{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:G6TCUP24BKZFYVG2D4MOV7C2I7","short_pith_number":"pith:G6TCUP24","schema_version":"1.0","canonical_sha256":"37a62a3f5c0ab25c54da1f18eafc5a47f48abba625731332942fecb7f75a0fcb","source":{"kind":"arxiv","id":"2512.12954","version":2},"attestation_state":"computed","paper":{"title":"Linear convergence of relocated fixed-point iterations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Farhana Ahmed Simi, Felipe Atenas, Matthew K Tam","submitted_at":"2025-12-15T03:39:54Z","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2512.12954","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-12-15T03:39:54Z","cross_cats_sorted":[],"title_canon_sha256":"3490b1af6a6b8350d3a597f38b31c9715ed7c14bc3699183aa5fba9c296e2d54","abstract_canon_sha256":"a520224e925748ebca4146840e972983a7d39bdaacad1c609bac713e62953cde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:22.780965Z","signature_b64":"umCXHfoonraYHQrXEbJVb6aT9zayfC/6YJh1AJ6gWpHI+Kq0ctYv2lzdWwYR/eIyKHBw+ERHKIY0dD+XSfxsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37a62a3f5c0ab25c54da1f18eafc5a47f48abba625731332942fecb7f75a0fcb","last_reissued_at":"2026-07-08T01:18:22.780400Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:22.780400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear convergence of relocated fixed-point iterations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Farhana Ahmed Simi, Felipe Atenas, Matthew K Tam","submitted_at":"2025-12-15T03:39:54Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.12954","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.12954/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2512.12954","created_at":"2026-07-08T01:18:22.780477+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.12954v2","created_at":"2026-07-08T01:18:22.780477+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.12954","created_at":"2026-07-08T01:18:22.780477+00:00"},{"alias_kind":"pith_short_12","alias_value":"G6TCUP24BKZF","created_at":"2026-07-08T01:18:22.780477+00:00"},{"alias_kind":"pith_short_16","alias_value":"G6TCUP24BKZFYVG2","created_at":"2026-07-08T01:18:22.780477+00:00"},{"alias_kind":"pith_short_8","alias_value":"G6TCUP24","created_at":"2026-07-08T01:18:22.780477+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G6TCUP24BKZFYVG2D4MOV7C2I7","json":"https://pith.science/pith/G6TCUP24BKZFYVG2D4MOV7C2I7.json","graph_json":"https://pith.science/api/pith-number/G6TCUP24BKZFYVG2D4MOV7C2I7/graph.json","events_json":"https://pith.science/api/pith-number/G6TCUP24BKZFYVG2D4MOV7C2I7/events.json","paper":"https://pith.science/paper/G6TCUP24"},"agent_actions":{"view_html":"https://pith.science/pith/G6TCUP24BKZFYVG2D4MOV7C2I7","download_json":"https://pith.science/pith/G6TCUP24BKZFYVG2D4MOV7C2I7.json","view_paper":"https://pith.science/paper/G6TCUP24","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.12954&json=true","fetch_graph":"https://pith.science/api/pith-number/G6TCUP24BKZFYVG2D4MOV7C2I7/graph.json","fetch_events":"https://pith.science/api/pith-number/G6TCUP24BKZFYVG2D4MOV7C2I7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G6TCUP24BKZFYVG2D4MOV7C2I7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G6TCUP24BKZFYVG2D4MOV7C2I7/action/storage_attestation","attest_author":"https://pith.science/pith/G6TCUP24BKZFYVG2D4MOV7C2I7/action/author_attestation","sign_citation":"https://pith.science/pith/G6TCUP24BKZFYVG2D4MOV7C2I7/action/citation_signature","submit_replication":"https://pith.science/pith/G6TCUP24BKZFYVG2D4MOV7C2I7/action/replication_record"}},"created_at":"2026-07-08T01:18:22.780477+00:00","updated_at":"2026-07-08T01:18:22.780477+00:00"}