{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UP77UCQ6RJU5T4AAHH37WWWFKI","short_pith_number":"pith:UP77UCQ6","canonical_record":{"source":{"id":"1705.07411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-21T08:11:44Z","cross_cats_sorted":["math.AC","stat.TH"],"title_canon_sha256":"c380b94d990eb87bca4551cd74416ed4abd759ee039d6802a0f9bfa447f60227","abstract_canon_sha256":"e328bb20e747a27b6b5e18b7d7268f4fe41e4167616e99e4d6b8905237504ee0"},"schema_version":"1.0"},"canonical_sha256":"a3fffa0a1e8a69d9f00039f7fb5ac5521b25981f6d92a622c4a6769ec879cff9","source":{"kind":"arxiv","id":"1705.07411","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07411","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07411v1","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07411","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"pith_short_12","alias_value":"UP77UCQ6RJU5","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UP77UCQ6RJU5T4AA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UP77UCQ6","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UP77UCQ6RJU5T4AAHH37WWWFKI","target":"record","payload":{"canonical_record":{"source":{"id":"1705.07411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-21T08:11:44Z","cross_cats_sorted":["math.AC","stat.TH"],"title_canon_sha256":"c380b94d990eb87bca4551cd74416ed4abd759ee039d6802a0f9bfa447f60227","abstract_canon_sha256":"e328bb20e747a27b6b5e18b7d7268f4fe41e4167616e99e4d6b8905237504ee0"},"schema_version":"1.0"},"canonical_sha256":"a3fffa0a1e8a69d9f00039f7fb5ac5521b25981f6d92a622c4a6769ec879cff9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:05.671966Z","signature_b64":"o/ZR54EHTvHqcv7LDaNU6tsHqchc7ln4+zpTgDy4CaEmkzXXyiiQNFXwx2yDBtuaazseurBtur4TtXw6iNhqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3fffa0a1e8a69d9f00039f7fb5ac5521b25981f6d92a622c4a6769ec879cff9","last_reissued_at":"2026-05-18T00:44:05.671430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:05.671430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.07411","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":"2026-05-18T00:44:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rDWzFaYkMB4dLOttB38xy5UdlYEOXu9FFWmUpSPX8v2wN6vi6aIU0sU/TMC6d8AWKFlVep+ZYotv5ZtTqrOrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:31:45.287070Z"},"content_sha256":"7839cca5d66bbb0df178dd1e5064e141f2a2bf4d3e545c424cb5fade5e311bc4","schema_version":"1.0","event_id":"sha256:7839cca5d66bbb0df178dd1e5064e141f2a2bf4d3e545c424cb5fade5e311bc4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UP77UCQ6RJU5T4AAHH37WWWFKI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Aspects of Conditional Independence and Graphical Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","stat.TH"],"primary_cat":"math.ST","authors_text":"Johannes Rauh, Seth Sullivant, Thomas Kahle","submitted_at":"2017-05-21T08:11:44Z","abstract_excerpt":"This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional independence and graphical models. It also introduces binomial ideals and some ideas from real algebraic geometry. When random variables are discrete or Gaussian, tools from computational algebraic geometry can be used to understand implications between conditional independence statements. This is accomplished by computing primary decompositions of conditional independence ideals. As examples the chapt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07411","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":"2026-05-18T00:44:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gu4eol/wtuwIG4+hboCD6MPU+3YkVWwoXCE5cfnpSGW05L3c3ATybhKcpN8NcXxpSLxtKt0AG9CgHF94aNnNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:31:45.287814Z"},"content_sha256":"b5c79f5c50eccd069a30e6cbeb40144be82d4edf962146e7beeaa12f3b1c59fb","schema_version":"1.0","event_id":"sha256:b5c79f5c50eccd069a30e6cbeb40144be82d4edf962146e7beeaa12f3b1c59fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UP77UCQ6RJU5T4AAHH37WWWFKI/bundle.json","state_url":"https://pith.science/pith/UP77UCQ6RJU5T4AAHH37WWWFKI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UP77UCQ6RJU5T4AAHH37WWWFKI/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":"2026-05-31T20:31:45Z","links":{"resolver":"https://pith.science/pith/UP77UCQ6RJU5T4AAHH37WWWFKI","bundle":"https://pith.science/pith/UP77UCQ6RJU5T4AAHH37WWWFKI/bundle.json","state":"https://pith.science/pith/UP77UCQ6RJU5T4AAHH37WWWFKI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UP77UCQ6RJU5T4AAHH37WWWFKI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UP77UCQ6RJU5T4AAHH37WWWFKI","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":"e328bb20e747a27b6b5e18b7d7268f4fe41e4167616e99e4d6b8905237504ee0","cross_cats_sorted":["math.AC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-21T08:11:44Z","title_canon_sha256":"c380b94d990eb87bca4551cd74416ed4abd759ee039d6802a0f9bfa447f60227"},"schema_version":"1.0","source":{"id":"1705.07411","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07411","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07411v1","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07411","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"pith_short_12","alias_value":"UP77UCQ6RJU5","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UP77UCQ6RJU5T4AA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UP77UCQ6","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:b5c79f5c50eccd069a30e6cbeb40144be82d4edf962146e7beeaa12f3b1c59fb","target":"graph","created_at":"2026-05-18T00:44:05Z","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":"This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional independence and graphical models. It also introduces binomial ideals and some ideas from real algebraic geometry. When random variables are discrete or Gaussian, tools from computational algebraic geometry can be used to understand implications between conditional independence statements. This is accomplished by computing primary decompositions of conditional independence ideals. As examples the chapt","authors_text":"Johannes Rauh, Seth Sullivant, Thomas Kahle","cross_cats":["math.AC","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-21T08:11:44Z","title":"Algebraic Aspects of Conditional Independence and Graphical Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07411","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":"sha256:7839cca5d66bbb0df178dd1e5064e141f2a2bf4d3e545c424cb5fade5e311bc4","target":"record","created_at":"2026-05-18T00:44:05Z","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":"e328bb20e747a27b6b5e18b7d7268f4fe41e4167616e99e4d6b8905237504ee0","cross_cats_sorted":["math.AC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-21T08:11:44Z","title_canon_sha256":"c380b94d990eb87bca4551cd74416ed4abd759ee039d6802a0f9bfa447f60227"},"schema_version":"1.0","source":{"id":"1705.07411","kind":"arxiv","version":1}},"canonical_sha256":"a3fffa0a1e8a69d9f00039f7fb5ac5521b25981f6d92a622c4a6769ec879cff9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3fffa0a1e8a69d9f00039f7fb5ac5521b25981f6d92a622c4a6769ec879cff9","first_computed_at":"2026-05-18T00:44:05.671430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:05.671430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o/ZR54EHTvHqcv7LDaNU6tsHqchc7ln4+zpTgDy4CaEmkzXXyiiQNFXwx2yDBtuaazseurBtur4TtXw6iNhqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:05.671966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07411","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7839cca5d66bbb0df178dd1e5064e141f2a2bf4d3e545c424cb5fade5e311bc4","sha256:b5c79f5c50eccd069a30e6cbeb40144be82d4edf962146e7beeaa12f3b1c59fb"],"state_sha256":"4407b82998be1a8d8c3b0caa6dd8117a4a81c12748cd336b42c62fc2e3855019"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jtxnznaqpvvtHkYJlGETdgIm9kBo5RxGO6R++0JObkjAUIsp/P+1ZXnhGgBFk7jLyO7euSSpZrYVCY32fT+dAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:31:45.291459Z","bundle_sha256":"e56c45c7c66f992df2e2a0c1a37fa424aaf494f1362852c63a2e669ca2d45c4d"}}