{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TQO3WWSFNZOONIREWS22GLKHZK","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":"182cdb83d8c0a893a9d92594bfc15ebb8e63eeaf6db0fb37592d9b25ec0246ad","cross_cats_sorted":["cond-mat.stat-mech","cs.IT","math.IT","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-01-03T22:50:47Z","title_canon_sha256":"10237f561b9a853b87973f6073a1bd8fcdd62064630569ebe32fab7193f85a5c"},"schema_version":"1.0","source":{"id":"1701.00858","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00858","created_at":"2026-05-18T00:36:43Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00858v3","created_at":"2026-05-18T00:36:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00858","created_at":"2026-05-18T00:36:43Z"},{"alias_kind":"pith_short_12","alias_value":"TQO3WWSFNZOO","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TQO3WWSFNZOONIRE","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TQO3WWSF","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:22ebe5b0e1f948eb0960da733d5ba44b46f158d72e790964d7389049ee7fb917","target":"graph","created_at":"2026-05-18T00:36:43Z","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":"This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic methods used in data analysis for unsupervised learning of relevant features and other types of dimensionality reduction. We present a framework to study the constrained low-rank matrix estimation for a general prior on the factors, and a general output channel through which the matrix is observed. We draw a paralel with the study of vector-spin glass models","authors_text":"Florent Krzakala, Lenka Zdeborov\\'a, Thibault Lesieur","cross_cats":["cond-mat.stat-mech","cs.IT","math.IT","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-01-03T22:50:47Z","title":"Constrained Low-rank Matrix Estimation: Phase Transitions, Approximate Message Passing and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00858","kind":"arxiv","version":3},"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":"sha256:1f06f7e4c411c2272e82cf267f7c4eea2799e5f66d89a2dd8efdd2e0b2a22a45","target":"record","created_at":"2026-05-18T00:36:43Z","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":"182cdb83d8c0a893a9d92594bfc15ebb8e63eeaf6db0fb37592d9b25ec0246ad","cross_cats_sorted":["cond-mat.stat-mech","cs.IT","math.IT","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-01-03T22:50:47Z","title_canon_sha256":"10237f561b9a853b87973f6073a1bd8fcdd62064630569ebe32fab7193f85a5c"},"schema_version":"1.0","source":{"id":"1701.00858","kind":"arxiv","version":3}},"canonical_sha256":"9c1dbb5a456e5ce6a224b4b5a32d47ca90b652e9d66425eaeae6837712e2608f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c1dbb5a456e5ce6a224b4b5a32d47ca90b652e9d66425eaeae6837712e2608f","first_computed_at":"2026-05-18T00:36:43.619553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:43.619553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K+v/d8mixyA9C0j5Y2EpQ5xg3ULqsjLWaWwz2b9+CUQynkeHE0YoMdFxSE5V38IjDQaJjzg4rXPnK10Xgu72Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:43.620117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00858","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f06f7e4c411c2272e82cf267f7c4eea2799e5f66d89a2dd8efdd2e0b2a22a45","sha256:22ebe5b0e1f948eb0960da733d5ba44b46f158d72e790964d7389049ee7fb917"],"state_sha256":"0bf5393b9ac1fb27aab27f175d4c195adf39de6c41d5114a87aedb76e7f51820"}