{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GEULRN5UPEQ7EV3LHEMUQZSNB5","short_pith_number":"pith:GEULRN5U","canonical_record":{"source":{"id":"1906.08922","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-21T02:32:21Z","cross_cats_sorted":[],"title_canon_sha256":"e863a12a6107a36bad5aefcc925de219dc466e750c3f4feca9281f7d22194a77","abstract_canon_sha256":"c42b8ad9707df0e7361ed6dd400df73130446e9fcd81243a2c943ac327b43ad1"},"schema_version":"1.0"},"canonical_sha256":"3128b8b7b47921f2576b391948664d0f5f305300c170fd4a4b55dd37825bcb41","source":{"kind":"arxiv","id":"1906.08922","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.08922","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1906.08922v2","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08922","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"GEULRN5UPEQ7","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GEULRN5UPEQ7EV3L","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GEULRN5U","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GEULRN5UPEQ7EV3LHEMUQZSNB5","target":"record","payload":{"canonical_record":{"source":{"id":"1906.08922","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-21T02:32:21Z","cross_cats_sorted":[],"title_canon_sha256":"e863a12a6107a36bad5aefcc925de219dc466e750c3f4feca9281f7d22194a77","abstract_canon_sha256":"c42b8ad9707df0e7361ed6dd400df73130446e9fcd81243a2c943ac327b43ad1"},"schema_version":"1.0"},"canonical_sha256":"3128b8b7b47921f2576b391948664d0f5f305300c170fd4a4b55dd37825bcb41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:13.312194Z","signature_b64":"PiIlM+4vG4pejsPpdvdBjxKTD5L/kd4MavE0K9WO1quAt+1ASfyCdUoi1dKksNd6sBmdAhIvROKCZB/vkrXiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3128b8b7b47921f2576b391948664d0f5f305300c170fd4a4b55dd37825bcb41","last_reissued_at":"2026-05-17T23:42:13.311493Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:13.311493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.08922","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HKoMK8Sld4Ef34E7SQJZpZ0vu2pThO06OTO0UPwS2aKNwpn4ZSbCavqXT65gZFXsLa78fXwUJeKGQgF7u+l7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:36:37.178191Z"},"content_sha256":"8ebe870cd4c07793a8eb8f9c7bd0514e8985bb0ad68bce135710ab2dbfd5d0d5","schema_version":"1.0","event_id":"sha256:8ebe870cd4c07793a8eb8f9c7bd0514e8985bb0ad68bce135710ab2dbfd5d0d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GEULRN5UPEQ7EV3LHEMUQZSNB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Several classes of stationary points for rank regularized minimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Shaohua Pan, Yulan Liu","submitted_at":"2019-06-21T02:32:21Z","abstract_excerpt":"For the rank regularized minimization problem, we introduce several kinds of stationary points by the problem itself and its equivalent reformulations including the mathematical program with an equilibrium constraint (MPEC), the global exact penalty of the MPEC,the surrogate yielded by eliminating the dual part in the exact penalty. A clear relation chart is established for these stationary points, which guides the user to choose an appropriate reformulation for seeking a low-rank solution. As a byproduct, we also provide a weaker condition for a local minimizer of the MPEC to be the M-station"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08922","kind":"arxiv","version":2},"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":"2026-05-17T23:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tq6hPRuCQroj3G2Tex++OkZX3i7BArYdc1BQ6BNIDhATCSb4hJ9BVxAuxK/ePPf2CZE8v5UGdngHXgvjDZdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:36:37.178932Z"},"content_sha256":"183ad01543184353ba54d9da74cb2f8aab0f457dc3a30f15dd9f9dbfd1d9e32b","schema_version":"1.0","event_id":"sha256:183ad01543184353ba54d9da74cb2f8aab0f457dc3a30f15dd9f9dbfd1d9e32b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GEULRN5UPEQ7EV3LHEMUQZSNB5/bundle.json","state_url":"https://pith.science/pith/GEULRN5UPEQ7EV3LHEMUQZSNB