{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:35KOWJAGBGXT6EIFSBGUXB7LVL","short_pith_number":"pith:35KOWJAG","canonical_record":{"source":{"id":"1102.3947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-19T01:31:05Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"70084f9792e2e0ff83107615e1bfd1de762668a7c79ef19ef81270a8fd7eb949","abstract_canon_sha256":"90c7d6200e1ce1d7a12c55e4cdd9595d91ef9de56fcb2e6c5954ea6741b4b4de"},"schema_version":"1.0"},"canonical_sha256":"df54eb240609af3f1105904d4b87ebaafcefaab4632f518bbacd0953ee7db7c2","source":{"kind":"arxiv","id":"1102.3947","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3947","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3947v1","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3947","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"pith_short_12","alias_value":"35KOWJAGBGXT","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"35KOWJAGBGXT6EIF","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"35KOWJAG","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:35KOWJAGBGXT6EIFSBGUXB7LVL","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-19T01:31:05Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"70084f9792e2e0ff83107615e1bfd1de762668a7c79ef19ef81270a8fd7eb949","abstract_canon_sha256":"90c7d6200e1ce1d7a12c55e4cdd9595d91ef9de56fcb2e6c5954ea6741b4b4de"},"schema_version":"1.0"},"canonical_sha256":"df54eb240609af3f1105904d4b87ebaafcefaab4632f518bbacd0953ee7db7c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:19.479915Z","signature_b64":"m6gLfkzg4YqfMkcLfHlyIsrZQX4wUc0zzs8vvOWJhJcyfxPto+ImllZT9EUy8LsTRVslmueQSJZh9tPLN1nUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df54eb240609af3f1105904d4b87ebaafcefaab4632f518bbacd0953ee7db7c2","last_reissued_at":"2026-05-18T04:28:19.479498Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:19.479498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3947","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":"2026-05-18T04:28:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YCi/Eyq3knrNwhYAaykcnz9J3HWdwDSAH+x33E8TpZOVBgHOOPqLavk9/Fm9Uohf4CgkiK+oG6pw0mVPEenNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T01:19:05.485448Z"},"content_sha256":"bffb8b86950f055df666df991d4080f58c5a56a6a760da9463e0ec286a380951","schema_version":"1.0","event_id":"sha256:bffb8b86950f055df666df991d4080f58c5a56a6a760da9463e0ec286a380951"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:35KOWJAGBGXT6EIFSBGUXB7LVL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subspace Expanders and Matrix Rank Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amin Khajehnejad, Babak Hassibi, Samet Oymak","submitted_at":"2011-02-19T01:31:05Z","abstract_excerpt":"Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that satisfies a set of linear constraints. The existing algorithms include nuclear norm minimization (NNM) and singular value thresholding. Thus far, most of the attention has been on i.i.d. Gaussian measurement operators. In this work, we introduce a new class of measurement operators, and a novel recovery algorithm, which is notably faster than NNM. The proposed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3947","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":"2026-05-18T04:28:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cA+hgf4aeAk5VinnWdWSswstWELyLxTHh9lzxsS85I6bTRw2w6Ye/CaNxti88lxAWTFXZjlfG5uK2HeJxTXGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T01:19:05.485792Z"},"content_sha256":"b259e22a0ec4c4af8b353a2d90ac0d3977550ef1f1717ff4617e8e28c4640ed7","schema_version":"1.0","event_id":"sha256:b259e22a0ec4c4af8b353a2d90ac0d3977550ef1f1717ff4617e8e28c4640ed7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/35KOWJAGBGXT6EIFSBGUXB7LVL/bundle.json","state_url":"https://pith.science/pith/35KOWJAGBGXT6EIFSBGUXB7LVL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/35KOWJAGBGXT6EIFSBGUXB7LVL/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":"2026-06-06T01:19:05Z","links":{"resolver":"https://pith.science/pith/35KOWJAGBGXT6EIFSBGUXB7LVL","bundle":"https://pith.science/pith/35KOWJAGBGXT6EIFSBGUXB7LVL/bundle.json","state":"https://pith.science/pith/35KOWJAGBGXT6EIFSBGUXB7LVL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/35KOWJAGBGXT6EIFSBGUXB7LVL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:35KOWJAGBGXT6EIFSBGUXB7LVL","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":"90c7d6200e1ce1d7a12c55e4cdd9595d91ef9de56fcb2e6c5954ea6741b4b4de","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-19T01:31:05Z","title_canon_sha256":"70084f9792e2e0ff83107615e1bfd1de762668a7c79ef19ef81270a8fd7eb949"},"schema_version":"1.0","source":{"id":"1102.3947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3947","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3947v1","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3947","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"pith_short_12","alias_value":"35KOWJAGBGXT","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"35KOWJAGBGXT6EIF","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"35KOWJAG","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:b259e22a0ec4c4af8b353a2d90ac0d3977550ef1f1717ff4617e8e28c4640ed7","target":"graph","created_at":"2026-05-18T04:28:19Z","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":"Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that satisfies a set of linear constraints. The existing algorithms include nuclear norm minimization (NNM) and singular value thresholding. Thus far, most of the attention has been on i.i.d. Gaussian measurement operators. In this work, we introduce a new class of measurement operators, and a novel recovery algorithm, which is notably faster than NNM. The proposed","authors_text":"Amin Khajehnejad, Babak Hassibi, Samet Oymak","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-19T01:31:05Z","title":"Subspace Expanders and Matrix Rank Minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3947","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:bffb8b86950f055df666df991d4080f58c5a56a6a760da9463e0ec286a380951","target":"record","created_at":"2026-05-18T04:28:19Z","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":"90c7d6200e1ce1d7a12c55e4cdd9595d91ef9de56fcb2e6c5954ea6741b4b4de","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-19T01:31:05Z","title_canon_sha256":"70084f9792e2e0ff83107615e1bfd1de762668a7c79ef19ef81270a8fd7eb949"},"schema_version":"1.0","source":{"id":"1102.3947","kind":"arxiv","version":1}},"canonical_sha256":"df54eb240609af3f1105904d4b87ebaafcefaab4632f518bbacd0953ee7db7c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df54eb240609af3f1105904d4b87ebaafcefaab4632f518bbacd0953ee7db7c2","first_computed_at":"2026-05-18T04:28:19.479498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:19.479498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m6gLfkzg4YqfMkcLfHlyIsrZQX4wUc0zzs8vvOWJhJcyfxPto+ImllZT9EUy8LsTRVslmueQSJZh9tPLN1nUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:19.479915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bffb8b86950f055df666df991d4080f58c5a56a6a760da9463e0ec286a380951","sha256:b259e22a0ec4c4af8b353a2d90ac0d3977550ef1f1717ff4617e8e28c4640ed7"],"state_sha256":"ff758daa1e816360605b5336c1559771309952b75491785cb6edc5da1623fad5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RE8g3Ha6XehlXO6HJaQI5NPh3HkhGrNqf2LfF8pI9iAIxp55xajyRPHL1yqKMKepmcKl2CApmi7A8H80IlI/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T01:19:05.487742Z","bundle_sha256":"8068a845aaaf98f4770f8730b75ddf12ff01a1579a257e8567f63ba2498714ad"}}