{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:2I7R4LNUIB2VHDCJUXMAZRHAPO","short_pith_number":"pith:2I7R4LNU","canonical_record":{"source":{"id":"2311.08741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-11-15T07:13:34Z","cross_cats_sorted":[],"title_canon_sha256":"d7f67d6d44be1a7015e39eeee73dff9a84d42ac4ef6179df3a2f00b13f451261","abstract_canon_sha256":"54adcdbdfaf54aba1bbb591f568d24a1adf7653fbe9e960002d29ab7c332df3a"},"schema_version":"1.0"},"canonical_sha256":"d23f1e2db44075538c49a5d80cc4e07bbf34dd0f8bddccbc5b6fe86a47953bdb","source":{"kind":"arxiv","id":"2311.08741","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.08741","created_at":"2026-07-05T07:13:02Z"},{"alias_kind":"arxiv_version","alias_value":"2311.08741v1","created_at":"2026-07-05T07:13:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.08741","created_at":"2026-07-05T07:13:02Z"},{"alias_kind":"pith_short_12","alias_value":"2I7R4LNUIB2V","created_at":"2026-07-05T07:13:02Z"},{"alias_kind":"pith_short_16","alias_value":"2I7R4LNUIB2VHDCJ","created_at":"2026-07-05T07:13:02Z"},{"alias_kind":"pith_short_8","alias_value":"2I7R4LNU","created_at":"2026-07-05T07:13:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:2I7R4LNUIB2VHDCJUXMAZRHAPO","target":"record","payload":{"canonical_record":{"source":{"id":"2311.08741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-11-15T07:13:34Z","cross_cats_sorted":[],"title_canon_sha256":"d7f67d6d44be1a7015e39eeee73dff9a84d42ac4ef6179df3a2f00b13f451261","abstract_canon_sha256":"54adcdbdfaf54aba1bbb591f568d24a1adf7653fbe9e960002d29ab7c332df3a"},"schema_version":"1.0"},"canonical_sha256":"d23f1e2db44075538c49a5d80cc4e07bbf34dd0f8bddccbc5b6fe86a47953bdb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:13:02.725211Z","signature_b64":"VOXXUm4i1rwVpvi8VHU+azTkNrsWmtvMKBHZ7C1H2fK6j+DmDG3Mw6QRu8fe7ANjR5TJRy0bjyYWVvO4eA/JAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d23f1e2db44075538c49a5d80cc4e07bbf34dd0f8bddccbc5b6fe86a47953bdb","last_reissued_at":"2026-07-05T07:13:02.724732Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:13:02.724732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.08741","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:13:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rm9iYf9A4Ez8OUfk8LdJ4yCze6h6znkjZRG6D51pSa8l2x8P9RDH06TeWJlBwY6234hAgMhie1QVfvRIU0YSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:04:48.789994Z"},"content_sha256":"07b60a993e7783fab36eef4fd26a1f426084d78a1313d0d89fa6b8f2f1e3f372","schema_version":"1.0","event_id":"sha256:07b60a993e7783fab36eef4fd26a1f426084d78a1313d0d89fa6b8f2f1e3f372"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:2I7R4LNUIB2VHDCJUXMAZRHAPO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Formulas for calculating of generalized differentials with respect to a set and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jen-Chih Yao, Vo Duc Thinh, Xiaolong Qin","submitted_at":"2023-11-15T07:13:34Z","abstract_excerpt":"This paper provides formulas for calculating of Fr\\'{e}chet and limiting normal cones with respect to a set of sets and the limiting coderivative with respect to a set of set-valued mappings. These calculations are obtained under some qualification constraints and are expressed in the similar forms of these ones of Fr\\'{e}chet and limiting normal cones and the limiting coderivative. By using these obtained formulas, we state explicit necessary optimality conditions with respect to a set for optimization problems with equilibrium constraints under certain qualification conditions. Some illustra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.08741","kind":"arxiv","version":1},"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/2311.08741/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":"2026-07-05T07:13:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oNINlkxlwsljfXpsEyjPpS9NKXBmhMUbFfxsDtSdMQeL8DrRxHaWyefEHXdt+TmPilDsnr4zcbyTsbxvI0YTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:04:48.799171Z"},"content_sha256":"7c765bdaa7ec2acbd0f9234c1620881bdf4a35fa908911fed0ac07397bdee654","schema_version":"1.0","event_id":"sha256:7c765bdaa7ec2acbd0f9234c1620881bdf4a35fa908911fed0ac07397bdee654"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2I7R4LNUIB2VHDCJUXMAZRHAPO/bundle.json","state_url":"https