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GEULRN5UPEQ7EV3LHEMUQZSNB5/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":"2026-05-26T16:36:37Z","links":{"resolver":"https://pith.science/pith/GEULRN5UPEQ7EV3LHEMUQZSNB5","bundle":"https://pith.science/pith/GEULRN5UPEQ7EV3LHEMUQZSNB5/bundle.json","state":"https://pith.science/pith/GEULRN5UPEQ7EV3LHEMUQZSNB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GEULRN5UPEQ7EV3LHEMUQZSNB5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GEULRN5UPEQ7EV3LHEMUQZSNB5","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":"c42b8ad9707df0e7361ed6dd400df73130446e9fcd81243a2c943ac327b43ad1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-21T02:32:21Z","title_canon_sha256":"e863a12a6107a36bad5aefcc925de219dc466e750c3f4feca9281f7d22194a77"},"schema_version":"1.0","source":{"id":"1906.08922","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.08922","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1906.08922v2","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08922","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"GEULRN5UPEQ7","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GEULRN5UPEQ7EV3L","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GEULRN5U","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:183ad01543184353ba54d9da74cb2f8aab0f457dc3a30f15dd9f9dbfd1d9e32b","target":"graph","created_at":"2026-05-17T23:42:13Z","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":"For the rank regularized minimization problem, we introduce several kinds of stationary points by the problem itself and its equivalent reformulations including the mathematical program with an equilibrium constraint (MPEC), the global exact penalty of the MPEC,the surrogate yielded by eliminating the dual part in the exact penalty. A clear relation chart is established for these stationary points, which guides the user to choose an appropriate reformulation for seeking a low-rank solution. As a byproduct, we also provide a weaker condition for a local minimizer of the MPEC to be the M-station","authors_text":"Shaohua Pan, Yulan Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-21T02:32:21Z","title":"Several classes of stationary points for rank regularized minimization problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08922","kind":"arxiv","version":2},"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":"sha256:8ebe870cd4c07793a8eb8f9c7bd0514e8985bb0ad68bce135710ab2dbfd5d0d5","target":"record","created_at":"2026-05-17T23:42:13Z","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":"c42b8ad9707df0e7361ed6dd400df73130446e9fcd81243a2c943ac327b43ad1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-21T02:32:21Z","title_canon_sha256":"e863a12a6107a36bad5aefcc925de219dc466e750c3f4feca9281f7d22194a77"},"schema_version":"1.0","source":{"id":"1906.08922","kind":"arxiv","version":2}},"canonical_sha256":"3128b8b7b47921f2576b391948664d0f5f305300c170fd4a4b55dd37825bcb41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3128b8b7b47921f2576b391948664d0f5f305300c170fd4a4b55dd37825bcb41","first_computed_at":"2026-05-17T23:42:13.311493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:13.311493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PiIlM+4vG4pejsPpdvdBjxKTD5L/kd4MavE0K9WO1quAt+1ASfyCdUoi1dKksNd6sBmdAhIvROKCZB/vkrXiAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:13.312194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.08922","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ebe870cd4c07793a8eb8f9c7bd0514e8985bb0ad68bce135710ab2dbfd5d0d5","sha256:183ad01543184353ba54d9da74cb2f8aab0f457dc3a30f15dd9f9dbfd1d9e32b"],"state_sha256":"4a80eacc1b191931b73677d0b520f324dd95b46dc2c4f5a0ec74b48fa81c81bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFz/9Sz8CmmN3TBSrB/qfGL29nvvqUN+lDw3v6d8wh5R1nL4OhhZMXb2SaA369Mli/3KbmvhoQ3NrTRxMtdACA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:36:37.182962Z","bundle_sha256":"d1c9d66ea273a8e0010dabb25d503bce3ff5b650cfcfed9409d846c72ee5087f"}}