{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SWWLLM4ATAYF5737EXXW67PSH6","short_pith_number":"pith:SWWLLM4A","canonical_record":{"source":{"id":"1410.6913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-25T11:24:50Z","cross_cats_sorted":["math.IT","math.PR","quant-ph"],"title_canon_sha256":"f3477d41be7ea7cf6af23aa15d0b19458caded4d7b1112e69f615fecb1acc8f6","abstract_canon_sha256":"683e044dfff4b5d833acc7f65272faa0e5a286475d2632e8e94116c89bdc4af5"},"schema_version":"1.0"},"canonical_sha256":"95acb5b38098305eff7f25ef6f7df23f89331376568270f50e30a80969640121","source":{"kind":"arxiv","id":"1410.6913","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6913","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6913v1","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6913","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"SWWLLM4ATAYF","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SWWLLM4ATAYF5737","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SWWLLM4A","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SWWLLM4ATAYF5737EXXW67PSH6","target":"record","payload":{"canonical_record":{"source":{"id":"1410.6913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-25T11:24:50Z","cross_cats_sorted":["math.IT","math.PR","quant-ph"],"title_canon_sha256":"f3477d41be7ea7cf6af23aa15d0b19458caded4d7b1112e69f615fecb1acc8f6","abstract_canon_sha256":"683e044dfff4b5d833acc7f65272faa0e5a286475d2632e8e94116c89bdc4af5"},"schema_version":"1.0"},"canonical_sha256":"95acb5b38098305eff7f25ef6f7df23f89331376568270f50e30a80969640121","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:18.337865Z","signature_b64":"Ee3FCRmVcsJByDecAzrGbXXX73OdC+pnUrYA7ozHL60Hh8uT8nnq2aFeyPF+bSCliz0GAEA1Vt5p8tPkGOGtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95acb5b38098305eff7f25ef6f7df23f89331376568270f50e30a80969640121","last_reissued_at":"2026-05-18T02:39:18.337362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:18.337362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.6913","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":"2026-05-18T02:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"znidvuaDWAYfcHFOT9tBiOyDdGbvZ/suayq+7NaQIzODeSIeyABMviR0TyAjmzkG8X1HNysm+DVKPI8rWRQsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:02:48.995588Z"},"content_sha256":"400708a922c781cf4248ec473781ebe5f5aa4586f04d62533b1357f4936d0305","schema_version":"1.0","event_id":"sha256:400708a922c781cf4248ec473781ebe5f5aa4586f04d62533b1357f4936d0305"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SWWLLM4ATAYF5737EXXW67PSH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low rank matrix recovery from rank one measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR","quant-ph"],"primary_cat":"cs.IT","authors_text":"Holger Rauhut, Richard Kueng, Ulrich Terstiege","submitted_at":"2014-10-25T11:24:50Z","abstract_excerpt":"We study the recovery of Hermitian low rank matrices $X \\in \\mathbb{C}^{n \\times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j a_j^*$ for some measurement vectors $a_1,...,a_m$, i.e., the measurements are given by $y_j = \\mathrm{tr}(X a_j a_j^*)$. The case where the matrix $X=x x^*$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements, $y_j = |\\langle x,a_j\\rangle|^2$ via the PhaseLift approach, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6913","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":"2026-05-18T02:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bziMnsCa9EhExgHEMKAigZGyRvj8cuQPesT3JphwSZC32h/Lm/lnrp86hwcon4pdu9K8yqa/fnMVdgxwSGmqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:02:48.996229Z"},"content_sha256":"bbf7f0c9e080c6f60a4d208ebf09e6ba04a60a40377ffc51abec392ddc578f97","schema_version":"1.0","event_id":"sha256:bbf7f0c9e080c6f60a4d208ebf09e6ba04a60a40377ffc51abec392ddc578f97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SWWLLM4ATAYF5737EXXW67PSH6/bundle.json","state_url":"https://pith.science/pith/SWWLLM4ATAYF5737EXXW67PSH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SWWLLM4ATAYF5737EXXW67PSH6/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":"2026-06-09T02:02:48Z","links":{"resolver":"https://pith.science/pith/SWWLLM4ATAYF5737EXXW67PSH6","bundle":"https://pith.science/pith/SWWLLM4ATAYF5737EXXW67PSH6/bundle.json","state":"https://pith.science/pith/SWWLLM4ATAYF5737EXXW67PSH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SWWLLM4ATAYF5737EXXW67PSH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SWWLLM4ATAYF5737EXXW67PSH6","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":"683e044dfff4b5d833acc7f65272faa0e5a286475d2632e8e94116c89bdc4af5","cross_cats_sorted":["math.IT","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-25T11:24:50Z","title_canon_sha256":"f3477d41be7ea7cf6af23aa15d0b19458caded4d7b1112e69f615fecb1acc8f6"},"schema_version":"1.0","source":{"id":"1410.6913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6913","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6913v1","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6913","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"SWWLLM4ATAYF","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SWWLLM4ATAYF5737","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SWWLLM4A","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:bbf7f0c9e080c6f60a4d208ebf09e6ba04a60a40377ffc51abec392ddc578f97","target":"graph","created_at":"2026-05-18T02:39:18Z","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":"We study the recovery of Hermitian low rank matrices $X \\in \\mathbb{C}^{n \\times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j a_j^*$ for some measurement vectors $a_1,...,a_m$, i.e., the measurements are given by $y_j = \\mathrm{tr}(X a_j a_j^*)$. The case where the matrix $X=x x^*$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements, $y_j = |\\langle x,a_j\\rangle|^2$ via the PhaseLift approach, wh","authors_text":"Holger Rauhut, Richard Kueng, Ulrich Terstiege","cross_cats":["math.IT","math.PR","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-25T11:24:50Z","title":"Low rank matrix recovery from rank one measurements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6913","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":"sha256:400708a922c781cf4248ec473781ebe5f5aa4586f04d62533b1357f4936d0305","target":"record","created_at":"2026-05-18T02:39:18Z","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":"683e044dfff4b5d833acc7f65272faa0e5a286475d2632e8e94116c89bdc4af5","cross_cats_sorted":["math.IT","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-25T11:24:50Z","title_canon_sha256":"f3477d41be7ea7cf6af23aa15d0b19458caded4d7b1112e69f615fecb1acc8f6"},"schema_version":"1.0","source":{"id":"1410.6913","kind":"arxiv","version":1}},"canonical_sha256":"95acb5b38098305eff7f25ef6f7df23f89331376568270f50e30a80969640121","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95acb5b38098305eff7f25ef6f7df23f89331376568270f50e30a80969640121","first_computed_at":"2026-05-18T02:39:18.337362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:18.337362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ee3FCRmVcsJByDecAzrGbXXX73OdC+pnUrYA7ozHL60Hh8uT8nnq2aFeyPF+bSCliz0GAEA1Vt5p8tPkGOGtBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:18.337865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:400708a922c781cf4248ec473781ebe5f5aa4586f04d62533b1357f4936d0305","sha256:bbf7f0c9e080c6f60a4d208ebf09e6ba04a60a40377ffc51abec392ddc578f97"],"state_sha256":"64f88403bb578c936f7abd52975df7bc9a72a9272287f65ce96fc3dd3a3172e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JDSk7sJqDTkUXI636rSlqYatFn0/Bdcior5uO19ShcToImQlAC3GreR3mfqVqKHJ1G5yxdWrIYEj+9SuHNKzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:02:49.000220Z","bundle_sha256":"082f42ff6e8b810095eada66d378baeff9b18ac175b4acddf08e24a34111b7e1"}}