{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YVTBZJBMS44INUUM5NOLZSI4X3","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":"472147fad3d8dbecbae6ad1dbf69266ee36ec517cfb2a2fe892a4355fed2a4bc","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2022-10-01T16:04:24Z","title_canon_sha256":"e76ec5414a3aa124c5584d2b566a686c1ad01aea52c123db3e139601400d4340"},"schema_version":"1.0","source":{"id":"2210.00307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.00307","created_at":"2026-07-05T05:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"2210.00307v1","created_at":"2026-07-05T05:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.00307","created_at":"2026-07-05T05:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"YVTBZJBMS44I","created_at":"2026-07-05T05:02:30Z"},{"alias_kind":"pith_short_16","alias_value":"YVTBZJBMS44INUUM","created_at":"2026-07-05T05:02:30Z"},{"alias_kind":"pith_short_8","alias_value":"YVTBZJBM","created_at":"2026-07-05T05:02:30Z"}],"graph_snapshots":[{"event_id":"sha256:c9aef83b401f39ab8c639d045cf4bc1073e1f91d71cc8229507d13d087a3d36e","target":"graph","created_at":"2026-07-05T05:02:30Z","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/2210.00307/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is devoted to primal conditions of error bounds for a general function. In terms of Bouligand tangent cones, lower Hadamard directional derivatives and the Hausdorff-Pompeiu excess of subsets, we provide several necessary and/or sufficient conditions of error bounds with mild assumptions. Then we use these primal results to characterize error bounds for composite-convex functions (i.e. the composition of a convex function with a continuously differentiable mapping). It is proved that the primal characterization of error bounds can be established via Bouligand tangent cones, directio","authors_text":"Jen-Chih Yao, Michel Th\\'era, Zhou Wei","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2022-10-01T16:04:24Z","title":"Primal Characterizations of Error Bounds for Composite-convex Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.00307","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":"sha256:02ef95affb7a220f9cc045b0ef21adca1e0d19c699b30a4dee93e5dc243bd863","target":"record","created_at":"2026-07-05T05:02:30Z","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":"472147fad3d8dbecbae6ad1dbf69266ee36ec517cfb2a2fe892a4355fed2a4bc","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2022-10-01T16:04:24Z","title_canon_sha256":"e76ec5414a3aa124c5584d2b566a686c1ad01aea52c123db3e139601400d4340"},"schema_version":"1.0","source":{"id":"2210.00307","kind":"arxiv","version":1}},"canonical_sha256":"c5661ca42c973886d28ceb5cbcc91cbec3faefcf6edd1bf3cdf9d7465f0bc768","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5661ca42c973886d28ceb5cbcc91cbec3faefcf6edd1bf3cdf9d7465f0bc768","first_computed_at":"2026-07-05T05:02:30.696388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:02:30.696388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0VpVHNSkocR1XywPyF3hx4bvgQHmy6aWtu7t7DJQBBVazRrON2wFo3Soy9SrJILhUv6e47zUsczoZWVROWvSAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:02:30.696752Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.00307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02ef95affb7a220f9cc045b0ef21adca1e0d19c699b30a4dee93e5dc243bd863","sha256:c9aef83b401f39ab8c639d045cf4bc1073e1f91d71cc8229507d13d087a3d36e"],"state_sha256":"7573e28cc9504b3731268a7cc5888cf458c5f28a6d47007f11bd8f71b067756d"}