{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7RTDWQX6XTJ36SUNPNAWFOMREA","short_pith_number":"pith:7RTDWQX6","canonical_record":{"source":{"id":"1509.00319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-09-01T14:39:45Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"77c3ef438f3e407218a43daf5c5dfa3a0d098ba9b0ac772b362a5a41a1beccd6","abstract_canon_sha256":"7d6cf84dda3e2a9d46fcb4690a259153f64fac7707f6c7878fb41e876ab53031"},"schema_version":"1.0"},"canonical_sha256":"fc663b42febcd3bf4a8d7b4162b9912028c5c53afbee4d72c8ec2f035cbb3a94","source":{"kind":"arxiv","id":"1509.00319","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00319","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00319v1","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00319","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"7RTDWQX6XTJ3","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7RTDWQX6XTJ36SUN","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7RTDWQX6","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7RTDWQX6XTJ36SUNPNAWFOMREA","target":"record","payload":{"canonical_record":{"source":{"id":"1509.00319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-09-01T14:39:45Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"77c3ef438f3e407218a43daf5c5dfa3a0d098ba9b0ac772b362a5a41a1beccd6","abstract_canon_sha256":"7d6cf84dda3e2a9d46fcb4690a259153f64fac7707f6c7878fb41e876ab53031"},"schema_version":"1.0"},"canonical_sha256":"fc663b42febcd3bf4a8d7b4162b9912028c5c53afbee4d72c8ec2f035cbb3a94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:14.423186Z","signature_b64":"ZfqIyGc1bJoMmvUEB6Fvda07DoGISMeY2scrmn/cAb5zftmm8+1v+tSohSURik5I82apzL/dPQWyAhoAg9sdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc663b42febcd3bf4a8d7b4162b9912028c5c53afbee4d72c8ec2f035cbb3a94","last_reissued_at":"2026-05-18T01:34:14.422461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:14.422461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.00319","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KNHFIStlbreUs+PwXzUmSU5Q1YXeuNyBxbocfjmcZY9Ti21ngBLCzNfjHV9whGcARSAwg3D49yDTrLLpDIj+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T06:51:25.965089Z"},"content_sha256":"322831dc17e44612bbd42fcd9e8ea309eaa9b9b75fd1b7ca13e1cbadc8e4e617","schema_version":"1.0","event_id":"sha256:322831dc17e44612bbd42fcd9e8ea309eaa9b9b75fd1b7ca13e1cbadc8e4e617"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7RTDWQX6XTJ36SUNPNAWFOMREA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimation of matrices with row sparsity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"A.B. Tsybakov (CREST), Modal'x), O. Klopp (CREST","submitted_at":"2015-09-01T14:39:45Z","abstract_excerpt":"An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of convergence for estimating matrices with row sparsity. A major focus in the present paper is on the derivation of lower bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00319","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z2KbaStpsIY/qgvApXUcb7+ruVFmpctKtbuqDW3ij6LgiSmSkoX9/tjpYgQjX9cnX/hYs+fiGxtY+IQEa+tQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T06:51:25.965727Z"},"content_sha256":"3168c305f11492727a8af3a287b3e22ccc3afaf7b3a127a36145d0e3e9b57899","schema_version":"1.0","event_id":"sha256:3168c305f11492727a8af3a287b3e22ccc3afaf7b3a127a36145d0e3e9b57899"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RTDWQX6XTJ36SUNPNAWFOMREA/bundle.json","state_url":"https://pith.science/pith/7RTDWQX6XTJ36SUNPNAWFOMREA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RTDWQX6XTJ36SUNPNAWFOMREA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T06:51:25Z","links":{"resolver":"https://pith.science/pith/7RTDWQX6XTJ36SUNPNAWFOMREA","bundle":"https://pith.science/pith/7RTDWQX6XTJ36SUNPNAWFOMREA/bundle.json","state":"https://pith.science/pith/7RTDWQX6XTJ36SUNPNAWFOMREA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RTDWQX6XTJ36SUNPNAWFOMREA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7RTDWQX6XTJ36SUNPNAWFOMREA","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":"7d6cf84dda3e2a9d46fcb4690a259153f64fac7707f6c7878fb41e876ab53031","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-09-01T14:39:45Z","title_canon_sha256":"77c3ef438f3e407218a43daf5c5dfa3a0d098ba9b0ac772b362a5a41a1beccd6"},"schema_version":"1.0","source":{"id":"1509.00319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00319","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00319v1","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00319","created_at":"2026-05-18T01:34:14Z"},{"alias_kind":"pith_short_12","alias_value":"7RTDWQX6XTJ3","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7RTDWQX6XTJ36SUN","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7RTDWQX6","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:3168c305f11492727a8af3a287b3e22ccc3afaf7b3a127a36145d0e3e9b57899","target":"graph","created_at":"2026-05-18T01:34:14Z","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":"An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of convergence for estimating matrices with row sparsity. A major focus in the present paper is on the derivation of lower bounds.","authors_text":"A.B. Tsybakov (CREST), Modal'x), O. Klopp (CREST","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-09-01T14:39:45Z","title":"Estimation of matrices with row sparsity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00319","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":"sha256:322831dc17e44612bbd42fcd9e8ea309eaa9b9b75fd1b7ca13e1cbadc8e4e617","target":"record","created_at":"2026-05-18T01:34:14Z","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":"7d6cf84dda3e2a9d46fcb4690a259153f64fac7707f6c7878fb41e876ab53031","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-09-01T14:39:45Z","title_canon_sha256":"77c3ef438f3e407218a43daf5c5dfa3a0d098ba9b0ac772b362a5a41a1beccd6"},"schema_version":"1.0","source":{"id":"1509.00319","kind":"arxiv","version":1}},"canonical_sha256":"fc663b42febcd3bf4a8d7b4162b9912028c5c53afbee4d72c8ec2f035cbb3a94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc663b42febcd3bf4a8d7b4162b9912028c5c53afbee4d72c8ec2f035cbb3a94","first_computed_at":"2026-05-18T01:34:14.422461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:14.422461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZfqIyGc1bJoMmvUEB6Fvda07DoGISMeY2scrmn/cAb5zftmm8+1v+tSohSURik5I82apzL/dPQWyAhoAg9sdAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:14.423186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:322831dc17e44612bbd42fcd9e8ea309eaa9b9b75fd1b7ca13e1cbadc8e4e617","sha256:3168c305f11492727a8af3a287b3e22ccc3afaf7b3a127a36145d0e3e9b57899"],"state_sha256":"739732932f48790edcb50b492795578aacab44cf6d0482e3e3390fba19bce7d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ePeSfr26C/suwhsOp2l4Vf2/VFKJ14FNQx//YAmUpuhjQ0RV7CccLoeA+2IQNYNekVZSLBqqkN/4tiamjzndCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T06:51:25.968815Z","bundle_sha256":"c2f85eacd1e822a3b096575c1e3a5bcf81e4922e9ad487162a2f74d43190a4bb"}}