{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6QHBKOHAU3CFTR7ZA4XQG6HCYZ","short_pith_number":"pith:6QHBKOHA","canonical_record":{"source":{"id":"1610.05671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-18T15:24:41Z","cross_cats_sorted":[],"title_canon_sha256":"92b66b938d06f5bbf445d9a1417af11416ffec3c0527c79c0df84fffc6c58089","abstract_canon_sha256":"3629ca945f49ebd479a74283b3b08c25556fe40e01a0356b54fa9f696fda6960"},"schema_version":"1.0"},"canonical_sha256":"f40e1538e0a6c459c7f9072f0378e2c67762305ad6635ef034360370aed4194f","source":{"kind":"arxiv","id":"1610.05671","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05671","created_at":"2026-05-18T01:01:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05671v1","created_at":"2026-05-18T01:01:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05671","created_at":"2026-05-18T01:01:58Z"},{"alias_kind":"pith_short_12","alias_value":"6QHBKOHAU3CF","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6QHBKOHAU3CFTR7Z","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6QHBKOHA","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6QHBKOHAU3CFTR7ZA4XQG6HCYZ","target":"record","payload":{"canonical_record":{"source":{"id":"1610.05671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-18T15:24:41Z","cross_cats_sorted":[],"title_canon_sha256":"92b66b938d06f5bbf445d9a1417af11416ffec3c0527c79c0df84fffc6c58089","abstract_canon_sha256":"3629ca945f49ebd479a74283b3b08c25556fe40e01a0356b54fa9f696fda6960"},"schema_version":"1.0"},"canonical_sha256":"f40e1538e0a6c459c7f9072f0378e2c67762305ad6635ef034360370aed4194f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:58.670750Z","signature_b64":"24K+ZwBKYyiVGjhuk7GWi6DlszDDiqhEtnIazXuwuAW1QrjpUapCrlTYKBLOa5Wl3G4LzzaEEEkmM8V/f4GhAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f40e1538e0a6c459c7f9072f0378e2c67762305ad6635ef034360370aed4194f","last_reissued_at":"2026-05-18T01:01:58.670144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:58.670144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.05671","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":"2026-05-18T01:01:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"suAnDA8O7cGNa7qud7jmviRYVECGnNhVxkWNSQn7Alp1DkTSJShIUom6E4G4OpMk2AWiB2/7YsdBETRU8zbQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T17:00:18.334178Z"},"content_sha256":"de02ea138e441272a6a98045ed8a3f67cf756ba23152f6c290251c9df7d41fac","schema_version":"1.0","event_id":"sha256:de02ea138e441272a6a98045ed8a3f67cf756ba23152f6c290251c9df7d41fac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6QHBKOHAU3CFTR7ZA4XQG6HCYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Metric Subregularity for Convex Constraint Systems by Primal Equivalent Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Liyun Huang, Zhou Wei","submitted_at":"2016-10-18T15:24:41Z","abstract_excerpt":"In this paper, we mainly study metric subregularity for a convex constraint system defined by a convex set-valued mapping and a convex constraint subset. The main work is to provide several primal equivalent conditions for metric subregularity by contingent cone and graphical derivative. Further it is proved that these primal equivalent conditions can characterize strong basic constraint qualification of convex constraint system given by Zheng and Ng [SIAM J. Optim., 18(2007), pp. 437-460]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05671","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":""},"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":"2026-05-18T01:01:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vX7gv6o7qyFCAOkPZyBMNtVcXzDUEzp70LAqufq9gykqbFEWg9n+wl/GnD1NzsELc1xlvYHE9tbT1CFkOMarCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T17:00:18.334537Z"},"content_sha256":"2605234857769f118d2d6a4547f95940473851e37feb8a7e53a9d8e579521ef8","schema_version":"1.0","event_id":"sha256:2605234857769f118d2d6a4547f95940473851e37feb8a7e53a9d8e579521ef8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