{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BC7HM4ODHYSJMT2WBG2C23HOAW","short_pith_number":"pith:BC7HM4OD","canonical_record":{"source":{"id":"1111.1020","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-11-04T00:28:59Z","cross_cats_sorted":["math.IT","stat.ML"],"title_canon_sha256":"841b331cb33da6aec4ad363cd2317208efcdcc708d6c762343674bf064f7039a","abstract_canon_sha256":"542eb2ca788e991c9b10161c2cbcc5c1e12506fa8a092950dfdbf569e8e99b26"},"schema_version":"1.0"},"canonical_sha256":"08be7671c33e24964f5609b42d6cee05b9d49ad7344bb4db3801833ef2ebd587","source":{"kind":"arxiv","id":"1111.1020","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1020","created_at":"2026-05-18T03:55:00Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1020v2","created_at":"2026-05-18T03:55:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1020","created_at":"2026-05-18T03:55:00Z"},{"alias_kind":"pith_short_12","alias_value":"BC7HM4ODHYSJ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BC7HM4ODHYSJMT2W","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BC7HM4OD","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BC7HM4ODHYSJMT2WBG2C23HOAW","target":"record","payload":{"canonical_record":{"source":{"id":"1111.1020","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-11-04T00:28:59Z","cross_cats_sorted":["math.IT","stat.ML"],"title_canon_sha256":"841b331cb33da6aec4ad363cd2317208efcdcc708d6c762343674bf064f7039a","abstract_canon_sha256":"542eb2ca788e991c9b10161c2cbcc5c1e12506fa8a092950dfdbf569e8e99b26"},"schema_version":"1.0"},"canonical_sha256":"08be7671c33e24964f5609b42d6cee05b9d49ad7344bb4db3801833ef2ebd587","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:00.323589Z","signature_b64":"bKZ7rMYR6uuD7uPUlOq2wAbJpVaYoSGEaBCvnvgk8llwehTBbGfuF5Ju55nXKb6gZ/JtHPIxJ5bdZa2WfteIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08be7671c33e24964f5609b42d6cee05b9d49ad7344bb4db3801833ef2ebd587","last_reissued_at":"2026-05-18T03:55:00.322991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:00.322991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.1020","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":"2026-05-18T03:55:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9XljFMfLOrgX1QgQLMHYetTu/JJ43VfqzlkcDT2FbkPV0niND9q050V+Ub6oN+XIWGp4szuXZtazq30q1S1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:12:29.198426Z"},"content_sha256":"f435e821e423d3d03df8bfdc29eee191053569cb4b00956171ff15ff226b75c5","schema_version":"1.0","event_id":"sha256:f435e821e423d3d03df8bfdc29eee191053569cb4b00956171ff15ff226b75c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BC7HM4ODHYSJMT2WBG2C23HOAW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Belief Propagation: A Low-Complexity Alternative to the Sum-Product Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","stat.ML"],"primary_cat":"cs.IT","authors_text":"Martin J. Wainwright, Nima Noorshams","submitted_at":"2011-11-04T00:28:59Z","abstract_excerpt":"The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a graphical model with pairwise interactions, lies a matrix-vector product with complexity that is quadratic in the state dimension $d$, and requires transmission of a $(d-1)$-dimensional vector of real numbers (messages) to its neighbors. Since various applications involve very large state dimensions, such computation and communication complexities can be prohibit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1020","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":"2026-05-18T03:55:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XHKjjJKnT1111dj2YGNqVw9xWXbnx8N08GIyOPi0SOimcFyR4CqHIUExxJnYTm0vzBKsuVvAWwVUUCD4XF3Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:12:29.198779Z"},"content_sha256":"cc93d09e852a78edae22868abc1937762fbb43b78118203cc5268bea690abc8e","schema_version":"1.0","event_id":"sha256:cc93d09e852a78edae22868abc1937762fbb43b78118203cc5268bea690abc8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BC7HM4ODHYSJMT2WBG2C23HOAW/bundle.json","state_url":"https://pith.science