{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:G6TCUP24BKZFYVG2D4MOV7C2I7","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":"a520224e925748ebca4146840e972983a7d39bdaacad1c609bac713e62953cde","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-15T03:39:54Z","title_canon_sha256":"3490b1af6a6b8350d3a597f38b31c9715ed7c14bc3699183aa5fba9c296e2d54"},"schema_version":"1.0","source":{"id":"2512.12954","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.12954","created_at":"2026-07-08T01:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"2512.12954v2","created_at":"2026-07-08T01:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.12954","created_at":"2026-07-08T01:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"G6TCUP24BKZF","created_at":"2026-07-08T01:18:22Z"},{"alias_kind":"pith_short_16","alias_value":"G6TCUP24BKZFYVG2","created_at":"2026-07-08T01:18:22Z"},{"alias_kind":"pith_short_8","alias_value":"G6TCUP24","created_at":"2026-07-08T01:18:22Z"}],"graph_snapshots":[{"event_id":"sha256:cf3b2787187361c755c1bee9257be3c17b752b76b3b692e3d4f0c1d21bcdfb20","target":"graph","created_at":"2026-07-08T01:18:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.12954/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2026) DOI: 10.1137/25M1776810 assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the algorithmic operator is a contraction. As a key application of our framework, we obtain linear convergence of the relocated Douglas--Rachford algorithm for finding a zero in the sum of two monotone operators in a setting with Lipschitz continuity and strong monotonicity assumptions. We also apply the framework to deduce linear convergence ","authors_text":"Farhana Ahmed Simi, Felipe Atenas, Matthew K Tam","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-15T03:39:54Z","title":"Linear convergence of relocated fixed-point iterations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.12954","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":"sha256:03ab83fd322afbec0f9ae55fcc077bd05b96b9388aa861d8fea6166222517ef2","target":"record","created_at":"2026-07-08T01:18:22Z","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":"a520224e925748ebca4146840e972983a7d39bdaacad1c609bac713e62953cde","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-15T03:39:54Z","title_canon_sha256":"3490b1af6a6b8350d3a597f38b31c9715ed7c14bc3699183aa5fba9c296e2d54"},"schema_version":"1.0","source":{"id":"2512.12954","kind":"arxiv","version":2}},"canonical_sha256":"37a62a3f5c0ab25c54da1f18eafc5a47f48abba625731332942fecb7f75a0fcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37a62a3f5c0ab25c54da1f18eafc5a47f48abba625731332942fecb7f75a0fcb","first_computed_at":"2026-07-08T01:18:22.780400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:18:22.780400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"umCXHfoonraYHQrXEbJVb6aT9zayfC/6YJh1AJ6gWpHI+Kq0ctYv2lzdWwYR/eIyKHBw+ERHKIY0dD+XSfxsBw==","signature_status":"signed_v1","signed_at":"2026-07-08T01:18:22.780965Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.12954","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03ab83fd322afbec0f9ae55fcc077bd05b96b9388aa861d8fea6166222517ef2","sha256:cf3b2787187361c755c1bee9257be3c17b752b76b3b692e3d4f0c1d21bcdfb20"],"state_sha256":"34779c6f20712d9ee76420a4dfabf97c9f457140c29f1343bf84d1cbc42e11b3"}