{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:S2SLCFWSGT7KWXBWIRCZEC2YUI","short_pith_number":"pith:S2SLCFWS","schema_version":"1.0","canonical_sha256":"96a4b116d234feab5c364445920b58a206b9955b72cc75774b5211f47b801087","source":{"kind":"arxiv","id":"0709.0145","version":1},"attestation_state":"computed","paper":{"title":"Estimating Random Variables from Random Sparse Observations","license":"","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Andrea Montanari","submitted_at":"2007-09-03T02:57:58Z","abstract_excerpt":"Let X_1,...., X_n be a collection of iid discrete random variables, and Y_1,..., Y_m a set of noisy observations of such variables. Assume each observation Y_a to be a random function of some a random subset of the X_i's, and consider the conditional distribution of X_i given the observations, namely \\mu_i(x_i)\\equiv\\prob\\{X_i=x_i|Y\\} (a posteriori probability).\n  We establish a general relation between the distribution of \\mu_i, and the fixed points of the associated density evolution operator. Such relation holds asymptotically in the large system limit, provided the average number of variab"},"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":"0709.0145","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2007-09-03T02:57:58Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"f8f811b060937ccd20a9cffb73d972bbf92283ffd51ef6fd28915cfff1f66181","abstract_canon_sha256":"713b0bf35fd13ee31ddd0830be77e047b7c07f5fddeb43ed1ec9dfff76d48bd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:03:58.921030Z","signature_b64":"SLCpvwI4FlcL6eE4pxk7ZqhFd7j0qYYcz0EWl6yr6ibcgMUiR5ul4WR10p6n7bSfby/wUIEGbKeq54EBN7sYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96a4b116d234feab5c364445920b58a206b9955b72cc75774b5211f47b801087","last_reissued_at":"2026-07-04T15:03:58.920644Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:03:58.920644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimating Random Variables from Random Sparse Observations","license":"","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Andrea Montanari","submitted_at":"2007-09-03T02:57:58Z","abstract_excerpt":"Let X_1,...., X_n be a collection of iid discrete random variables, and Y_1,..., Y_m a set of noisy observations of such variables. Assume each observation Y_a to be a random function of some a random subset of the X_i's, and consider the conditional distribution of X_i given the observations, namely \\mu_i(x_i)\\equiv\\prob\\{X_i=x_i|Y\\} (a posteriori probability).\n  We establish a general relation between the distribution of \\mu_i, and the fixed points of the associated density evolution operator. Such relation holds asymptotically in the large system limit, provided the average number of variab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0145","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0709.0145/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"0709.0145","created_at":"2026-07-04T15:03:58.920702+00:00"},{"alias_kind":"arxiv_version","alias_value":"0709.0145v1","created_at":"2026-07-04T15:03:58.920702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.0145","created_at":"2026-07-04T15:03:58.920702+00:00"},{"alias_kind":"pith_short_12","alias_value":"S2SLCFWSGT7K","created_at":"2026-07-04T15:03:58.920702+00:00"},{"alias_kind":"pith_short_16","alias_value":"S2SLCFWSGT7KWXBW","created_at":"2026-07-04T15:03:58.920702+00:00"},{"alias_kind":"pith_short_8","alias_value":"S2SLCFWS","created_at":"2026-07-04T15:03:58.920702+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.10147","citing_title":"A Simple Algorithm for Best Separable State","ref_index":403,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S2SLCFWSGT7KWXBWIRCZEC2YUI","json":"https://pith.science/pith/S2SLCFWSGT7KWXBWIRCZEC2YUI.json","graph_json":"https://pith.science/api/pith-number/S2SLCFWSGT7KWXBWIRCZEC2YUI/graph.json","events_json":"https://pith.science/api/pith-number/S2SLCFWSGT7KWXBWIRCZEC2YUI/events.json","paper":"https://pith.science/paper/S2SLCFWS"},"agent_actions":{"view_html":"https://pith.science/pith/S2SLCFWSGT7KWXBWIRCZEC2YUI","download_json":"https://pith.science/pith/S2SLCFWSGT7KWXBWIRCZEC2YUI.json","view_paper":"https://pith.science/paper/S2SLCFWS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0709.0145&json=true","fetch_graph":"https://pith.science/api/pith-number/S2SLCFWSGT7KWXBWIRCZEC2YUI/graph.json","fetch_events":"https://pith.science/api/pith-number/S2SLCFWSGT7KWXBWIRCZEC2YUI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S2SLCFWSGT7KWXBWIRCZEC2YUI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S2SLCFWSGT7KWXBWIRCZEC2YUI/action/storage_attestation","attest_author":"https://pith.science/pith/S2SLCFWSGT7KWXBWIRCZEC2YUI/action/author_attestation","sign_citation":"https://pith.science/pith/S2SLCFWSGT7KWXBWIRCZEC2YUI/action/citation_signature","submit_replication":"https://pith.science/pith/S2SLCFWSGT7KWXBWIRCZEC2YUI/action/replication_record"}},"created_at":"2026-07-04T15:03:58.920702+00:00","updated_at":"2026-07-04T15:03:58.920702+00:00"}