6QHBKOHAU3CFTR7ZA4XQG6HCYZ/bundle.json","state_url":"https://pith.science/pith/6QHBKOHAU3CFTR7ZA4XQG6HCYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6QHBKOHAU3CFTR7ZA4XQG6HCYZ/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":"2026-07-01T17:00:18Z","links":{"resolver":"https://pith.science/pith/6QHBKOHAU3CFTR7ZA4XQG6HCYZ","bundle":"https://pith.science/pith/6QHBKOHAU3CFTR7ZA4XQG6HCYZ/bundle.json","state":"https://pith.science/pith/6QHBKOHAU3CFTR7ZA4XQG6HCYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6QHBKOHAU3CFTR7ZA4XQG6HCYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6QHBKOHAU3CFTR7ZA4XQG6HCYZ","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":"3629ca945f49ebd479a74283b3b08c25556fe40e01a0356b54fa9f696fda6960","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-18T15:24:41Z","title_canon_sha256":"92b66b938d06f5bbf445d9a1417af11416ffec3c0527c79c0df84fffc6c58089"},"schema_version":"1.0","source":{"id":"1610.05671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05671","created_at":"2026-05-18T01:01:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05671v1","created_at":"2026-05-18T01:01:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05671","created_at":"2026-05-18T01:01:58Z"},{"alias_kind":"pith_short_12","alias_value":"6QHBKOHAU3CF","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6QHBKOHAU3CFTR7Z","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6QHBKOHA","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:2605234857769f118d2d6a4547f95940473851e37feb8a7e53a9d8e579521ef8","target":"graph","created_at":"2026-05-18T01:01:58Z","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 mainly study metric subregularity for a convex constraint system defined by a convex set-valued mapping and a convex constraint subset. The main work is to provide several primal equivalent conditions for metric subregularity by contingent cone and graphical derivative. Further it is proved that these primal equivalent conditions can characterize strong basic constraint qualification of convex constraint system given by Zheng and Ng [SIAM J. Optim., 18(2007), pp. 437-460].","authors_text":"Liyun Huang, Zhou Wei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-18T15:24:41Z","title":"On Metric Subregularity for Convex Constraint Systems by Primal Equivalent Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05671","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:de02ea138e441272a6a98045ed8a3f67cf756ba23152f6c290251c9df7d41fac","target":"record","created_at":"2026-05-18T01:01:58Z","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":"3629ca945f49ebd479a74283b3b08c25556fe40e01a0356b54fa9f696fda6960","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-18T15:24:41Z","title_canon_sha256":"92b66b938d06f5bbf445d9a1417af11416ffec3c0527c79c0df84fffc6c58089"},"schema_version":"1.0","source":{"id":"1610.05671","kind":"arxiv","version":1}},"canonical_sha256":"f40e1538e0a6c459c7f9072f0378e2c67762305ad6635ef034360370aed4194f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f40e1538e0a6c459c7f9072f0378e2c67762305ad6635ef034360370aed4194f","first_computed_at":"2026-05-18T01:01:58.670144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:58.670144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"24K+ZwBKYyiVGjhuk7GWi6DlszDDiqhEtnIazXuwuAW1QrjpUapCrlTYKBLOa5Wl3G4LzzaEEEkmM8V/f4GhAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:58.670750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de02ea138e441272a6a98045ed8a3f67cf756ba23152f6c290251c9df7d41fac","sha256:2605234857769f118d2d6a4547f95940473851e37feb8a7e53a9d8e579521ef8"],"state_sha256":"b47f834f4bbac370df4812f11434440d8865e4e4b39bb9129037ef44373778ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tGjBiGr2S5jkd5zaQHJ23b65Xokju51m6Uf0WrJ5BnLV7Mlkp5x8vNwN0rRytgFIsCLYBEB5z+xd7DXAMmKyAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T17:00:18.336460Z","bundle_sha256":"b5e524edcb2bc86904a4436b6bed73b7d5c154016aa4cc2a1901800e8d016895"}}