{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FVM7QQ5KVJZNMOGCVXFZMNYCX2","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":"d0b6fce7e386af53609021619dd8a8afb71d4e2ac8a5bed88d220653e45b9f90","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-02T05:44:44Z","title_canon_sha256":"9d3f90de7a73c0ae76588fe0faf269bbd0b0c9a5e8b5d714f845f534b46601f7"},"schema_version":"1.0","source":{"id":"2506.08031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08031","created_at":"2026-07-05T11:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08031v1","created_at":"2026-07-05T11:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08031","created_at":"2026-07-05T11:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"FVM7QQ5KVJZN","created_at":"2026-07-05T11:18:43Z"},{"alias_kind":"pith_short_16","alias_value":"FVM7QQ5KVJZNMOGC","created_at":"2026-07-05T11:18:43Z"},{"alias_kind":"pith_short_8","alias_value":"FVM7QQ5K","created_at":"2026-07-05T11:18:43Z"}],"graph_snapshots":[{"event_id":"sha256:5f36b49ea561ff5b824e2fb3f2218ed0a3abd06385903525b2f0f8b57751d698","target":"graph","created_at":"2026-07-05T11:18:43Z","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/2506.08031/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a generalization of the stochastic Krasnoselskil-Mann $(SKM)$ algorithm to reflexive Banach spaces endowed with Bregman distances. Under standard martingale-difference noise assumptions in the dual space and mild conditions on the distance-generating function, we establish almost-sure convergence to a fixed point and derive non-asymptotic residual bounds that depend on the uniform convexity modulus of the generating function. Extensions to adaptive Bregman geometries and robust noise models are also discussed. Numerical experiments on entropy-regularized reinforcement learning and m","authors_text":"Ehsan Lotfali Ghasab, Saeed Hashemi Sababe","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-02T05:44:44Z","title":"Stochastic Krasnosel skii-Mann Iterations in Banach Spaces with Bregman Distances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08031","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:edcd635bb1922add99d88c2fdd3f712794af48febf64e4685df57a3fa44d0ce3","target":"record","created_at":"2026-07-05T11:18:43Z","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":"d0b6fce7e386af53609021619dd8a8afb71d4e2ac8a5bed88d220653e45b9f90","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-02T05:44:44Z","title_canon_sha256":"9d3f90de7a73c0ae76588fe0faf269bbd0b0c9a5e8b5d714f845f534b46601f7"},"schema_version":"1.0","source":{"id":"2506.08031","kind":"arxiv","version":1}},"canonical_sha256":"2d59f843aaaa72d638c2adcb963702beb971c0fce45df3fa7f4420c1bec0da50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d59f843aaaa72d638c2adcb963702beb971c0fce45df3fa7f4420c1bec0da50","first_computed_at":"2026-07-05T11:18:43.909977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:43.909977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wnjHtJThSfNPVZkNyyAy9ji9KzDeeCMgLzNJ2z5yz5Ac+0BPMFFDYHE7D3w1BWiRDRdYJGww6USnr56bA/d+CA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:43.910367Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edcd635bb1922add99d88c2fdd3f712794af48febf64e4685df57a3fa44d0ce3","sha256:5f36b49ea561ff5b824e2fb3f2218ed0a3abd06385903525b2f0f8b57751d698"],"state_sha256":"20d684211d33b654e1b9e1cbe07ebc9dddce50d6a8a407284d171d0c9dbca553"}