{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WBCUDLV32WTGLKS4OHEM5OAPD4","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":"490bbee1bf28c4b6a388c176c5d3609c798bc12750735c217c0b96b76a78dc03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-01T17:21:14Z","title_canon_sha256":"02404e25ccd46514f9d5e544eea18e2a3e082d2b3f94ee491eaaf245a5460d3c"},"schema_version":"1.0","source":{"id":"1801.00480","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00480","created_at":"2026-05-18T00:10:38Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00480v2","created_at":"2026-05-18T00:10:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00480","created_at":"2026-05-18T00:10:38Z"},{"alias_kind":"pith_short_12","alias_value":"WBCUDLV32WTG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WBCUDLV32WTGLKS4","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WBCUDLV3","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:7d79b8890b4fb3cb08b46d66c735abf80017a2a4c0c4a0cb4dcb017156682aca","target":"graph","created_at":"2026-05-18T00:10:38Z","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":"The Douglas-Rachford (DR) algorithm is an iterative procedure that uses sequential reflections onto convex sets and which has become popular for convex feasibility problems. In this paper we propose a structural generalization that allows to use $r$-sets-DR operators in a cyclic fashion. We prove convergence and present numerical illustrations of the potential advantage of such operators with $r>2$ over the classical $2$-sets-DR operators in a cyclic algorithm.","authors_text":"Aviv Gibali, Francisco J. Arag\\'on Artacho, Yair Censor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-01T17:21:14Z","title":"The Cyclic Douglas-Rachford Algorithm with r-sets-Douglas-Rachford Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00480","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:e7ca665c63adc8cf5a48d31f35934a516fc2948c527c69fa4174a32c5ac9e4cd","target":"record","created_at":"2026-05-18T00:10:38Z","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":"490bbee1bf28c4b6a388c176c5d3609c798bc12750735c217c0b96b76a78dc03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-01T17:21:14Z","title_canon_sha256":"02404e25ccd46514f9d5e544eea18e2a3e082d2b3f94ee491eaaf245a5460d3c"},"schema_version":"1.0","source":{"id":"1801.00480","kind":"arxiv","version":2}},"canonical_sha256":"b04541aebbd5a665aa5c71c8ceb80f1f2acc6c91b2213e88b66b77ca032f4275","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b04541aebbd5a665aa5c71c8ceb80f1f2acc6c91b2213e88b66b77ca032f4275","first_computed_at":"2026-05-18T00:10:38.711874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:38.711874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7S019wnQe2Ja+Vhb9xSJdS0qohT8+MaarvI9egyE4oHnFnn8iOwnKymuxMKHHFWQoA/0WRmgK2EcJuRq/4n7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:38.712455Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00480","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7ca665c63adc8cf5a48d31f35934a516fc2948c527c69fa4174a32c5ac9e4cd","sha256:7d79b8890b4fb3cb08b46d66c735abf80017a2a4c0c4a0cb4dcb017156682aca"],"state_sha256":"61c506ddaff646671b54f7d8ee548c008e6612a6739a42dbb16a5ac7f06255dd"}