{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SNUGQI5BNL2KWCDXSD3HIIQ7B2","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":"f2c22734046827255be18cd5a1272fb12a99d17466d54435db166ad3aec1d3bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-20T00:18:24Z","title_canon_sha256":"3d50daac99779fb0c6b6897acbf3a44e57ac2825da59b49835c09b7422e0262b"},"schema_version":"1.0","source":{"id":"1808.06274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.06274","created_at":"2026-05-18T00:07:45Z"},{"alias_kind":"arxiv_version","alias_value":"1808.06274v1","created_at":"2026-05-18T00:07:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06274","created_at":"2026-05-18T00:07:45Z"},{"alias_kind":"pith_short_12","alias_value":"SNUGQI5BNL2K","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SNUGQI5BNL2KWCDX","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SNUGQI5B","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:fdd59f8730bcfec1e7f95c58ffdc0f89d8f583d8d8b4a078a5bf0d63a5f43a8e","target":"graph","created_at":"2026-05-18T00:07:45Z","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"},"paper":{"abstract_excerpt":"The subgradient method for convex optimization problems on complete Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. Iteration-complexity bounds of the subgradient method with exogenous step-size and Polyak's step-size are stablished, completing and improving recent results on the subject.","authors_text":"L. F. Prudente, M. S. Louzeiro, O. P. Ferreira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-20T00:18:24Z","title":"Iteration-Complexity of the Subgradient Method on Riemannian Manifolds with Lower Bounded Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06274","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:ff25c774753fb4f8a8430ed6a9c2ef51081dde8bd5a25c70d4f3d70a9437f091","target":"record","created_at":"2026-05-18T00:07:45Z","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":"f2c22734046827255be18cd5a1272fb12a99d17466d54435db166ad3aec1d3bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-20T00:18:24Z","title_canon_sha256":"3d50daac99779fb0c6b6897acbf3a44e57ac2825da59b49835c09b7422e0262b"},"schema_version":"1.0","source":{"id":"1808.06274","kind":"arxiv","version":1}},"canonical_sha256":"93686823a16af4ab087790f674221f0e91588f861a3b399d10fdfc9fc47d47c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93686823a16af4ab087790f674221f0e91588f861a3b399d10fdfc9fc47d47c2","first_computed_at":"2026-05-18T00:07:45.496424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:45.496424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gHOtDAJYoL8XBTwruL8ZEj4zbq4K1+9xjRZiD+HWcWcK/xlVMl3iY+3PQlbIvVyEFImypNtIVK4iqX3gxdESAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:45.497031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.06274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff25c774753fb4f8a8430ed6a9c2ef51081dde8bd5a25c70d4f3d70a9437f091","sha256:fdd59f8730bcfec1e7f95c58ffdc0f89d8f583d8d8b4a078a5bf0d63a5f43a8e"],"state_sha256":"0beb8ecebe1e3df6a5007939985297fc7d9d48b2ea891c8ed3d4e38235b97d33"}