{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DB7FJ7KQ2CYABYPLZOFLJQWLOA","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":"a5af3cf68324a9fba988d53f3d62cb7ac3d0bc393fb66f6a0a8250379676554c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-04T23:55:25Z","title_canon_sha256":"8e5883ba4ec078c951f99f7575ab178befeeb16a106f7bcd8f6d18eed60faf30"},"schema_version":"1.0","source":{"id":"1810.02463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02463","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02463v1","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02463","created_at":"2026-05-18T00:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"DB7FJ7KQ2CYA","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DB7FJ7KQ2CYABYPL","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DB7FJ7KQ","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:8bda86dadbab9dddeed06a15fbd402ac91ce253b037af5eb07e80adc60185800","target":"graph","created_at":"2026-05-18T00:04:01Z","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 focus on the convergence analysis of averaged relaxations of cutters, specifically for variants that---depending upon how parameters are chosen---resemble \\emph{alternating projections}, the \\emph{Douglas--Rachford method}, \\emph{relaxed reflect-reflect}, or the \\emph{Peaceman--Rachford} method. Such methods are frequently used to solve convex feasibility problems. The standard convergence analyses of projection algorithms are based on the \\emph{firm nonexpansivity} property of the relevant operators. However if the projections onto the constraint sets are replaced by cutters (projections o","authors_text":"R. D\\'iaz Mill\\'an, Scott B. Lindstrom, Vera Roshchina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-04T23:55:25Z","title":"Comparing Averaged Relaxed Cutters and Projection Methods: Theory and Examples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02463","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":"sha256:2c4672bf5248805d098c325d23e7d5e3ddce300da0f2cdcaaee5ea72145c3dc8","target":"record","created_at":"2026-05-18T00:04:01Z","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":"a5af3cf68324a9fba988d53f3d62cb7ac3d0bc393fb66f6a0a8250379676554c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-04T23:55:25Z","title_canon_sha256":"8e5883ba4ec078c951f99f7575ab178befeeb16a106f7bcd8f6d18eed60faf30"},"schema_version":"1.0","source":{"id":"1810.02463","kind":"arxiv","version":1}},"canonical_sha256":"187e54fd50d0b000e1ebcb8ab4c2cb70133573a1c5ceda4857f0b935ee36a491","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"187e54fd50d0b000e1ebcb8ab4c2cb70133573a1c5ceda4857f0b935ee36a491","first_computed_at":"2026-05-18T00:04:01.821112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:01.821112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hvxpcXvX96kI6vTsxKS7XZ7MG52690G1GcUldpkh1cp78rAbShdVz5ptv9RAoXIkNBLZzBO+2jVL/1WP8rfZCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:01.821730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c4672bf5248805d098c325d23e7d5e3ddce300da0f2cdcaaee5ea72145c3dc8","sha256:8bda86dadbab9dddeed06a15fbd402ac91ce253b037af5eb07e80adc60185800"],"state_sha256":"3d8ecfd84e34aef2bec2f3513e5759917e7c30e146d5b491e0a35d85bdbb7efa"}