{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XVRUPAWLVR4RZRSTHYBOW3TV3T","short_pith_number":"pith:XVRUPAWL","canonical_record":{"source":{"id":"1210.2592","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-09T13:28:05Z","cross_cats_sorted":["cond-mat.stat-mech","math.IT"],"title_canon_sha256":"f6ac3b99de83282dc436904102f590d0d657c16349d6365ed7002958f930be2c","abstract_canon_sha256":"fae26215f08076a3adce159cd3e99dc1070a0759f282d6fcb8cb44acb9c50d6d"},"schema_version":"1.0"},"canonical_sha256":"bd634782cbac791cc6533e02eb6e75dce0eda981442e9df74e93b4e9667145ee","source":{"kind":"arxiv","id":"1210.2592","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2592","created_at":"2026-05-18T03:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2592v2","created_at":"2026-05-18T03:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2592","created_at":"2026-05-18T03:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"XVRUPAWLVR4R","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XVRUPAWLVR4RZRST","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XVRUPAWL","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XVRUPAWLVR4RZRSTHYBOW3TV3T","target":"record","payload":{"canonical_record":{"source":{"id":"1210.2592","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-09T13:28:05Z","cross_cats_sorted":["cond-mat.stat-mech","math.IT"],"title_canon_sha256":"f6ac3b99de83282dc436904102f590d0d657c16349d6365ed7002958f930be2c","abstract_canon_sha256":"fae26215f08076a3adce159cd3e99dc1070a0759f282d6fcb8cb44acb9c50d6d"},"schema_version":"1.0"},"canonical_sha256":"bd634782cbac791cc6533e02eb6e75dce0eda981442e9df74e93b4e9667145ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:31.714182Z","signature_b64":"z/JNyqjLB+rUvP3UOYBJqgS+rtVFaQlJMKshTtH+U7Wwj3ScfHrm0C7G6Wd/0+8pK3XlRWduMYDdbh6sc79pCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd634782cbac791cc6533e02eb6e75dce0eda981442e9df74e93b4e9667145ee","last_reissued_at":"2026-05-18T03:43:31.713506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:31.713506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.2592","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7YCn7tLqcBKF9By9hViZPwEECLq1prKXg00jfDPymHuHN6295WKKDCdRTXFU/ho+1Fee/MGLKlEXJ3uwUrjYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:40:56.961560Z"},"content_sha256":"5879662d439af049f30dcbeee584eb8633ad26eed624918561a0e810ec2b93d2","schema_version":"1.0","event_id":"sha256:5879662d439af049f30dcbeee584eb8633ad26eed624918561a0e810ec2b93d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XVRUPAWLVR4RZRSTHYBOW3TV3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Generalizations of the Bethe Approximation via Asymptotic Expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.IT"],"primary_cat":"cs.IT","authors_text":"Ryuhei Mori, Toshiyuki Tanaka","submitted_at":"2012-10-09T13:28:05Z","abstract_excerpt":"The Bethe approximation, discovered in statistical physics, gives an efficient algorithm called belief propagation (BP) for approximating a partition function. BP empirically gives an accurate approximation for many problems, e.g., low-density parity-check codes, compressed sensing, etc. Recently, Vontobel gives a novel characterization of the Bethe approximation using graph cover. In this paper, a new approximation based on the Bethe approximation is proposed. The new approximation is derived from Vontobel's characterization using graph cover, and expressed by using the edge zeta function, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2592","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mCgkHqpC2Ygw5WHx/CheOUGkRlAftm3meR+554xEo1TJ50Koc6TIuDEQSa/NhE2SF7og7OLvwtuMQl5ngJeOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:40:56.962185Z"},"content_sha256":"66ca282c03c4767183b48f75a05c3b64b0877d0f6d8b3befb359c2b2c00de0d5","schema_version":"1.0","event_id":"sha256:66ca282c03c4767183b48f75a05c3b64b0877d0f6d8b3befb359c2b2c00de0d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XVRUPAWLVR4RZRSTHYBOW3TV3T/bundle.json","state_url":"https://pith.science/pith/XVRUPAWLVR4RZRSTHYBOW3TV3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XVRUPAWLVR4RZRSTHYBOW3TV3T/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":"2026-05-26T12:40:56Z","links":{"resolver":"https://pith.science/pith/XVRUPAWLVR4RZRSTHYBOW3TV3T","bundle":"https://pith.science/pith/XVRUPAWLVR4RZRSTHYBOW3TV3T/bundle.json","state":"https://pith.science/pith/XVRUPAWLVR4RZRSTHYBOW3TV3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XVRUPAWLVR4RZRSTHYBOW3TV3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XVRUPAWLVR4RZRSTHYBOW3TV3T","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":"fae26215f08076a3adce159cd3e99dc1070a0759f282d6fcb8cb44acb9c50d6d","cross_cats_sorted":["cond-mat.stat-mech","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-09T13:28:05Z","title_canon_sha256":"f6ac3b99de83282dc436904102f590d0d657c16349d6365ed7002958f930be2c"},"schema_version":"1.0","source":{"id":"1210.2592","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2592","created_at":"2026-05-18T03:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2592v2","created_at":"2026-05-18T03:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2592","created_at":"2026-05-18T03:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"XVRUPAWLVR4R","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XVRUPAWLVR4RZRST","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XVRUPAWL","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:66ca282c03c4767183b48f75a05c3b64b0877d0f6d8b3befb359c2b2c00de0d5","target":"graph","created_at":"2026-05-18T03:43:31Z","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 Bethe approximation, discovered in statistical physics, gives an efficient algorithm called belief propagation (BP) for approximating a partition function. BP empirically gives an accurate approximation for many problems, e.g., low-density parity-check codes, compressed sensing, etc. Recently, Vontobel gives a novel characterization of the Bethe approximation using graph cover. In this paper, a new approximation based on the Bethe approximation is proposed. The new approximation is derived from Vontobel's characterization using graph cover, and expressed by using the edge zeta function, wh","authors_text":"Ryuhei Mori, Toshiyuki Tanaka","cross_cats":["cond-mat.stat-mech","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-09T13:28:05Z","title":"New Generalizations of the Bethe Approximation via Asymptotic Expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2592","kind":"arxiv","version":2},"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":"sha256:5879662d439af049f30dcbeee584eb8633ad26eed624918561a0e810ec2b93d2","target":"record","created_at":"2026-05-18T03:43:31Z","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":"fae26215f08076a3adce159cd3e99dc1070a0759f282d6fcb8cb44acb9c50d6d","cross_cats_sorted":["cond-mat.stat-mech","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-09T13:28:05Z","title_canon_sha256":"f6ac3b99de83282dc436904102f590d0d657c16349d6365ed7002958f930be2c"},"schema_version":"1.0","source":{"id":"1210.2592","kind":"arxiv","version":2}},"canonical_sha256":"bd634782cbac791cc6533e02eb6e75dce0eda981442e9df74e93b4e9667145ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd634782cbac791cc6533e02eb6e75dce0eda981442e9df74e93b4e9667145ee","first_computed_at":"2026-05-18T03:43:31.713506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:31.713506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z/JNyqjLB+rUvP3UOYBJqgS+rtVFaQlJMKshTtH+U7Wwj3ScfHrm0C7G6Wd/0+8pK3XlRWduMYDdbh6sc79pCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:31.714182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2592","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5879662d439af049f30dcbeee584eb8633ad26eed624918561a0e810ec2b93d2","sha256:66ca282c03c4767183b48f75a05c3b64b0877d0f6d8b3befb359c2b2c00de0d5"],"state_sha256":"531d8aee1a6cea9bf6abd97e2d4def10ea84860a70c2bdcf96848cdd12fa3949"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"05AoTUMELzCpa0lFmhgLdVWRNuh9j4IkIYNtQuE5N3X1+UsURR55/muNQr2SZNXX93u7O3VBrGfgBuKeZRzBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:40:56.965125Z","bundle_sha256":"ddd2140deb6f53ff3d6ca2d22b13e1bae287bce2b6fa928177b1c32e5e3233d1"}}