{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:J5RLNAIOXYGWGHMTCEEX6OO6IV","short_pith_number":"pith:J5RLNAIO","canonical_record":{"source":{"id":"2007.09450","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2020-07-18T15:16:13Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"3ab3eee00582e9a43b9ef6b3f2d968639e8280e971364e8d79fe3f7d9ad350f9","abstract_canon_sha256":"9b50d8efb10f4da86038ef781dd9bf57bbed293737c7c2b0c1c1b1dadc393eea"},"schema_version":"1.0"},"canonical_sha256":"4f62b6810ebe0d631d9311097f39de455fc48b0d5b4369446111bf508555ad2c","source":{"kind":"arxiv","id":"2007.09450","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.09450","created_at":"2026-07-05T01:22:02Z"},{"alias_kind":"arxiv_version","alias_value":"2007.09450v2","created_at":"2026-07-05T01:22:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.09450","created_at":"2026-07-05T01:22:02Z"},{"alias_kind":"pith_short_12","alias_value":"J5RLNAIOXYGW","created_at":"2026-07-05T01:22:02Z"},{"alias_kind":"pith_short_16","alias_value":"J5RLNAIOXYGWGHMT","created_at":"2026-07-05T01:22:02Z"},{"alias_kind":"pith_short_8","alias_value":"J5RLNAIO","created_at":"2026-07-05T01:22:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:J5RLNAIOXYGWGHMTCEEX6OO6IV","target":"record","payload":{"canonical_record":{"source":{"id":"2007.09450","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2020-07-18T15:16:13Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"3ab3eee00582e9a43b9ef6b3f2d968639e8280e971364e8d79fe3f7d9ad350f9","abstract_canon_sha256":"9b50d8efb10f4da86038ef781dd9bf57bbed293737c7c2b0c1c1b1dadc393eea"},"schema_version":"1.0"},"canonical_sha256":"4f62b6810ebe0d631d9311097f39de455fc48b0d5b4369446111bf508555ad2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:22:02.793271Z","signature_b64":"MAT44cFM9G1JlSO8j+Wp2kz2apMP31J5NkF33KR1BABpS6CP2serHfGNzsNxD9fbrU//gN31s+rHWyc6+xq4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f62b6810ebe0d631d9311097f39de455fc48b0d5b4369446111bf508555ad2c","last_reissued_at":"2026-07-05T01:22:02.792873Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:22:02.792873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.09450","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":"2026-07-05T01:22:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RTcu5xQ1Qevr9l/XiRBWTZNwn6rSbQgy97GiINvHcZr/3epS/XmuVMvRX3//1sdC6ZaUFvXXGeaQWVNO+ri5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T03:54:31.502586Z"},"content_sha256":"771dd8602f343ecfe136e34864a9e90eb633cadeac80f000d50160505f636741","schema_version":"1.0","event_id":"sha256:771dd8602f343ecfe136e34864a9e90eb633cadeac80f000d50160505f636741"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:J5RLNAIOXYGWGHMTCEEX6OO6IV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of Bayesian Networks via Prob-Solvable Loops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"cs.AI","authors_text":"Ezio Bartocci, Laura Kov\\'acs, Miroslav Stankovi\\v{c}","submitted_at":"2020-07-18T15:16:13Z","abstract_excerpt":"Prob-solvable loops are probabilistic programs with polynomial assignments over random variables and parametrised distributions, for which the full automation of moment-based invariant generation is decidable. In this paper we extend Prob-solvable loops with new features essential for encoding Bayesian networks (BNs). We show that various BNs, such as discrete, Gaussian, conditional linear Gaussian and dynamic BNs, can be naturally encoded as Prob-solvable loops. Thanks to these encodings, we can automatically solve several BN related problems, including exact inference, sensitivity analysis, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.09450","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.09450/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":"2026-07-05T01:22:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ycqo+TzfINGg83B8H+TfY1j5yJaF7XCbHxjdiT5PKSBVVtVfiUJHo2fSRc1bAV59oV72AEOCJuV0iRfU4dUIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T03:54:31.502964Z"},"content_sha256":"373b2ceed87935b23fabe5790250a81b227b4f3fc076b1034a8aa4d2e6a6bf0c","schema_version":"1.0","event_id":"sha256:373b2ceed87935b23fabe5790250a81b227b4f3fc076b1034a8aa4d2e6a6bf0c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5RLNAIOXYGWGHMTCEEX6OO6IV/bundle.json","state_url":"https://pith.science