{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:ONFNETVHLPQWAUS6UAHLWYH256","short_pith_number":"pith:ONFNETVH","canonical_record":{"source":{"id":"0911.1419","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-11-08T04:15:01Z","cross_cats_sorted":["cond-mat.stat-mech","cs.DM","cs.LG","cs.NA","math.OC"],"title_canon_sha256":"ac917d69e646eba224977e4e0106f1a1d8902ce24dc92fea57b8adc2df0c956d","abstract_canon_sha256":"2b7784c1e719f24e853f280ba6158673462584c780d53951b042fff03b9c864f"},"schema_version":"1.0"},"canonical_sha256":"734ad24ea75be160525ea00ebb60faefbe91704511d82c4aa80574bb4d7f46d2","source":{"kind":"arxiv","id":"0911.1419","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1419","created_at":"2026-05-18T02:10:58Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1419v2","created_at":"2026-05-18T02:10:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1419","created_at":"2026-05-18T02:10:58Z"},{"alias_kind":"pith_short_12","alias_value":"ONFNETVHLPQW","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"ONFNETVHLPQWAUS6","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"ONFNETVH","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:ONFNETVHLPQWAUS6UAHLWYH256","target":"record","payload":{"canonical_record":{"source":{"id":"0911.1419","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-11-08T04:15:01Z","cross_cats_sorted":["cond-mat.stat-mech","cs.DM","cs.LG","cs.NA","math.OC"],"title_canon_sha256":"ac917d69e646eba224977e4e0106f1a1d8902ce24dc92fea57b8adc2df0c956d","abstract_canon_sha256":"2b7784c1e719f24e853f280ba6158673462584c780d53951b042fff03b9c864f"},"schema_version":"1.0"},"canonical_sha256":"734ad24ea75be160525ea00ebb60faefbe91704511d82c4aa80574bb4d7f46d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:58.376181Z","signature_b64":"uVi2/2l83PZUaNE6V8O7jKpfCR0MKxrS8odG/rZnWkXf9mOYyMQv9xg8CymqQvqBIKHbMZzZ6PaG84NzKcrODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"734ad24ea75be160525ea00ebb60faefbe91704511d82c4aa80574bb4d7f46d2","last_reissued_at":"2026-05-18T02:10:58.375358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:58.375358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.1419","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":"2026-05-18T02:10:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pTcrzuWfTBT+28Rp8FQRN8sHLRIWUZIMGNndnsvQeOYDuxd9EnAtema91uyAkQeCY+pgSCGgI5CUzzWcn8LUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:09.792644Z"},"content_sha256":"db0680b56fda6ae36cea1bb8bf4681d7cbbb16d1ed5014f17d2bad92a1abcead","schema_version":"1.0","event_id":"sha256:db0680b56fda6ae36cea1bb8bf4681d7cbbb16d1ed5014f17d2bad92a1abcead"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:ONFNETVHLPQWAUS6UAHLWYH256","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Belief Propagation and Loop Calculus for the Permanent of a Non-Negative Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.DM","cs.LG","cs.NA","math.OC"],"primary_cat":"cs.DS","authors_text":"Michael Chertkov, Yusuke Watanabe","submitted_at":"2009-11-08T04:15:01Z","abstract_excerpt":"We consider computation of permanent of a positive $(N\\times N)$ non-negative matrix, $P=(P_i^j|i,j=1,\\cdots,N)$, or equivalently the problem of weighted counting of the perfect matchings over the complete bipartite graph $K_{N,N}$. The problem is known to be of likely exponential complexity. Stated as the partition function $Z$ of a graphical model, the problem allows exact Loop Calculus representation [Chertkov, Chernyak '06] in terms of an interior minimum of the Bethe Free Energy functional over non-integer doubly stochastic matrix of marginal beliefs, $\\beta=(\\beta_i^j|i,j=1,\\cdots,N)$, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1419","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":"2026-05-18T02:10:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YFVU0JHuaJnqSE2CQ7mC3BJ3+RaouDyBLpOZqqZrqyIq8pHvx6p363qdqqo4CQ+uF4L4ktOK8EZzoa9fAzvNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:09.793008Z"},"content_sha256":"1791eb7fcf939c0003ceb3a49def60a9faba8f6e41788760c8e58ff93093e37e","schema_version":"1.0","event_id":"sha256:1791eb7fcf939c0003ceb3a49def60a9faba8f6e41788760c8e58ff93093e37e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ONFNETVHLPQWAUS6UAHLWYH256/bundle.json","state_url":"https://pith.science