{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:X5DQEDGG6RB2MIT2KKLASKZGZM","short_pith_number":"pith:X5DQEDGG","schema_version":"1.0","canonical_sha256":"bf47020cc6f443a6227a5296092b26cb2a3ce36da264471f809b3284ea42cf10","source":{"kind":"arxiv","id":"2505.16970","version":1},"attestation_state":"computed","paper":{"title":"Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DG","math.NA"],"primary_cat":"math.OC","authors_text":"Christopher Criscitiello, Jungbin Kim","submitted_at":"2025-05-22T17:50:10Z","abstract_excerpt":"Geodesic convexity (g-convexity) is a natural generalization of convexity to Riemannian manifolds. However, g-convexity lacks many desirable properties satisfied by Euclidean convexity. For instance, the natural notions of half-spaces and affine functions are themselves not g-convex. Moreover, recent studies have shown that the oracle complexity of geodesically convex optimization necessarily depends on the curvature of the manifold (Criscitiello and Boumal, 2022; Criscitiello and Boumal, 2023; Hamilton and Moitra, 2021), a computational bottleneck for several problems, e.g., tensor scaling. R"},"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":"2505.16970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-05-22T17:50:10Z","cross_cats_sorted":["cs.NA","math.DG","math.NA"],"title_canon_sha256":"c370123cc1f3e2fefbc35036192a1e65ce85a1f908ffdaf1a10295fdb21b1850","abstract_canon_sha256":"bdc06bca7ae2b1ac3ac539eca0efe379d0f10ccb7b845c97ff03957c0b1b6a54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:07:43.875767Z","signature_b64":"B3trcbvoWpWTbIVP/az3cX7bSTFS+TjF73OzFTvVmFg5sATUg5JIKGtb/AQ3ilMOajc4UO9KSsK7xXcJHhp2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf47020cc6f443a6227a5296092b26cb2a3ce36da264471f809b3284ea42cf10","last_reissued_at":"2026-07-05T11:07:43.875251Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:07:43.875251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DG","math.NA"],"primary_cat":"math.OC","authors_text":"Christopher Criscitiello, Jungbin Kim","submitted_at":"2025-05-22T17:50:10Z","abstract_excerpt":"Geodesic convexity (g-convexity) is a natural generalization of convexity to Riemannian manifolds. However, g-convexity lacks many desirable properties satisfied by Euclidean convexity. For instance, the natural notions of half-spaces and affine functions are themselves not g-convex. Moreover, recent studies have shown that the oracle complexity of geodesically convex optimization necessarily depends on the curvature of the manifold (Criscitiello and Boumal, 2022; Criscitiello and Boumal, 2023; Hamilton and Moitra, 2021), a computational bottleneck for several problems, e.g., tensor scaling. R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.16970","kind":"arxiv","version":1},"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/2505.16970/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":"2505.16970","created_at":"2026-07-05T11:07:43.875320+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.16970v1","created_at":"2026-07-05T11:07:43.875320+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.16970","created_at":"2026-07-05T11:07:43.875320+00:00"},{"alias_kind":"pith_short_12","alias_value":"X5DQEDGG6RB2","created_at":"2026-07-05T11:07:43.875320+00:00"},{"alias_kind":"pith_short_16","alias_value":"X5DQEDGG6RB2MIT2","created_at":"2026-07-05T11:07:43.875320+00:00"},{"alias_kind":"pith_short_8","alias_value":"X5DQEDGG","created_at":"2026-07-05T11:07:43.875320+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2603.15488","citing_title":"Minimal enclosing balls via geodesics","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X5DQEDGG6RB2MIT2KKLASKZGZM","json":"https://pith.science/pith/X5DQEDGG6RB2MIT2KKLASKZGZM.json","graph_json":"https://pith.science/api/pith-number/X5DQEDGG6RB2MIT2KKLASKZGZM/graph.json","events_json":"https://pith.science/api/pith-number/X5DQEDGG6RB2MIT2KKLASKZGZM/events.json","paper":"https://pith.science/paper/X5DQEDGG"},"agent_actions":{"view_html":"https://pith.science/pith/X5DQEDGG6RB2MIT2KKLASKZGZM","download_json":"https://pith.science/pith/X5DQEDGG6RB2MIT2KKLASKZGZM.json","view_paper":"https://pith.science/paper/X5DQEDGG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.16970&json=true","fetch_graph":"https://pith.science/api/pith-number/X5DQEDGG6RB2MIT2KKLASKZGZM/graph.json","fetch_events":"https://pith.science/api/pith-number/X5DQEDGG6RB2MIT2KKLASKZGZM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X5DQEDGG6RB2MIT2KKLASKZGZM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X5DQEDGG6RB2MIT2KKLASKZGZM/action/storage_attestation","attest_author":"https://pith.science/pith/X5DQEDGG6RB2MIT2KKLASKZGZM/action/author_attestation","sign_citation":"https://pith.science/pith/X5DQEDGG6RB2MIT2KKLASKZGZM/action/citation_signature","submit_replication":"https://pith.science/pith/X5DQEDGG6RB2MIT2KKLASKZGZM/action/replication_record"}},"created_at":"2026-07-05T11:07:43.875320+00:00","updated_at":"2026-07-05T11:07:43.875320+00:00"}