{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SHAVXKLXIHO5FB6GQM33KSCK52","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":"ca838b87728aae23f215d90cf31b954a34ee11cf5636b02e31674a4a28a14d8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-15T01:23:06Z","title_canon_sha256":"811e58f46571b07fe1994d46e667008ed552b8d0882dd5940ee040634e67249e"},"schema_version":"1.0","source":{"id":"1303.3654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3654","created_at":"2026-05-18T01:37:38Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3654v1","created_at":"2026-05-18T01:37:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3654","created_at":"2026-05-18T01:37:38Z"},{"alias_kind":"pith_short_12","alias_value":"SHAVXKLXIHO5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SHAVXKLXIHO5FB6G","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SHAVXKLX","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:49071f9ae24f48bd3620f71e4ac2c89b428c66463a05532c6f8ce4cb2546a5a8","target":"graph","created_at":"2026-05-18T01:37:38Z","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 [2] we characterized in terms of a quadratic growth condition various metric regularity properties of the subdifferential of a lower semicontinuous convex function acting in a Hilbert space. Motivated by some recent results in [16] where the authors extend to Banach spaces the characterization of the strong regularity, we extend as well the characterizations for the metric subregularity and the strong subregularity given in [2] to Banach spaces. We also notice that at least one implication in these characterizations remains valid for the limiting subdifferential without assuming convexity o","authors_text":"Francisco J. Arag\\'on Artacho, Michel H. Geoffroy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-15T01:23:06Z","title":"Metric subregularity of the convex subdifferential in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3654","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:d0a4115971d25d3cdfa0f9871efee4c4de61579dbfc1352ab587ba402b8e70d0","target":"record","created_at":"2026-05-18T01:37:38Z","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":"ca838b87728aae23f215d90cf31b954a34ee11cf5636b02e31674a4a28a14d8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-15T01:23:06Z","title_canon_sha256":"811e58f46571b07fe1994d46e667008ed552b8d0882dd5940ee040634e67249e"},"schema_version":"1.0","source":{"id":"1303.3654","kind":"arxiv","version":1}},"canonical_sha256":"91c15ba97741ddd287c68337b5484aeebfdec7f661ee8e7b4aecb95577689f70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91c15ba97741ddd287c68337b5484aeebfdec7f661ee8e7b4aecb95577689f70","first_computed_at":"2026-05-18T01:37:38.243221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:38.243221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qsaZd3DBrevOhTnsF5hKUCedVJA4q8FIgxg+VAxM8oyxkWGT3R6BnjyND0+bKqFfQX9hCKIJ01JSqLUu4vryDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:38.243767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0a4115971d25d3cdfa0f9871efee4c4de61579dbfc1352ab587ba402b8e70d0","sha256:49071f9ae24f48bd3620f71e4ac2c89b428c66463a05532c6f8ce4cb2546a5a8"],"state_sha256":"09ea5e60282f277da8efcf0ade15c72501a13edcc72a343a77f3795f9568e98d"}