{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KO7DX7NDWVA2YOL6QZPGWEDXA5","short_pith_number":"pith:KO7DX7ND","canonical_record":{"source":{"id":"1303.1499","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-03-06T14:22:41Z","cross_cats_sorted":[],"title_canon_sha256":"c869c15c78e075766fde0b24734e35173222e169070e8582ab2dd34c18d86106","abstract_canon_sha256":"7d9dfcb9b29a1947fb1597055ee31899eeb4a101936895b41ded3187cbe24242"},"schema_version":"1.0"},"canonical_sha256":"53be3bfda3b541ac397e865e6b1077077cdfc937f36b35e546d5c5c3b737d0c4","source":{"kind":"arxiv","id":"1303.1499","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1499","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1499v1","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1499","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"pith_short_12","alias_value":"KO7DX7NDWVA2","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KO7DX7NDWVA2YOL6","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KO7DX7ND","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KO7DX7NDWVA2YOL6QZPGWEDXA5","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1499","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-03-06T14:22:41Z","cross_cats_sorted":[],"title_canon_sha256":"c869c15c78e075766fde0b24734e35173222e169070e8582ab2dd34c18d86106","abstract_canon_sha256":"7d9dfcb9b29a1947fb1597055ee31899eeb4a101936895b41ded3187cbe24242"},"schema_version":"1.0"},"canonical_sha256":"53be3bfda3b541ac397e865e6b1077077cdfc937f36b35e546d5c5c3b737d0c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:42.532506Z","signature_b64":"JJwm1AFJ7EXfTyHxbKYJ9Y2GFVMk3uQ6JkEYB1K4TW3z5lXjN3K98icU0bNGpIzaZpwMLRtj7PToJ07fnmzMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53be3bfda3b541ac397e865e6b1077077cdfc937f36b35e546d5c5c3b737d0c4","last_reissued_at":"2026-05-18T03:31:42.532017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:42.532017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1499","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":"2026-05-18T03:31:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kwhbDZJGgRYF3lpvlLB5Uxcr16IThsEmzipz6eL2dBqZXx1iyFSZzNkI5b24BJ4XlSAePuzjjii7sxhVdqHiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:12:06.057032Z"},"content_sha256":"7bc61871a11e589c024a92c56a4e55cdeea941c37457c107e6958507ffdacee8","schema_version":"1.0","event_id":"sha256:7bc61871a11e589c024a92c56a4e55cdeea941c37457c107e6958507ffdacee8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KO7DX7NDWVA2YOL6QZPGWEDXA5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Using Tree-Decomposable Structures to Approximate Belief Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Sumit Sarkar","submitted_at":"2013-03-06T14:22:41Z","abstract_excerpt":"Tree structures have been shown to provide an efficient framework for propagating beliefs [Pearl,1986].  This paper studies the problem of finding an optimal approximating tree.  The star decomposition scheme for sets of three binary variables [Lazarsfeld,1966; Pearl,1986] is shown to enhance the class of probability distributions that can support tree structures; such structures are called tree-decomposable structures.  The logarithm scoring rule is found to be an appropriate optimality criterion to evaluate different tree-decomposable structures.  Characteristics of such structures closest t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1499","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":"2026-05-18T03:31:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yL1HdLsLddr1r8d7FIaGLReDbhQnDhAFDOBPWj8Ip84bfSFUB9D1KeIpC7YuNdlF2eVQlrvszcUNxGV77I18CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:12:06.057689Z"},"content_sha256":"5dd341c18f5ecb8b87030c98d3a21b4f82a20f0bb056a1e4e69055b005940d41","schema_version":"1.0","event_id":"sha256:5dd341c18f5ecb8b87030c98d3a21b4f82a20f0bb056a1e4e69055b005940d41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KO7DX7NDWVA2YOL6QZPGWEDXA5/bundle.json","state_url":"https://pith.science/pith/KO7DX7NDWVA2YOL6QZPGWEDXA5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KO7DX7NDWVA2YOL6QZPGWEDXA5/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":"2026-06-07T22:12:06Z","links":{"resolver":"https://pith.science/pith/KO7DX7NDWVA2YOL6QZPGWEDXA5","bundle":"https://pith.science/pith/KO7DX7NDWVA2YOL6QZPGWEDXA5/bundle.json","state":"https://pith.science/pith/KO7DX7NDWVA2YOL6QZPGWEDXA5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KO7DX7NDWVA2YOL6QZPGWEDXA5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KO7DX7NDWVA2YOL6QZPGWEDXA5","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":"7d9dfcb9b29a1947fb1597055ee31899eeb4a101936895b41ded3187cbe24242","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-03-06T14:22:41Z","title_canon_sha256":"c869c15c78e075766fde0b24734e35173222e169070e8582ab2dd34c18d86106"},"schema_version":"1.0","source":{"id":"1303.1499","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1499","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1499v1","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1499","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"pith_short_12","alias_value":"KO7DX7NDWVA2","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KO7DX7NDWVA2YOL6","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KO7DX7ND","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:5dd341c18f5ecb8b87030c98d3a21b4f82a20f0bb056a1e4e69055b005940d41","target":"graph","created_at":"2026-05-18T03:31:42Z","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":"Tree structures have been shown to provide an efficient framework for propagating beliefs [Pearl,1986].  This paper studies the problem of finding an optimal approximating tree.  The star decomposition scheme for sets of three binary variables [Lazarsfeld,1966; Pearl,1986] is shown to enhance the class of probability distributions that can support tree structures; such structures are called tree-decomposable structures.  The logarithm scoring rule is found to be an appropriate optimality criterion to evaluate different tree-decomposable structures.  Characteristics of such structures closest t","authors_text":"Sumit Sarkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-03-06T14:22:41Z","title":"Using Tree-Decomposable Structures to Approximate Belief Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1499","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":"sha256:7bc61871a11e589c024a92c56a4e55cdeea941c37457c107e6958507ffdacee8","target":"record","created_at":"2026-05-18T03:31:42Z","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":"7d9dfcb9b29a1947fb1597055ee31899eeb4a101936895b41ded3187cbe24242","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-03-06T14:22:41Z","title_canon_sha256":"c869c15c78e075766fde0b24734e35173222e169070e8582ab2dd34c18d86106"},"schema_version":"1.0","source":{"id":"1303.1499","kind":"arxiv","version":1}},"canonical_sha256":"53be3bfda3b541ac397e865e6b1077077cdfc937f36b35e546d5c5c3b737d0c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53be3bfda3b541ac397e865e6b1077077cdfc937f36b35e546d5c5c3b737d0c4","first_computed_at":"2026-05-18T03:31:42.532017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:42.532017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JJwm1AFJ7EXfTyHxbKYJ9Y2GFVMk3uQ6JkEYB1K4TW3z5lXjN3K98icU0bNGpIzaZpwMLRtj7PToJ07fnmzMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:42.532506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1499","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bc61871a11e589c024a92c56a4e55cdeea941c37457c107e6958507ffdacee8","sha256:5dd341c18f5ecb8b87030c98d3a21b4f82a20f0bb056a1e4e69055b005940d41"],"state_sha256":"137c9acc07d551233ecf27e35bcddd855b84f11564bcba02d2f8c0c1afceb681"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lOABeucYPLRXKR2WvgEaGsh/3iKtpYHcUc6yaUbIwwanAKZ8CUPJBCExaUWk5DFSfniHXAA1aLTToLZTPWmLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:12:06.060846Z","bundle_sha256":"3f6d1549964d59d2fb65149db33c040ef7f2fc8dfc42746286a2159ba5d6b472"}}