{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WJCEH6VMUITHQVCCR7ED7NRV6I","short_pith_number":"pith:WJCEH6VM","canonical_record":{"source":{"id":"1804.11029","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-30T02:38:51Z","cross_cats_sorted":[],"title_canon_sha256":"f58e2b581682cab44556b659754c8a195dc9f87b29352181ec5e8caf3411d33d","abstract_canon_sha256":"81d40a42d2217f93fefe6e5c64b153bbfd0ae04765aee8834e910a700915f7e0"},"schema_version":"1.0"},"canonical_sha256":"b24443faaca2267854428fc83fb635f203621d0bcadf694a69e19903849e46cb","source":{"kind":"arxiv","id":"1804.11029","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.11029","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"arxiv_version","alias_value":"1804.11029v3","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.11029","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"pith_short_12","alias_value":"WJCEH6VMUITH","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WJCEH6VMUITHQVCC","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WJCEH6VM","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WJCEH6VMUITHQVCCR7ED7NRV6I","target":"record","payload":{"canonical_record":{"source":{"id":"1804.11029","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-30T02:38:51Z","cross_cats_sorted":[],"title_canon_sha256":"f58e2b581682cab44556b659754c8a195dc9f87b29352181ec5e8caf3411d33d","abstract_canon_sha256":"81d40a42d2217f93fefe6e5c64b153bbfd0ae04765aee8834e910a700915f7e0"},"schema_version":"1.0"},"canonical_sha256":"b24443faaca2267854428fc83fb635f203621d0bcadf694a69e19903849e46cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:08.590730Z","signature_b64":"XQu4+8M4bolllVF7EVz+O3bJ5kcWPW4bEF46VG7Z33pg894fXLVXl0DC9x3LzqPOgJYzdmrwYIS3xUPK+ZoLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b24443faaca2267854428fc83fb635f203621d0bcadf694a69e19903849e46cb","last_reissued_at":"2026-05-18T00:00:08.590304Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:08.590304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.11029","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fgnx+VCZia63lzlJTrmVjbSbvioAPr5i0yfV52sBAFB18YLk/krOsqQIexEW6Cvufkt/7YUDSgdJsECoYTS9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:00:00.803355Z"},"content_sha256":"c77fc0c593e376aa57511b8db377faf7981f8bec4bfdf7dd4290bd7b0d40a419","schema_version":"1.0","event_id":"sha256:c77fc0c593e376aa57511b8db377faf7981f8bec4bfdf7dd4290bd7b0d40a419"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WJCEH6VMUITHQVCCR7ED7NRV6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Nonconvex Strategy to Affine Matrix Rank Minimization Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Angang Cui, Haiyang Li, Jigen Peng, Junxiong Jia, Meng Wen","submitted_at":"2018-04-30T02:38:51Z","abstract_excerpt":"The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important areas such as control, recommender systems, matrix completion and network localization. However, the problem (AMRM) is NP-hard in general due to the combinational nature of the matrix rank function. There are many alternative functions have been proposed to substitute the matrix rank function, which lead to many corresponding alternative minimization problems solved efficiently by some popular convex or nonconvex opti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11029","kind":"arxiv","version":3},"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":"2026-05-18T00:00:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j2hLFCGpyRLYFMhNHaeiFh3OewnEXJTylqiOVlniAvm9bNeazk0++aFR/qNA+w/QPyc4CQoN5T02Wm+mDuiCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:00:00.803692Z"},"content_sha256":"f7806c30a630f85c3a34b874d3c190a2c01ae84c315a5f11943a55a79c9e3f52","schema_version":"1.0","event_id":"sha256:f7806c30a630f85c3a34b874d3c190a2c01ae84c315a5f11943a55a79c9e3f52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJCEH6VMUITHQVCCR7ED7NRV6I/bundle.json","state_url":"https://pith.science/pith/WJCEH6VMUITHQVCCR7ED7NRV6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJCEH6VMUITHQVCCR7ED7NRV6I/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":"2026-06-03T18:00:00Z","links":{"resolver":"https://pith.science/pith/WJCEH6VMUITHQVCCR7ED7NRV6I","bundle":"https://pith.science/pith/WJCEH6VMUITHQVCCR7ED7NRV6I/bundle.json","state":"https://pith.science/pith/WJCEH6VMUITHQVCCR7ED7NRV6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJCEH6VMUITHQVCCR7ED7NRV6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WJCEH6VMUITHQVCCR7ED7NRV6I","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":"81d40a42d2217f93fefe6e5c64b153bbfd0ae04765aee8834e910a700915f7e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-30T02:38:51Z","title_canon_sha256":"f58e2b581682cab44556b659754c8a195dc9f87b29352181ec5e8caf3411d33d"},"schema_version":"1.0","source":{"id":"1804.11029","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.11029","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"arxiv_version","alias_value":"1804.11029v3","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.11029","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"pith_short_12","alias_value":"WJCEH6VMUITH","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WJCEH6VMUITHQVCC","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WJCEH6VM","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:f7806c30a630f85c3a34b874d3c190a2c01ae84c315a5f11943a55a79c9e3f52","target":"graph","created_at":"2026-05-18T00:00:08Z","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":"The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important areas such as control, recommender systems, matrix completion and network localization. However, the problem (AMRM) is NP-hard in general due to the combinational nature of the matrix rank function. There are many alternative functions have been proposed to substitute the matrix rank function, which lead to many corresponding alternative minimization problems solved efficiently by some popular convex or nonconvex opti","authors_text":"Angang Cui, Haiyang Li, Jigen Peng, Junxiong Jia, Meng Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-30T02:38:51Z","title":"A New Nonconvex Strategy to Affine Matrix Rank Minimization Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11029","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:c77fc0c593e376aa57511b8db377faf7981f8bec4bfdf7dd4290bd7b0d40a419","target":"record","created_at":"2026-05-18T00:00:08Z","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":"81d40a42d2217f93fefe6e5c64b153bbfd0ae04765aee8834e910a700915f7e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-30T02:38:51Z","title_canon_sha256":"f58e2b581682cab44556b659754c8a195dc9f87b29352181ec5e8caf3411d33d"},"schema_version":"1.0","source":{"id":"1804.11029","kind":"arxiv","version":3}},"canonical_sha256":"b24443faaca2267854428fc83fb635f203621d0bcadf694a69e19903849e46cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b24443faaca2267854428fc83fb635f203621d0bcadf694a69e19903849e46cb","first_computed_at":"2026-05-18T00:00:08.590304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:08.590304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XQu4+8M4bolllVF7EVz+O3bJ5kcWPW4bEF46VG7Z33pg894fXLVXl0DC9x3LzqPOgJYzdmrwYIS3xUPK+ZoLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:08.590730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.11029","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c77fc0c593e376aa57511b8db377faf7981f8bec4bfdf7dd4290bd7b0d40a419","sha256:f7806c30a630f85c3a34b874d3c190a2c01ae84c315a5f11943a55a79c9e3f52"],"state_sha256":"873e85e7255f1add1ee3f5ca036da5ab4abdf1b4960cb6b3790cf7cc984bb750"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+iuk9RwFYRNKD+dp8Oo+o/pM6yZYFkJmcnkIr24BQUqS87+N2MkvscoOU3rdVPP8naUYGMxlGpRCjqiReyuXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:00:00.808184Z","bundle_sha256":"f54d6ca85f8793e3e5cbe6df04262c5374ccb2c0290353e3f97f1c2b56ee09cb"}}