{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BV46NDWJATF2OHM5YJLJBEBTUJ","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":"46cf8ae74b690c4932214c876cc99916d97cae9b2ad9b7fa0aeba14551cd8519","cross_cats_sorted":["cs.LG","cs.MA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-22T16:03:43Z","title_canon_sha256":"51a9b679a0d0736d2c79b96cd81f1c71dd21581bd1e38cc932e2fa24083d2813"},"schema_version":"1.0","source":{"id":"2607.20316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.20316","created_at":"2026-07-23T01:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.20316v1","created_at":"2026-07-23T01:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20316","created_at":"2026-07-23T01:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"BV46NDWJATF2","created_at":"2026-07-23T01:25:13Z"},{"alias_kind":"pith_short_16","alias_value":"BV46NDWJATF2OHM5","created_at":"2026-07-23T01:25:13Z"},{"alias_kind":"pith_short_8","alias_value":"BV46NDWJ","created_at":"2026-07-23T01:25:13Z"}],"graph_snapshots":[{"event_id":"sha256:0fe4fa2ea703b70b44f506a647d53f6b825ba7924e6a09c7ddee052f45d26b4b","target":"graph","created_at":"2026-07-23T01:25:13Z","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/2607.20316/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study decentralized online optimization for strongly geodesically convex (strongly g-convex) losses on Riemannian manifolds with bounded sectional curvature, including positively curved manifolds. In centralized Riemannian optimization, strong g-convexity tightens the optimal regret from $O(\\sqrt{T})$ to $O(\\log T)$, where $T$ is the time horizon; in the decentralized Riemannian setting, however, existing methods address only g-convex losses, leaving the strongly g-convex regime unexplored. One challenge is that the required decaying step size in the centralized regime is incompatible with ","authors_text":"Emre Sahinoglu, Shahin Shahrampour, Zhanyuan Cai","cross_cats":["cs.LG","cs.MA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-22T16:03:43Z","title":"Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20316","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":"sha256:11299e6ce3baba4474651abbf514c4fe388b1186bcdc46311b726d0e710dc374","target":"record","created_at":"2026-07-23T01:25:13Z","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":"46cf8ae74b690c4932214c876cc99916d97cae9b2ad9b7fa0aeba14551cd8519","cross_cats_sorted":["cs.LG","cs.MA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-22T16:03:43Z","title_canon_sha256":"51a9b679a0d0736d2c79b96cd81f1c71dd21581bd1e38cc932e2fa24083d2813"},"schema_version":"1.0","source":{"id":"2607.20316","kind":"arxiv","version":1}},"canonical_sha256":"0d79e68ec904cba71d9dc256909033a251dc1957336efd421ad6c739fbeeeb97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d79e68ec904cba71d9dc256909033a251dc1957336efd421ad6c739fbeeeb97","first_computed_at":"2026-07-23T01:25:13.973270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-23T01:25:13.973270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iEfVCI/byeHGvCpMa8Gm2eYwKgvq0yGl7+1J86xILuWKqFCnRBAmH5eG+1bIVpMf/WcplandD6OFnzDpJB3LAA==","signature_status":"signed_v1","signed_at":"2026-07-23T01:25:13.974194Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.20316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11299e6ce3baba4474651abbf514c4fe388b1186bcdc46311b726d0e710dc374","sha256:0fe4fa2ea703b70b44f506a647d53f6b825ba7924e6a09c7ddee052f45d26b4b"],"state_sha256":"0367525e7fe7da0a19ad0197c4eee05aace6870aa16f5ac265737cc867318abd"}