{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7NEZKAHJN6SGV44XA2GIDJNTZN","short_pith_number":"pith:7NEZKAHJ","schema_version":"1.0","canonical_sha256":"fb499500e96fa46af397068c81a5b3cb53cdf134913e23149479bb8fcf840d01","source":{"kind":"arxiv","id":"1105.0807","version":2},"attestation_state":"computed","paper":{"title":"Chains of Mean Field Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.IT","math.IT"],"primary_cat":"cs.DM","authors_text":"Nicolas Macris, Ruediger Urbanke, S. Hamed Hassani","submitted_at":"2011-05-04T12:49:20Z","abstract_excerpt":"We consider a collection of Curie-Weiss (CW) spin systems, possibly with a random field, each of which is placed along the positions of a one-dimensional chain. The CW systems are coupled together by a Kac-type interaction in the longitudinal direction of the chain and by an infinite range interaction in the direction transverse to the chain. Our motivations for studying this model come from recent findings in the theory of error correcting codes based on spatially coupled graphs. We find that, although much simpler than the codes, the model studied here already displays similar behaviors. We "},"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":"1105.0807","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-05-04T12:49:20Z","cross_cats_sorted":["cond-mat.stat-mech","cs.IT","math.IT"],"title_canon_sha256":"4f6e3335a5561b9563c5e6f23a93440bf0ea136911e037dcc2a57788836a2ff2","abstract_canon_sha256":"47eb9a82e7bada801d5b6d4f7db131964e45a5630bba80ff2a5f97644ae30e93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:08.979011Z","signature_b64":"S/YaFOHYQblzS4HRnjakLBH/pwq+01zLxRGDIRLjGGnFcoyebeCnDmFhVgbb+TcPaLlJwziKjuyPrGOmwcNkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb499500e96fa46af397068c81a5b3cb53cdf134913e23149479bb8fcf840d01","last_reissued_at":"2026-05-18T02:02:08.978391Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:08.978391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chains of Mean Field Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.IT","math.IT"],"primary_cat":"cs.DM","authors_text":"Nicolas Macris, Ruediger Urbanke, S. Hamed Hassani","submitted_at":"2011-05-04T12:49:20Z","abstract_excerpt":"We consider a collection of Curie-Weiss (CW) spin systems, possibly with a random field, each of which is placed along the positions of a one-dimensional chain. The CW systems are coupled together by a Kac-type interaction in the longitudinal direction of the chain and by an infinite range interaction in the direction transverse to the chain. Our motivations for studying this model come from recent findings in the theory of error correcting codes based on spatially coupled graphs. We find that, although much simpler than the codes, the model studied here already displays similar behaviors. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0807","kind":"arxiv","version":2},"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":"1105.0807","created_at":"2026-05-18T02:02:08.978479+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.0807v2","created_at":"2026-05-18T02:02:08.978479+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0807","created_at":"2026-05-18T02:02:08.978479+00:00"},{"alias_kind":"pith_short_12","alias_value":"7NEZKAHJN6SG","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7NEZKAHJN6SGV44X","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7NEZKAHJ","created_at":"2026-05-18T12:26:22.705136+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/7NEZKAHJN6SGV44XA2GIDJNTZN","json":"https://pith.science/pith/7NEZKAHJN6SGV44XA2GIDJNTZN.json","graph_json":"https://pith.science/api/pith-number/7NEZKAHJN6SGV44XA2GIDJNTZN/graph.json","events_json":"https://pith.science/api/pith-number/7NEZKAHJN6SGV44XA2GIDJNTZN/events.json","paper":"https://pith.science/paper/7NEZKAHJ"},"agent_actions":{"view_html":"https://pith.science/pith/7NEZKAHJN6SGV44XA2GIDJNTZN","download_json":"https://pith.science/pith/7NEZKAHJN6SGV44XA2GIDJNTZN.json","view_paper":"https://pith.science/paper/7NEZKAHJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.0807&json=true","fetch_graph":"https://pith.science/api/pith-number/7NEZKAHJN6SGV44XA2GIDJNTZN/graph.json","fetch_events":"https://pith.science/api/pith-number/7NEZKAHJN6SGV44XA2GIDJNTZN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7NEZKAHJN6SGV44XA2GIDJNTZN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7NEZKAHJN6SGV44XA2GIDJNTZN/action/storage_attestation","attest_author":"https://pith.science/pith/7NEZKAHJN6SGV44XA2GIDJNTZN/action/author_attestation","sign_citation":"https://pith.science/pith/7NEZKAHJN6SGV44XA2GIDJNTZN/action/citation_signature","submit_replication":"https://pith.science/pith/7NEZKAHJN6SGV44XA2GIDJNTZN/action/replication_record"}},"created_at":"2026-05-18T02:02:08.978479+00:00","updated_at":"2026-05-18T02:02:08.978479+00:00"}