{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CGSK5IBHWI2DID3WOOUMIQUMUQ","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":"dea58d005b06ef0495b9d1ef5802ccd22c186802e4e261c02c10e9df7b762cba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-22T01:16:11Z","title_canon_sha256":"ec4fc42eea2655750a31a8e5179b329746ef634bea9a527008cbbdbf2c945e6a"},"schema_version":"1.0","source":{"id":"1502.06159","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06159","created_at":"2026-05-18T00:13:08Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06159v2","created_at":"2026-05-18T00:13:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06159","created_at":"2026-05-18T00:13:08Z"},{"alias_kind":"pith_short_12","alias_value":"CGSK5IBHWI2D","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CGSK5IBHWI2DID3W","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CGSK5IBH","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:ed2a83b7b8ee85cff3291b3c2958b13e647f2fc4230903358a8fdcc4bcc900d4","target":"graph","created_at":"2026-05-18T00:13:08Z","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 article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error bounds for extended real-valued functions of two variables developed in A. Y. Kruger, Error bounds and metric subregularity, Optimization 64, 1 (2015) 49-79. Several primal and dual space local quantitative and qualitative criteria of nonlinear metric subregularity are formulated. The relationships between the criteria are established and illustrated.","authors_text":"Alexander Y. Kruger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-22T01:16:11Z","title":"Nonlinear Metric Subregularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06159","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:d98a22aa4755a6163ce410d498e2c4f91a691d83b31e93782e647f4ce586eddf","target":"record","created_at":"2026-05-18T00:13:08Z","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":"dea58d005b06ef0495b9d1ef5802ccd22c186802e4e261c02c10e9df7b762cba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-02-22T01:16:11Z","title_canon_sha256":"ec4fc42eea2655750a31a8e5179b329746ef634bea9a527008cbbdbf2c945e6a"},"schema_version":"1.0","source":{"id":"1502.06159","kind":"arxiv","version":2}},"canonical_sha256":"11a4aea027b234340f7673a8c4428ca42ccdb42891bf8837599e5476c0379c15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11a4aea027b234340f7673a8c4428ca42ccdb42891bf8837599e5476c0379c15","first_computed_at":"2026-05-18T00:13:08.304681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:08.304681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DqTwlAqTyKuv2ppLEtLFAe0noVqsE7dUW8InSg4bxUL/m4yTLPVxlFPkqn9SE/Ih6ZePEN23OM6jI/JsJMnfDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:08.305267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d98a22aa4755a6163ce410d498e2c4f91a691d83b31e93782e647f4ce586eddf","sha256:ed2a83b7b8ee85cff3291b3c2958b13e647f2fc4230903358a8fdcc4bcc900d4"],"state_sha256":"e5fb9e708b3f091110f8d6069124f20edcd15cfe6e320989fd72730d2beac533"}