/pith/BC7HM4ODHYSJMT2WBG2C23HOAW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BC7HM4ODHYSJMT2WBG2C23HOAW/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":"2026-06-01T20:12:29Z","links":{"resolver":"https://pith.science/pith/BC7HM4ODHYSJMT2WBG2C23HOAW","bundle":"https://pith.science/pith/BC7HM4ODHYSJMT2WBG2C23HOAW/bundle.json","state":"https://pith.science/pith/BC7HM4ODHYSJMT2WBG2C23HOAW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BC7HM4ODHYSJMT2WBG2C23HOAW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BC7HM4ODHYSJMT2WBG2C23HOAW","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":"542eb2ca788e991c9b10161c2cbcc5c1e12506fa8a092950dfdbf569e8e99b26","cross_cats_sorted":["math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-11-04T00:28:59Z","title_canon_sha256":"841b331cb33da6aec4ad363cd2317208efcdcc708d6c762343674bf064f7039a"},"schema_version":"1.0","source":{"id":"1111.1020","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1020","created_at":"2026-05-18T03:55:00Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1020v2","created_at":"2026-05-18T03:55:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1020","created_at":"2026-05-18T03:55:00Z"},{"alias_kind":"pith_short_12","alias_value":"BC7HM4ODHYSJ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BC7HM4ODHYSJMT2W","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BC7HM4OD","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:cc93d09e852a78edae22868abc1937762fbb43b78118203cc5268bea690abc8e","target":"graph","created_at":"2026-05-18T03:55:00Z","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 sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a graphical model with pairwise interactions, lies a matrix-vector product with complexity that is quadratic in the state dimension $d$, and requires transmission of a $(d-1)$-dimensional vector of real numbers (messages) to its neighbors. Since various applications involve very large state dimensions, such computation and communication complexities can be prohibit","authors_text":"Martin J. Wainwright, Nima Noorshams","cross_cats":["math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-11-04T00:28:59Z","title":"Stochastic Belief Propagation: A Low-Complexity Alternative to the Sum-Product Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1020","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:f435e821e423d3d03df8bfdc29eee191053569cb4b00956171ff15ff226b75c5","target":"record","created_at":"2026-05-18T03:55:00Z","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":"542eb2ca788e991c9b10161c2cbcc5c1e12506fa8a092950dfdbf569e8e99b26","cross_cats_sorted":["math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-11-04T00:28:59Z","title_canon_sha256":"841b331cb33da6aec4ad363cd2317208efcdcc708d6c762343674bf064f7039a"},"schema_version":"1.0","source":{"id":"1111.1020","kind":"arxiv","version":2}},"canonical_sha256":"08be7671c33e24964f5609b42d6cee05b9d49ad7344bb4db3801833ef2ebd587","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08be7671c33e24964f5609b42d6cee05b9d49ad7344bb4db3801833ef2ebd587","first_computed_at":"2026-05-18T03:55:00.322991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:00.322991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bKZ7rMYR6uuD7uPUlOq2wAbJpVaYoSGEaBCvnvgk8llwehTBbGfuF5Ju55nXKb6gZ/JtHPIxJ5bdZa2WfteIBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:00.323589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1020","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f435e821e423d3d03df8bfdc29eee191053569cb4b00956171ff15ff226b75c5","sha256:cc93d09e852a78edae22868abc1937762fbb43b78118203cc5268bea690abc8e"],"state_sha256":"4574542ba18a9dc003064e15a86a20efd18acc7c90b02d407ed2104f714a1b24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGxE1bEjdVXsZvtRX0mr8W20Mgulg9UsteesZVjVPKud3lRCgEP1bZ45rPhRulCnN+yTv1zCnZQ1amDO2MAVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:12:29.200592Z","bundle_sha256":"098c07025b1945a5cc2b46e61d2c198f1b7cf9088e8ae67f0fb79ec0d0feafb9"}}