{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2YLMCPKR4MOVYRRGJG4C6DTYHA","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":"0f3b3089c3e07ce1e01d6433ddf0771e4b4c77afbb31c228eb04cd52fad7f6d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-02-16T08:05:31Z","title_canon_sha256":"91dd0493efe170a32b057bba0c2ce3ee0af897c5f4362c228df1d5a6e256c909"},"schema_version":"1.0","source":{"id":"1602.04935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04935","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04935v1","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04935","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"2YLMCPKR4MOV","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YLMCPKR4MOVYRRG","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YLMCPKR","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:25bf7b3c7ce48c613b59d90cf38a196e52b546797399ac370f5365cb309e7324","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":"We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between seemingly different ideas and point to possible necessary conditions for local linear convergence of fundamental algorithms.","authors_text":"Alexander Y. Kruger, D. Russell Luke, Nguyen H. Thao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-02-16T08:05:31Z","title":"Set Regularities and Feasibility Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04935","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":"sha256:5d65c0df3bd3686bf7194d197e81a30300bfbf5f55ed0172f62c9a6535c41e5d","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":"0f3b3089c3e07ce1e01d6433ddf0771e4b4c77afbb31c228eb04cd52fad7f6d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-02-16T08:05:31Z","title_canon_sha256":"91dd0493efe170a32b057bba0c2ce3ee0af897c5f4362c228df1d5a6e256c909"},"schema_version":"1.0","source":{"id":"1602.04935","kind":"arxiv","version":1}},"canonical_sha256":"d616c13d51e31d5c462649b82f0e783819316ea0cb014ec3ce2a2a8cf0cbe56c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d616c13d51e31d5c462649b82f0e783819316ea0cb014ec3ce2a2a8cf0cbe56c","first_computed_at":"2026-05-18T00:16:09.812580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:09.812580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uUI/X6GXEp6tvVr3LTdiCATQ+LWhSVxK450XX/tzdGBlFufYJ/zjZ7v9tDe8y3yhnD8m8dJ7LO+Tf4fqkFvjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:09.813259Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d65c0df3bd3686bf7194d197e81a30300bfbf5f55ed0172f62c9a6535c41e5d","sha256:25bf7b3c7ce48c613b59d90cf38a196e52b546797399ac370f5365cb309e7324"],"state_sha256":"8fe638beadeed00e6554bbfd5577d4863ce09baf47983c7c18e39d62ddcfdc9a"}