{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:TCCN5OV6DSAFA3CRMTCKYZIKW2","short_pith_number":"pith:TCCN5OV6","schema_version":"1.0","canonical_sha256":"9884debabe1c80506c5164c4ac650ab6b0cf556c3316857c4d74b0ab0c14efcc","source":{"kind":"arxiv","id":"2503.24075","version":4},"attestation_state":"computed","paper":{"title":"Optimization on the Oblique Manifold for Sparse Simplex Constraints via Multiplicative Updates","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Andersen Ang, Flavia Esposito","submitted_at":"2025-03-31T13:31:05Z","abstract_excerpt":"Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank structures and constraints. These problems arise in various applications, including machine learning, signal processing, environmental fields, and computational biology. In this work, we propose a novel manifold optimization approach to efficiently tackle these problems. Our method leverages the geometry of oblique manifolds to reformulate the problem and intr"},"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":"2503.24075","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-03-31T13:31:05Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"ec0c4445d5150e6ac98d155b3893d191f0c7361d73d816c90059c683e7ca1c45","abstract_canon_sha256":"a9904e28546d4b26cf71a7bf3aeab8dc73ef87d7fb6fd86c93b0d243ac3bb5ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T00:18:10.063682Z","signature_b64":"qoDA3cndmLIx4ZSLE20vqqNCa0e5HrW3WYR8lcTdLMLvCdgZi8BST8gYo6LwQNpm1Z71Btdx9ECo+dEs7LeiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9884debabe1c80506c5164c4ac650ab6b0cf556c3316857c4d74b0ab0c14efcc","last_reissued_at":"2026-07-02T00:18:10.062950Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T00:18:10.062950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimization on the Oblique Manifold for Sparse Simplex Constraints via Multiplicative Updates","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Andersen Ang, Flavia Esposito","submitted_at":"2025-03-31T13:31:05Z","abstract_excerpt":"Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank structures and constraints. These problems arise in various applications, including machine learning, signal processing, environmental fields, and computational biology. In this work, we propose a novel manifold optimization approach to efficiently tackle these problems. Our method leverages the geometry of oblique manifolds to reformulate the problem and intr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.24075","kind":"arxiv","version":4},"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/2503.24075/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":"2503.24075","created_at":"2026-07-02T00:18:10.063042+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.24075v4","created_at":"2026-07-02T00:18:10.063042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.24075","created_at":"2026-07-02T00:18:10.063042+00:00"},{"alias_kind":"pith_short_12","alias_value":"TCCN5OV6DSAF","created_at":"2026-07-02T00:18:10.063042+00:00"},{"alias_kind":"pith_short_16","alias_value":"TCCN5OV6DSAFA3CR","created_at":"2026-07-02T00:18:10.063042+00:00"},{"alias_kind":"pith_short_8","alias_value":"TCCN5OV6","created_at":"2026-07-02T00:18:10.063042+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/TCCN5OV6DSAFA3CRMTCKYZIKW2","json":"https://pith.science/pith/TCCN5OV6DSAFA3CRMTCKYZIKW2.json","graph_json":"https://pith.science/api/pith-number/TCCN5OV6DSAFA3CRMTCKYZIKW2/graph.json","events_json":"https://pith.science/api/pith-number/TCCN5OV6DSAFA3CRMTCKYZIKW2/events.json","paper":"https://pith.science/paper/TCCN5OV6"},"agent_actions":{"view_html":"https://pith.science/pith/TCCN5OV6DSAFA3CRMTCKYZIKW2","download_json":"https://pith.science/pith/TCCN5OV6DSAFA3CRMTCKYZIKW2.json","view_paper":"https://pith.science/paper/TCCN5OV6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.24075&json=true","fetch_graph":"https://pith.science/api/pith-number/TCCN5OV6DSAFA3CRMTCKYZIKW2/graph.json","fetch_events":"https://pith.science/api/pith-number/TCCN5OV6DSAFA3CRMTCKYZIKW2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TCCN5OV6DSAFA3CRMTCKYZIKW2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TCCN5OV6DSAFA3CRMTCKYZIKW2/action/storage_attestation","attest_author":"https://pith.science/pith/TCCN5OV6DSAFA3CRMTCKYZIKW2/action/author_attestation","sign_citation":"https://pith.science/pith/TCCN5OV6DSAFA3CRMTCKYZIKW2/action/citation_signature","submit_replication":"https://pith.science/pith/TCCN5OV6DSAFA3CRMTCKYZIKW2/action/replication_record"}},"created_at":"2026-07-02T00:18:10.063042+00:00","updated_at":"2026-07-02T00:18:10.063042+00:00"}