1dd27a25bbacb6e2aa8d5194c21e"}}