{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:BHFMI67RKPQIAVMT4TKE3CU64P","short_pith_number":"pith:BHFMI67R","canonical_record":{"source":{"id":"cond-mat/0609367","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2006-09-15T08:43:55Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"4dd6c10eb49a92d2dd43be673796961da748026f467cf9c3c2f8c853138e1dda","abstract_canon_sha256":"827ebd1d24ff0263a0cc51d99cabeeb04764300c3f17ea82de1780e3d02a993a"},"schema_version":"1.0"},"canonical_sha256":"09cac47bf153e0805593e4d44d8a9ee3ca7f0a0ae2ecbb14bbd1ae257f45a95f","source":{"kind":"arxiv","id":"cond-mat/0609367","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0609367","created_at":"2026-07-04T17:01:06Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0609367v3","created_at":"2026-07-04T17:01:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0609367","created_at":"2026-07-04T17:01:06Z"},{"alias_kind":"pith_short_12","alias_value":"BHFMI67RKPQI","created_at":"2026-07-04T17:01:06Z"},{"alias_kind":"pith_short_16","alias_value":"BHFMI67RKPQIAVMT","created_at":"2026-07-04T17:01:06Z"},{"alias_kind":"pith_short_8","alias_value":"BHFMI67R","created_at":"2026-07-04T17:01:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:BHFMI67RKPQIAVMT4TKE3CU64P","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0609367","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2006-09-15T08:43:55Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"4dd6c10eb49a92d2dd43be673796961da748026f467cf9c3c2f8c853138e1dda","abstract_canon_sha256":"827ebd1d24ff0263a0cc51d99cabeeb04764300c3f17ea82de1780e3d02a993a"},"schema_version":"1.0"},"canonical_sha256":"09cac47bf153e0805593e4d44d8a9ee3ca7f0a0ae2ecbb14bbd1ae257f45a95f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:01:06.633268Z","signature_b64":"HZ790AGMddVvkCn7YJXHlDTLOLJ97uiMRFJqC3q1axAFyFRmhDPpYfQfiZWqNLpwIGIvktgQ7sjPBDDzm/IlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09cac47bf153e0805593e4d44d8a9ee3ca7f0a0ae2ecbb14bbd1ae257f45a95f","last_reissued_at":"2026-07-04T17:01:06.632937Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:01:06.632937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0609367","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T17:01:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XgL26FS0uz+2CCBL/LAGF7SPJ4k/yJ/lFutuG+EH+PgFvD/Z9N77XKzlbwZT8ZYmCqvs4QH5zXAkuD+FZcigBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T19:45:35.446921Z"},"content_sha256":"80b5d34e981d0c67f74379e97768e88385c1d9257212ff3e208fadcce6b60e08","schema_version":"1.0","event_id":"sha256:80b5d34e981d0c67f74379e97768e88385c1d9257212ff3e208fadcce6b60e08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:BHFMI67RKPQIAVMT4TKE3CU64P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"D. Saad, K. Y. Michael Wong","submitted_at":"2006-09-15T08:43:55Z","abstract_excerpt":"Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge-variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0609367","kind":"arxiv","version":3},"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/cond-mat/0609367/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T17:01:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4uYhCTH429MBzL4gZ/w1s0+VUiobku+T6jl034KSf9TdYXhTwtmCoI6IfM1ouCFg6Xql6MyYayOdFLqLArcdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T19:45:35.447442Z"},"content_sha256":"ac44f311b5a10d52399bdbc2c40c5f40b6ef48220702a8691ef0238b4a1b94ec","schema_version":"1.0","event_id":"sha256:ac44f311b5a10d52399bdbc2c40c5f40b6ef48220702a8691ef0238b4a1b94ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BHFMI67RKPQIAVMT4TKE3CU64P/bundle.json","state_url":"https://pith.science/pith/BHFMI67RKPQIAVMT4TKE3CU64P