{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DRAXUPGLJRKYHTAG5QGIYUPQFI","short_pith_number":"pith:DRAXUPGL","schema_version":"1.0","canonical_sha256":"1c417a3ccb4c5583cc06ec0c8c51f02a1586998ea1226eea14ddd290b71b3f7b","source":{"kind":"arxiv","id":"2509.07779","version":2},"attestation_state":"computed","paper":{"title":"Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.MA"],"primary_cat":"math.OC","authors_text":"Emre Sahinoglu, Shahin Shahrampour","submitted_at":"2025-09-09T14:14:46Z","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"},"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":"2509.07779","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-09T14:14:46Z","cross_cats_sorted":["cs.LG","cs.MA"],"title_canon_sha256":"a39117c9acd9ff0c3a617fd1190caed037f253c224dd67eff2ea5fb438f90057","abstract_canon_sha256":"f87f71c41448420458a54acf7e068c57207474e13c0c3a5b76f40c6aa0ae3adc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:09.259667Z","signature_b64":"C3+zalIp5yrzSsSPrbbXdyXcELSyhtUpqJySHjja8znwt5gJOKlk6ZpfuhjXpOFsoL0C5CovkFJLA8RBSnzoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c417a3ccb4c5583cc06ec0c8c51f02a1586998ea1226eea14ddd290b71b3f7b","last_reissued_at":"2026-06-09T01:05:09.259192Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:09.259192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.MA"],"primary_cat":"math.OC","authors_text":"Emre Sahinoglu, Shahin Shahrampour","submitted_at":"2025-09-09T14:14:46Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07779","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/2509.07779/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":"2509.07779","created_at":"2026-06-09T01:05:09.259243+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.07779v2","created_at":"2026-06-09T01:05:09.259243+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07779","created_at":"2026-06-09T01:05:09.259243+00:00"},{"alias_kind":"pith_short_12","alias_value":"DRAXUPGLJRKY","created_at":"2026-06-09T01:05:09.259243+00:00"},{"alias_kind":"pith_short_16","alias_value":"DRAXUPGLJRKYHTAG","created_at":"2026-06-09T01:05:09.259243+00:00"},{"alias_kind":"pith_short_8","alias_value":"DRAXUPGL","created_at":"2026-06-09T01:05:09.259243+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/DRAXUPGLJRKYHTAG5QGIYUPQFI","json":"https://pith.science/pith/DRAXUPGLJRKYHTAG5QGIYUPQFI.json","graph_json":"https://pith.science/api/pith-number/DRAXUPGLJRKYHTAG5QGIYUPQFI/graph.json","events_json":"https://pith.science/api/pith-number/DRAXUPGLJRKYHTAG5QGIYUPQFI/events.json","paper":"https://pith.science/paper/DRAXUPGL"},"agent_actions":{"view_html":"https://pith.science/pith/DRAXUPGLJRKYHTAG5QGIYUPQFI","download_json":"https://pith.science/pith/DRAXUPGLJRKYHTAG5QGIYUPQFI.json","view_paper":"https://pith.science/paper/DRAXUPGL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.07779&json=true","fetch_graph":"https://pith.science/api/pith-number/DRAXUPGLJRKYHTAG5QGIYUPQFI/graph.json","fetch_events":"https://pith.science/api/pith-number/DRAXUPGLJRKYHTAG5QGIYUPQFI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DRAXUPGLJRKYHTAG5QGIYUPQFI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DRAXUPGLJRKYHTAG5QGIYUPQFI/action/storage_attestation","attest_author":"https://pith.science/pith/DRAXUPGLJRKYHTAG5QGIYUPQFI/action/author_attestation","sign_citation":"https://pith.science/pith/DRAXUPGLJRKYHTAG5QGIYUPQFI/action/citation_signature","submit_replication":"https://pith.science/pith/DRAXUPGLJRKYHTAG5QGIYUPQFI/action/replication_record"}},"created_at":"2026-06-09T01:05:09.259243+00:00","updated_at":"2026-06-09T01:05:09.259243+00:00"}