{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:43IEUIUXGVYTGSYJINETVS3FHQ","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":"e6fb346f218546f5e5407b0ef80798e8108e9159543b0f711fa1d5c8268aa151","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-15T11:52:06Z","title_canon_sha256":"282d9a846a8c4d397ecd3a2dfdbc63c0cb70108323766623133708317e4edb8a"},"schema_version":"1.0","source":{"id":"1512.04742","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04742","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04742v2","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04742","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"43IEUIUXGVYT","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"43IEUIUXGVYTGSYJ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"43IEUIUX","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:2da3a6df39e99f18353d94b1880790df8e41fa4a9a170df210f268847008b585","target":"graph","created_at":"2026-05-18T00:16:09Z","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":"Our aim in the current article is to extend the developments in Kruger, Ngai & Th\\'era, SIAM J. Optim. 20(6), 3280-3296 (2010) and, more precisely, to characterize, in the Banach space setting, the stability of the local and global error bound property of inequalities determined by proper lower semicontinuous under data perturbations. We propose new concepts of (arbitrary, convex and linear) perturbations of the given function defining the system under consideration, which turn out to be a useful tool in our analysis. The characterizations of error bounds for families of perturbations can be i","authors_text":"A. Y. Kruger, M. A. L\\'Opez, M. A. Th\\'era","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-15T11:52:06Z","title":"Perturbation of error bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04742","kind":"arxiv","version":2},"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":"sha256:905ed0b6f27a91aa40d4e7681385684b2af01d4674fff5deb57d07194740c2b0","target":"record","created_at":"2026-05-18T00:16:09Z","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":"e6fb346f218546f5e5407b0ef80798e8108e9159543b0f711fa1d5c8268aa151","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-15T11:52:06Z","title_canon_sha256":"282d9a846a8c4d397ecd3a2dfdbc63c0cb70108323766623133708317e4edb8a"},"schema_version":"1.0","source":{"id":"1512.04742","kind":"arxiv","version":2}},"canonical_sha256":"e6d04a22973571334b0943493acb653c1c05d545bcb84494eb9a8eff49dcebb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6d04a22973571334b0943493acb653c1c05d545bcb84494eb9a8eff49dcebb3","first_computed_at":"2026-05-18T00:16:09.838322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:09.838322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggNtCoGIMriojprIh/U6snPCybB2Vv6T8A+t7fwg7BmTAvaU9nFx4JZoj6PQ5TPpf6BLf1m01AN7WVq4nXkNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:09.839020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04742","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:905ed0b6f27a91aa40d4e7681385684b2af01d4674fff5deb57d07194740c2b0","sha256:2da3a6df39e99f18353d94b1880790df8e41fa4a9a170df210f268847008b585"],"state_sha256":"6ef1f7bed12bd33dbf9a99349620528b487dbe26db1b4d0b8861479b67c6235d"}