{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:36E2KFKKZRMPIRQ3GU3ZVJH543","short_pith_number":"pith:36E2KFKK","canonical_record":{"source":{"id":"1105.0785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-05-04T10:24:47Z","cross_cats_sorted":["cond-mat.stat-mech","cs.DM","math.IT"],"title_canon_sha256":"72b6575c719214f2023560ebf86a33921e39a9c4a325d17ee6787c6e541c2782","abstract_canon_sha256":"da7538f30f683e6c282f26a134315b22dfe903b9c477a4891b3b4d7bc563f805"},"schema_version":"1.0"},"canonical_sha256":"df89a5154acc58f4461b35379aa4fde6ec9b7b61f23e311ba0f28691d4b41696","source":{"kind":"arxiv","id":"1105.0785","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0785","created_at":"2026-05-18T04:23:01Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0785v1","created_at":"2026-05-18T04:23:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0785","created_at":"2026-05-18T04:23:01Z"},{"alias_kind":"pith_short_12","alias_value":"36E2KFKKZRMP","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"36E2KFKKZRMPIRQ3","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"36E2KFKK","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:36E2KFKKZRMPIRQ3GU3ZVJH543","target":"record","payload":{"canonical_record":{"source":{"id":"1105.0785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-05-04T10:24:47Z","cross_cats_sorted":["cond-mat.stat-mech","cs.DM","math.IT"],"title_canon_sha256":"72b6575c719214f2023560ebf86a33921e39a9c4a325d17ee6787c6e541c2782","abstract_canon_sha256":"da7538f30f683e6c282f26a134315b22dfe903b9c477a4891b3b4d7bc563f805"},"schema_version":"1.0"},"canonical_sha256":"df89a5154acc58f4461b35379aa4fde6ec9b7b61f23e311ba0f28691d4b41696","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:01.830988Z","signature_b64":"jVAWaX1HBZDMNLlflzWAKdSz99hJXVvr/YdwPPRyRyE1qUuvppoVSoXmgKVNiipzITqwkwsEHtfjdRpUvzA4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df89a5154acc58f4461b35379aa4fde6ec9b7b61f23e311ba0f28691d4b41696","last_reissued_at":"2026-05-18T04:23:01.830518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:01.830518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.0785","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":"2026-05-18T04:23:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L60yEDC1FSfi5m6ojENCvUVfzfW96+DGaSQA3lNtOu4CwHpk5NgHT5a/9Hn2XUxMjKA3qACfu/hEshbGci78Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:11:16.578958Z"},"content_sha256":"66619a7a77a11e5c8dbcea24641ffa3de08a31033968cf0ad776c226e31bf7af","schema_version":"1.0","event_id":"sha256:66619a7a77a11e5c8dbcea24641ffa3de08a31033968cf0ad776c226e31bf7af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:36E2KFKKZRMPIRQ3GU3ZVJH543","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coupled Graphical Models and Their Thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.DM","math.IT"],"primary_cat":"cs.IT","authors_text":"Nicolas Macris, Ruediger Urbanke, S. Hamed Hassani","submitted_at":"2011-05-04T10:24:47Z","abstract_excerpt":"The excellent performance of convolutional low-density parity-check codes is the result of the spatial coupling of individual underlying codes across a window of growing size, but much smaller than the length of the individual codes. Remarkably, the belief-propagation threshold of the coupled ensemble is boosted to the maximum-a-posteriori one of the individual system. We investigate the generality of this phenomenon beyond coding theory: we couple general graphical models into a one-dimensional chain of large individual systems. For the later we take the Curie-Weiss, random field Curie-Weiss,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0785","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":"2026-05-18T04:23:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"whCTXH4BG/fg7MmFX1MO8iIRiFwgi8u1uyKBO4hJwDi7YhtsWxzyd6LIdDJ3/nLfYvWfaqVR6G31J0Uz97TzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:11:16.579384Z"},"content_sha256":"704602dbc6b390f0da433c5e191c82b76628e651de8369d3548b16e4b6fc76f3","schema_version":"1.0","event_id":"sha256:704602dbc6b390f0da433c5e191c82b76628e651de8369d3548b16e4b6fc76f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/36E2KFKKZRMPIRQ3GU3ZVJH543/bundle.json","state_url":"https://pith.science/pith/36E2KFKKZRMPIRQ3GU3ZVJH543/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/36E2KFKKZRMPIRQ3GU3ZVJH543/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":"2026-05-29T16:11:16Z","links":{"resolver":"https://pith.science/pith/36E2KFKKZRMPIRQ3GU3ZVJH543","bundle":"https://pith.science/pith/36E2KFKKZRMPIRQ3GU3ZVJH543/bundle.json","state":"https://pith.science/pith/36E2KFKKZRMPIRQ3GU3ZVJH543/state.json","well_known_bundle":"https://pith.science/.well-known/pith/36E2KFKKZRMPIRQ3GU3ZVJH543/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:36E2KFKKZRMPIRQ3GU3ZVJH543","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":"da7538f30f683e6c282f26a134315b22dfe903b9c477a4891b3b4d7bc563f805","cross_cats_sorted":["cond-mat.stat-mech","cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-05-04T10:24:47Z","title_canon_sha256":"72b6575c719214f2023560ebf86a33921e39a9c4a325d17ee6787c6e541c2782"},"schema_version":"1.0","source":{"id":"1105.0785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0785","created_at":"2026-05-18T04:23:01Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0785v1","created_at":"2026-05-18T04:23:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0785","created_at":"2026-05-18T04:23:01Z"},{"alias_kind":"pith_short_12","alias_value":"36E2KFKKZRMP","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"36E2KFKKZRMPIRQ3","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"36E2KFKK","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:704602dbc6b390f0da433c5e191c82b76628e651de8369d3548b16e4b6fc76f3","target":"graph","created_at":"2026-05-18T04:23:01Z","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":"The excellent performance of convolutional low-density parity-check codes is the result of the spatial coupling of individual underlying codes across a window of growing size, but much smaller than the length of the individual codes. Remarkably, the belief-propagation threshold of the coupled ensemble is boosted to the maximum-a-posteriori one of the individual system. We investigate the generality of this phenomenon beyond coding theory: we couple general graphical models into a one-dimensional chain of large individual systems. For the later we take the Curie-Weiss, random field Curie-Weiss,","authors_text":"Nicolas Macris, Ruediger Urbanke, S. Hamed Hassani","cross_cats":["cond-mat.stat-mech","cs.DM","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-05-04T10:24:47Z","title":"Coupled Graphical Models and Their Thresholds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0785","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":"sha256:66619a7a77a11e5c8dbcea24641ffa3de08a31033968cf0ad776c226e31bf7af","target":"record","created_at":"2026-05-18T04:23:01Z","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":"da7538f30f683e6c282f26a134315b22dfe903b9c477a4891b3b4d7bc563f805","cross_cats_sorted":["cond-mat.stat-mech","cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-05-04T10:24:47Z","title_canon_sha256":"72b6575c719214f2023560ebf86a33921e39a9c4a325d17ee6787c6e541c2782"},"schema_version":"1.0","source":{"id":"1105.0785","kind":"arxiv","version":1}},"canonical_sha256":"df89a5154acc58f4461b35379aa4fde6ec9b7b61f23e311ba0f28691d4b41696","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df89a5154acc58f4461b35379aa4fde6ec9b7b61f23e311ba0f28691d4b41696","first_computed_at":"2026-05-18T04:23:01.830518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:01.830518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jVAWaX1HBZDMNLlflzWAKdSz99hJXVvr/YdwPPRyRyE1qUuvppoVSoXmgKVNiipzITqwkwsEHtfjdRpUvzA4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:01.830988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.0785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66619a7a77a11e5c8dbcea24641ffa3de08a31033968cf0ad776c226e31bf7af","sha256:704602dbc6b390f0da433c5e191c82b76628e651de8369d3548b16e4b6fc76f3"],"state_sha256":"653df480ed8c586bdb9ef5dfd5bdfdb4e4f169a15ea42b844d8eb3ba1617eb04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"czXvpWuwWOYzRJq/QYAawJYdB9PumNqMO3H3mbwawoKI6Lm4zVmddxby2/H5tDSjj4zT7gjqo8cDIJ1As1rMCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T16:11:16.582034Z","bundle_sha256":"1bdd3eefbfc24f0ecb34d738b5995822b2d59d984b0b47313ff042646dee0821"}}