{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DRAXUPGLJRKYHTAG5QGIYUPQFI","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":"f87f71c41448420458a54acf7e068c57207474e13c0c3a5b76f40c6aa0ae3adc","cross_cats_sorted":["cs.LG","cs.MA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-09T14:14:46Z","title_canon_sha256":"a39117c9acd9ff0c3a617fd1190caed037f253c224dd67eff2ea5fb438f90057"},"schema_version":"1.0","source":{"id":"2509.07779","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.07779","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"2509.07779v2","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07779","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"DRAXUPGLJRKY","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"pith_short_16","alias_value":"DRAXUPGLJRKYHTAG","created_at":"2026-06-09T01:05:09Z"},{"alias_kind":"pith_short_8","alias_value":"DRAXUPGL","created_at":"2026-06-09T01:05:09Z"}],"graph_snapshots":[{"event_id":"sha256:4174a1d4b12ab4bd1304c9a103d7d07b45e6eb3973a86f40be9aebb4ca80abe8","target":"graph","created_at":"2026-06-09T01:05:09Z","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/2509.07779/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techniques rely on a consensus step that is well understood in Euclidean spaces because of their linearity. However, in positively curved Riemannian spaces, a main technical challenge is that geodesic distances may not induce a globally convex structure. In this work, we first analyze a curvature-aware Riemannian consensus step that enables a linear convergence beyond Hadamard manifolds. Building on this step, we establish","authors_text":"Emre Sahinoglu, Shahin Shahrampour","cross_cats":["cs.LG","cs.MA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-09T14:14:46Z","title":"Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07779","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:dbb43525ca4568bc96d6552ecb82f5ee259f99f67516c42b6c8d72c65d4f8032","target":"record","created_at":"2026-06-09T01:05:09Z","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":"f87f71c41448420458a54acf7e068c57207474e13c0c3a5b76f40c6aa0ae3adc","cross_cats_sorted":["cs.LG","cs.MA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-09T14:14:46Z","title_canon_sha256":"a39117c9acd9ff0c3a617fd1190caed037f253c224dd67eff2ea5fb438f90057"},"schema_version":"1.0","source":{"id":"2509.07779","kind":"arxiv","version":2}},"canonical_sha256":"1c417a3ccb4c5583cc06ec0c8c51f02a1586998ea1226eea14ddd290b71b3f7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c417a3ccb4c5583cc06ec0c8c51f02a1586998ea1226eea14ddd290b71b3f7b","first_computed_at":"2026-06-09T01:05:09.259192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:09.259192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C3+zalIp5yrzSsSPrbbXdyXcELSyhtUpqJySHjja8znwt5gJOKlk6ZpfuhjXpOFsoL0C5CovkFJLA8RBSnzoBQ==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:09.259667Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.07779","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbb43525ca4568bc96d6552ecb82f5ee259f99f67516c42b6c8d72c65d4f8032","sha256:4174a1d4b12ab4bd1304c9a103d7d07b45e6eb3973a86f40be9aebb4ca80abe8"],"state_sha256":"a1691352ddd478349ad7e857edd784fede2f58e8facc9d32a53f71bccd5aa0ca"}