{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:J34QQFOGURCFME5MQJNPKRK5UL","short_pith_number":"pith:J34QQFOG","schema_version":"1.0","canonical_sha256":"4ef90815c6a4445613ac825af5455da2d27fa3acb912702a1c09f3b356989f23","source":{"kind":"arxiv","id":"1206.3953","version":1},"attestation_state":"computed","paper":{"title":"Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cond-mat.stat-mech","authors_text":"Florent Krzakala, Fran\\c{c}ois Sausset, Lenka Zdeborov\\'a, Marc M\\'ezard, Yifan Sun","submitted_at":"2012-06-18T14:41:52Z","abstract_excerpt":"Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement protocols in a wide range of applications. Using an interdisciplinary approach, we have recently proposed in [arXiv:1109.4424] a strategy that allows compressed sensing to be performed at acquisition rates approaching to the theoretical optimal limits. In this paper, we give a more thorough presentation of our approach, and introduce many new results. We pre"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1206.3953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-18T14:41:52Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"b245d7251f0efcfca48ab1b6d8fc1c71ac0ce115eadb8fad2d97d15b9d85b9e8","abstract_canon_sha256":"60f1f094fa9a89187925cef11ac83d900de02496918c2e601e65a777235eb5c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:35.275398Z","signature_b64":"NgGfgf7MbsQbf6bR2SU/imgGE0Pdib4xOrdlFlgQqh2m03OiS+1LXdLEb1jFvbLVw5B4t/AME27X7mhVk9BYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ef90815c6a4445613ac825af5455da2d27fa3acb912702a1c09f3b356989f23","last_reissued_at":"2026-05-18T03:48:35.274871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:35.274871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cond-mat.stat-mech","authors_text":"Florent Krzakala, Fran\\c{c}ois Sausset, Lenka Zdeborov\\'a, Marc M\\'ezard, Yifan Sun","submitted_at":"2012-06-18T14:41:52Z","abstract_excerpt":"Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement protocols in a wide range of applications. Using an interdisciplinary approach, we have recently proposed in [arXiv:1109.4424] a strategy that allows compressed sensing to be performed at acquisition rates approaching to the theoretical optimal limits. In this paper, we give a more thorough presentation of our approach, and introduce many new results. We pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3953","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1206.3953","created_at":"2026-05-18T03:48:35.274946+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.3953v1","created_at":"2026-05-18T03:48:35.274946+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3953","created_at":"2026-05-18T03:48:35.274946+00:00"},{"alias_kind":"pith_short_12","alias_value":"J34QQFOGURCF","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"J34QQFOGURCFME5M","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"J34QQFOG","created_at":"2026-05-18T12:27:09.501522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J34QQFOGURCFME5MQJNPKRK5UL","json":"https://pith.science/pith/J34QQFOGURCFME5MQJNPKRK5UL.json","graph_json":"https://pith.science/api/pith-number/J34QQFOGURCFME5MQJNPKRK5UL/graph.json","events_json":"https://pith.science/api/pith-number/J34QQFOGURCFME5MQJNPKRK5UL/events.json","paper":"https://pith.science/paper/J34QQFOG"},"agent_actions":{"view_html":"https://pith.science/pith/J34QQFOGURCFME5MQJNPKRK5UL","download_json":"https://pith.science/pith/J34QQFOGURCFME5MQJNPKRK5UL.json","view_paper":"https://pith.science/paper/J34QQFOG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.3953&json=true","fetch_graph":"https://pith.science/api/pith-number/J34QQFOGURCFME5MQJNPKRK5UL/graph.json","fetch_events":"https://pith.science/api/pith-number/J34QQFOGURCFME5MQJNPKRK5UL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J34QQFOGURCFME5MQJNPKRK5UL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J34QQFOGURCFME5MQJNPKRK5UL/action/storage_attestation","attest_author":"https://pith.science/pith/J34QQFOGURCFME5MQJNPKRK5UL/action/author_attestation","sign_citation":"https://pith.science/pith/J34QQFOGURCFME5MQJNPKRK5UL/action/citation_signature","submit_replication":"https://pith.science/pith/J34QQFOGURCFME5MQJNPKRK5UL/action/replication_record"}},"created_at":"2026-05-18T03:48:35.274946+00:00","updated_at":"2026-05-18T03:48:35.274946+00:00"}