{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VMK7PU73DXTKWKYHZGNZ6YJT72","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":"ae3202e1197d546a714a9b125862dfaca78c0cf4078f46c7fb3884579732e6e7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-08T00:13:48Z","title_canon_sha256":"bbb1abd3ec973c2ea2bc3a0e8560eb909b6c434089a5718700779b131b31cbbc"},"schema_version":"1.0","source":{"id":"1303.1859","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1859","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1859v4","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1859","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"VMK7PU73DXTK","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VMK7PU73DXTKWKYH","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VMK7PU73","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:611e25144180cc371bcf27ed66f7d4d52d32e30bfd3e3c00f5706c7bf0084ecc","target":"graph","created_at":"2026-05-18T00:15:02Z","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 paper we present two Douglas-Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the N sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our methods to the classical (product-space) Douglas-Rachford scheme, are promising.","authors_text":"Jonathan M. Borwein, Matthew K. Tam","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-08T00:13:48Z","title":"A Cyclic Douglas-Rachford Iteration Scheme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1859","kind":"arxiv","version":4},"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:d7e694eec8382c7cb6b6731928fb77d1367369c7fec4f82e031df91f0ab5ef69","target":"record","created_at":"2026-05-18T00:15:02Z","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":"ae3202e1197d546a714a9b125862dfaca78c0cf4078f46c7fb3884579732e6e7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-08T00:13:48Z","title_canon_sha256":"bbb1abd3ec973c2ea2bc3a0e8560eb909b6c434089a5718700779b131b31cbbc"},"schema_version":"1.0","source":{"id":"1303.1859","kind":"arxiv","version":4}},"canonical_sha256":"ab15f7d3fb1de6ab2b07c99b9f6133feaae06e5a0ac06c910dcbea65d9d66225","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab15f7d3fb1de6ab2b07c99b9f6133feaae06e5a0ac06c910dcbea65d9d66225","first_computed_at":"2026-05-18T00:15:02.692323Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:02.692323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EDUafl9Fhxx3Wq+ZAIf+oGTspANFgVZnv4HVQgUhlqqNzjuBp+yOMkxLEn5I0iyiXuMGO+olV1NouFLJpCJMAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:02.693191Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1859","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7e694eec8382c7cb6b6731928fb77d1367369c7fec4f82e031df91f0ab5ef69","sha256:611e25144180cc371bcf27ed66f7d4d52d32e30bfd3e3c00f5706c7bf0084ecc"],"state_sha256":"5bad81fbd2fd30d0b372a12a132ba91e8df612f0b6a3c4c1cb2fad434fa379f3"}