/pith/ONFNETVHLPQWAUS6UAHLWYH256/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ONFNETVHLPQWAUS6UAHLWYH256/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":"2026-06-03T18:37:09Z","links":{"resolver":"https://pith.science/pith/ONFNETVHLPQWAUS6UAHLWYH256","bundle":"https://pith.science/pith/ONFNETVHLPQWAUS6UAHLWYH256/bundle.json","state":"https://pith.science/pith/ONFNETVHLPQWAUS6UAHLWYH256/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ONFNETVHLPQWAUS6UAHLWYH256/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ONFNETVHLPQWAUS6UAHLWYH256","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":"2b7784c1e719f24e853f280ba6158673462584c780d53951b042fff03b9c864f","cross_cats_sorted":["cond-mat.stat-mech","cs.DM","cs.LG","cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-11-08T04:15:01Z","title_canon_sha256":"ac917d69e646eba224977e4e0106f1a1d8902ce24dc92fea57b8adc2df0c956d"},"schema_version":"1.0","source":{"id":"0911.1419","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1419","created_at":"2026-05-18T02:10:58Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1419v2","created_at":"2026-05-18T02:10:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1419","created_at":"2026-05-18T02:10:58Z"},{"alias_kind":"pith_short_12","alias_value":"ONFNETVHLPQW","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"ONFNETVHLPQWAUS6","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"ONFNETVH","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:1791eb7fcf939c0003ceb3a49def60a9faba8f6e41788760c8e58ff93093e37e","target":"graph","created_at":"2026-05-18T02:10:58Z","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":"We consider computation of permanent of a positive $(N\\times N)$ non-negative matrix, $P=(P_i^j|i,j=1,\\cdots,N)$, or equivalently the problem of weighted counting of the perfect matchings over the complete bipartite graph $K_{N,N}$. The problem is known to be of likely exponential complexity. Stated as the partition function $Z$ of a graphical model, the problem allows exact Loop Calculus representation [Chertkov, Chernyak '06] in terms of an interior minimum of the Bethe Free Energy functional over non-integer doubly stochastic matrix of marginal beliefs, $\\beta=(\\beta_i^j|i,j=1,\\cdots,N)$, a","authors_text":"Michael Chertkov, Yusuke Watanabe","cross_cats":["cond-mat.stat-mech","cs.DM","cs.LG","cs.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-11-08T04:15:01Z","title":"Belief Propagation and Loop Calculus for the Permanent of a Non-Negative Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1419","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:db0680b56fda6ae36cea1bb8bf4681d7cbbb16d1ed5014f17d2bad92a1abcead","target":"record","created_at":"2026-05-18T02:10:58Z","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":"2b7784c1e719f24e853f280ba6158673462584c780d53951b042fff03b9c864f","cross_cats_sorted":["cond-mat.stat-mech","cs.DM","cs.LG","cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-11-08T04:15:01Z","title_canon_sha256":"ac917d69e646eba224977e4e0106f1a1d8902ce24dc92fea57b8adc2df0c956d"},"schema_version":"1.0","source":{"id":"0911.1419","kind":"arxiv","version":2}},"canonical_sha256":"734ad24ea75be160525ea00ebb60faefbe91704511d82c4aa80574bb4d7f46d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"734ad24ea75be160525ea00ebb60faefbe91704511d82c4aa80574bb4d7f46d2","first_computed_at":"2026-05-18T02:10:58.375358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:58.375358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uVi2/2l83PZUaNE6V8O7jKpfCR0MKxrS8odG/rZnWkXf9mOYyMQv9xg8CymqQvqBIKHbMZzZ6PaG84NzKcrODA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:58.376181Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1419","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db0680b56fda6ae36cea1bb8bf4681d7cbbb16d1ed5014f17d2bad92a1abcead","sha256:1791eb7fcf939c0003ceb3a49def60a9faba8f6e41788760c8e58ff93093e37e"],"state_sha256":"b1b7b0d828d07673fe6962965d78e86c24d74aa450d314408e72071936778c53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i3JEt2UTvkS3I2aWlV/27ioEEK6VAjJkjmmLGrutqkOJwRUG9F8vN6UeTo4fl+hLEofM9ownDfpQZKLjW057Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:37:09.795095Z","bundle_sha256":"068f8c5c50f311402d71cee07972a3266b936a9b3922901e0e2f62af875156a5"}}