/pith/J5RLNAIOXYGWGHMTCEEX6OO6IV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5RLNAIOXYGWGHMTCEEX6OO6IV/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":"2026-07-17T03:54:31Z","links":{"resolver":"https://pith.science/pith/J5RLNAIOXYGWGHMTCEEX6OO6IV","bundle":"https://pith.science/pith/J5RLNAIOXYGWGHMTCEEX6OO6IV/bundle.json","state":"https://pith.science/pith/J5RLNAIOXYGWGHMTCEEX6OO6IV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5RLNAIOXYGWGHMTCEEX6OO6IV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:J5RLNAIOXYGWGHMTCEEX6OO6IV","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":"9b50d8efb10f4da86038ef781dd9bf57bbed293737c7c2b0c1c1b1dadc393eea","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2020-07-18T15:16:13Z","title_canon_sha256":"3ab3eee00582e9a43b9ef6b3f2d968639e8280e971364e8d79fe3f7d9ad350f9"},"schema_version":"1.0","source":{"id":"2007.09450","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.09450","created_at":"2026-07-05T01:22:02Z"},{"alias_kind":"arxiv_version","alias_value":"2007.09450v2","created_at":"2026-07-05T01:22:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.09450","created_at":"2026-07-05T01:22:02Z"},{"alias_kind":"pith_short_12","alias_value":"J5RLNAIOXYGW","created_at":"2026-07-05T01:22:02Z"},{"alias_kind":"pith_short_16","alias_value":"J5RLNAIOXYGWGHMT","created_at":"2026-07-05T01:22:02Z"},{"alias_kind":"pith_short_8","alias_value":"J5RLNAIO","created_at":"2026-07-05T01:22:02Z"}],"graph_snapshots":[{"event_id":"sha256:373b2ceed87935b23fabe5790250a81b227b4f3fc076b1034a8aa4d2e6a6bf0c","target":"graph","created_at":"2026-07-05T01:22:02Z","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/2007.09450/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Prob-solvable loops are probabilistic programs with polynomial assignments over random variables and parametrised distributions, for which the full automation of moment-based invariant generation is decidable. In this paper we extend Prob-solvable loops with new features essential for encoding Bayesian networks (BNs). We show that various BNs, such as discrete, Gaussian, conditional linear Gaussian and dynamic BNs, can be naturally encoded as Prob-solvable loops. Thanks to these encodings, we can automatically solve several BN related problems, including exact inference, sensitivity analysis, ","authors_text":"Ezio Bartocci, Laura Kov\\'acs, Miroslav Stankovi\\v{c}","cross_cats":["cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2020-07-18T15:16:13Z","title":"Analysis of Bayesian Networks via Prob-Solvable Loops"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.09450","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":"sha256:771dd8602f343ecfe136e34864a9e90eb633cadeac80f000d50160505f636741","target":"record","created_at":"2026-07-05T01:22:02Z","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":"9b50d8efb10f4da86038ef781dd9bf57bbed293737c7c2b0c1c1b1dadc393eea","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2020-07-18T15:16:13Z","title_canon_sha256":"3ab3eee00582e9a43b9ef6b3f2d968639e8280e971364e8d79fe3f7d9ad350f9"},"schema_version":"1.0","source":{"id":"2007.09450","kind":"arxiv","version":2}},"canonical_sha256":"4f62b6810ebe0d631d9311097f39de455fc48b0d5b4369446111bf508555ad2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f62b6810ebe0d631d9311097f39de455fc48b0d5b4369446111bf508555ad2c","first_computed_at":"2026-07-05T01:22:02.792873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:22:02.792873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MAT44cFM9G1JlSO8j+Wp2kz2apMP31J5NkF33KR1BABpS6CP2serHfGNzsNxD9fbrU//gN31s+rHWyc6+xq4BA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:22:02.793271Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.09450","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:771dd8602f343ecfe136e34864a9e90eb633cadeac80f000d50160505f636741","sha256:373b2ceed87935b23fabe5790250a81b227b4f3fc076b1034a8aa4d2e6a6bf0c"],"state_sha256":"e49aaabc0578985bbc1c664ea0540c9f7a51982ab1f9a9e9cc4a5171da717f7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xt+ZBKkcAyKkqZhI6Pv+6KPEqYf580ci9w67+cAhqhVIn/EhcvMp27mdXaOZ8belb30kMWzIbxFegf9/cmy0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-17T03:54:31.505412Z","bundle_sha256":"745c24808385d6f5eea27dc312a0ab05b4f29b73055f5a395f3ea1069c10ccde"}}