://pith.science/pith/2I7R4LNUIB2VHDCJUXMAZRHAPO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2I7R4LNUIB2VHDCJUXMAZRHAPO/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":"2026-08-05T14:04:48Z","links":{"resolver":"https://pith.science/pith/2I7R4LNUIB2VHDCJUXMAZRHAPO","bundle":"https://pith.science/pith/2I7R4LNUIB2VHDCJUXMAZRHAPO/bundle.json","state":"https://pith.science/pith/2I7R4LNUIB2VHDCJUXMAZRHAPO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2I7R4LNUIB2VHDCJUXMAZRHAPO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2I7R4LNUIB2VHDCJUXMAZRHAPO","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":"54adcdbdfaf54aba1bbb591f568d24a1adf7653fbe9e960002d29ab7c332df3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-11-15T07:13:34Z","title_canon_sha256":"d7f67d6d44be1a7015e39eeee73dff9a84d42ac4ef6179df3a2f00b13f451261"},"schema_version":"1.0","source":{"id":"2311.08741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.08741","created_at":"2026-07-05T07:13:02Z"},{"alias_kind":"arxiv_version","alias_value":"2311.08741v1","created_at":"2026-07-05T07:13:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.08741","created_at":"2026-07-05T07:13:02Z"},{"alias_kind":"pith_short_12","alias_value":"2I7R4LNUIB2V","created_at":"2026-07-05T07:13:02Z"},{"alias_kind":"pith_short_16","alias_value":"2I7R4LNUIB2VHDCJ","created_at":"2026-07-05T07:13:02Z"},{"alias_kind":"pith_short_8","alias_value":"2I7R4LNU","created_at":"2026-07-05T07:13:02Z"}],"graph_snapshots":[{"event_id":"sha256:7c765bdaa7ec2acbd0f9234c1620881bdf4a35fa908911fed0ac07397bdee654","target":"graph","created_at":"2026-07-05T07:13:02Z","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/2311.08741/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper provides formulas for calculating of Fr\\'{e}chet and limiting normal cones with respect to a set of sets and the limiting coderivative with respect to a set of set-valued mappings. These calculations are obtained under some qualification constraints and are expressed in the similar forms of these ones of Fr\\'{e}chet and limiting normal cones and the limiting coderivative. By using these obtained formulas, we state explicit necessary optimality conditions with respect to a set for optimization problems with equilibrium constraints under certain qualification conditions. Some illustra","authors_text":"Jen-Chih Yao, Vo Duc Thinh, Xiaolong Qin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-11-15T07:13:34Z","title":"Formulas for calculating of generalized differentials with respect to a set and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.08741","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":"sha256:07b60a993e7783fab36eef4fd26a1f426084d78a1313d0d89fa6b8f2f1e3f372","target":"record","created_at":"2026-07-05T07:13:02Z","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":"54adcdbdfaf54aba1bbb591f568d24a1adf7653fbe9e960002d29ab7c332df3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-11-15T07:13:34Z","title_canon_sha256":"d7f67d6d44be1a7015e39eeee73dff9a84d42ac4ef6179df3a2f00b13f451261"},"schema_version":"1.0","source":{"id":"2311.08741","kind":"arxiv","version":1}},"canonical_sha256":"d23f1e2db44075538c49a5d80cc4e07bbf34dd0f8bddccbc5b6fe86a47953bdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d23f1e2db44075538c49a5d80cc4e07bbf34dd0f8bddccbc5b6fe86a47953bdb","first_computed_at":"2026-07-05T07:13:02.724732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:13:02.724732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VOXXUm4i1rwVpvi8VHU+azTkNrsWmtvMKBHZ7C1H2fK6j+DmDG3Mw6QRu8fe7ANjR5TJRy0bjyYWVvO4eA/JAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:13:02.725211Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.08741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07b60a993e7783fab36eef4fd26a1f426084d78a1313d0d89fa6b8f2f1e3f372","sha256:7c765bdaa7ec2acbd0f9234c1620881bdf4a35fa908911fed0ac07397bdee654"],"state_sha256":"ca530501d0623ed70844ef942f76fe1bb947bca18494a99b88bb278fc575ea0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LPgM++OhX55mhVHdYrvkOal7qUuBEpbCIpjkigufcRfo78vuL3Fm0K3jdYHXXKNxuV+unqY2dsnf7R56LBNZAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T14:04:48.806355Z","bundle_sha256":"b3b2994f3ceb76821d5556ce88cbb92b29a260148729d3991c02996f900a3db6"}}