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BHFMI67RKPQIAVMT4TKE3CU64P/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":"2026-07-31T19:45:35Z","links":{"resolver":"https://pith.science/pith/BHFMI67RKPQIAVMT4TKE3CU64P","bundle":"https://pith.science/pith/BHFMI67RKPQIAVMT4TKE3CU64P/bundle.json","state":"https://pith.science/pith/BHFMI67RKPQIAVMT4TKE3CU64P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BHFMI67RKPQIAVMT4TKE3CU64P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:BHFMI67RKPQIAVMT4TKE3CU64P","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":"827ebd1d24ff0263a0cc51d99cabeeb04764300c3f17ea82de1780e3d02a993a","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2006-09-15T08:43:55Z","title_canon_sha256":"4dd6c10eb49a92d2dd43be673796961da748026f467cf9c3c2f8c853138e1dda"},"schema_version":"1.0","source":{"id":"cond-mat/0609367","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0609367","created_at":"2026-07-04T17:01:06Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0609367v3","created_at":"2026-07-04T17:01:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0609367","created_at":"2026-07-04T17:01:06Z"},{"alias_kind":"pith_short_12","alias_value":"BHFMI67RKPQI","created_at":"2026-07-04T17:01:06Z"},{"alias_kind":"pith_short_16","alias_value":"BHFMI67RKPQIAVMT","created_at":"2026-07-04T17:01:06Z"},{"alias_kind":"pith_short_8","alias_value":"BHFMI67R","created_at":"2026-07-04T17:01:06Z"}],"graph_snapshots":[{"event_id":"sha256:ac44f311b5a10d52399bdbc2c40c5f40b6ef48220702a8691ef0238b4a1b94ec","target":"graph","created_at":"2026-07-04T17:01:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/0609367/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge-variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods","authors_text":"D. Saad, K. Y. Michael Wong","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2006-09-15T08:43:55Z","title":"Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0609367","kind":"arxiv","version":3},"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":"sha256:80b5d34e981d0c67f74379e97768e88385c1d9257212ff3e208fadcce6b60e08","target":"record","created_at":"2026-07-04T17:01:06Z","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":"827ebd1d24ff0263a0cc51d99cabeeb04764300c3f17ea82de1780e3d02a993a","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2006-09-15T08:43:55Z","title_canon_sha256":"4dd6c10eb49a92d2dd43be673796961da748026f467cf9c3c2f8c853138e1dda"},"schema_version":"1.0","source":{"id":"cond-mat/0609367","kind":"arxiv","version":3}},"canonical_sha256":"09cac47bf153e0805593e4d44d8a9ee3ca7f0a0ae2ecbb14bbd1ae257f45a95f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09cac47bf153e0805593e4d44d8a9ee3ca7f0a0ae2ecbb14bbd1ae257f45a95f","first_computed_at":"2026-07-04T17:01:06.632937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:01:06.632937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HZ790AGMddVvkCn7YJXHlDTLOLJ97uiMRFJqC3q1axAFyFRmhDPpYfQfiZWqNLpwIGIvktgQ7sjPBDDzm/IlAA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:01:06.633268Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0609367","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80b5d34e981d0c67f74379e97768e88385c1d9257212ff3e208fadcce6b60e08","sha256:ac44f311b5a10d52399bdbc2c40c5f40b6ef48220702a8691ef0238b4a1b94ec"],"state_sha256":"558e00537efbe8ced66ae436b0b3dafd5526a8291dbd42d9dbcbd7c9335eedf9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"riG1eoZhCbHTN+50whCLcx7rRCxQ1Wl2waTBFnxbIGVAFjGxVw2Ij8nmNGdUW1Ya8PjFhPrMs0iSLkQoVbHeAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T19:45:35.452054Z","bundle_sha256":"be5be252e1a815d11d9aa4cffc03afaf3fded1edbd9e4f83bd1d91e8f7e6ed9e"}}