{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QBL4Y2W6M7RBHCGN4HSC7GVW3V","short_pith_number":"pith:QBL4Y2W6","canonical_record":{"source":{"id":"1206.6825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-06-27T15:41:21Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"4939d8b8b3ad674f7e9336e7226ae1a40a07b6a2a61202c021c2d2d4d0c40712","abstract_canon_sha256":"088fdfde7a31bb6e84a98bee069075fd681f3f6c0e934273fa4bc5880df69634"},"schema_version":"1.0"},"canonical_sha256":"8057cc6ade67e21388cde1e42f9ab6dd7296a230e7dc387fe1659148479ee42a","source":{"kind":"arxiv","id":"1206.6825","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6825","created_at":"2026-05-18T03:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6825v1","created_at":"2026-05-18T03:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6825","created_at":"2026-05-18T03:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"QBL4Y2W6M7RB","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QBL4Y2W6M7RBHCGN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QBL4Y2W6","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QBL4Y2W6M7RBHCGN4HSC7GVW3V","target":"record","payload":{"canonical_record":{"source":{"id":"1206.6825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-06-27T15:41:21Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"4939d8b8b3ad674f7e9336e7226ae1a40a07b6a2a61202c021c2d2d4d0c40712","abstract_canon_sha256":"088fdfde7a31bb6e84a98bee069075fd681f3f6c0e934273fa4bc5880df69634"},"schema_version":"1.0"},"canonical_sha256":"8057cc6ade67e21388cde1e42f9ab6dd7296a230e7dc387fe1659148479ee42a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:15.785459Z","signature_b64":"KuhLXlH/CwBDKZDVJxrHcelSM4CEyzyEZSXs4bmvt486lhZNCR9qBv/jwvvjYMzyiPNBRYofPnkMoQp6zc4oAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8057cc6ade67e21388cde1e42f9ab6dd7296a230e7dc387fe1659148479ee42a","last_reissued_at":"2026-05-18T03:52:15.784882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:15.784882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.6825","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":"2026-05-18T03:52:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rhfVkN1sPGJxLXe6RQ5S6x11lip+r8RfPQdF50ghPbNyJgW0MxLVzpiaVFQuxeYj9lj+60S+AuEMvSZKkhpaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T04:29:13.331622Z"},"content_sha256":"63f8e403dbc19df0145b9bd26f0179253bbca377d85b2a6d6ff3456b5eba41e1","schema_version":"1.0","event_id":"sha256:63f8e403dbc19df0145b9bd26f0179253bbca377d85b2a6d6ff3456b5eba41e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QBL4Y2W6M7RBHCGN4HSC7GVW3V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Minimal Triangulations for Mixed Stochastic/Deterministic Graphical Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.AI","authors_text":"Chris Bartels, Jeff A. Bilmes","submitted_at":"2012-06-27T15:41:21Z","abstract_excerpt":"We observe that certain large-clique graph triangulations can be useful to reduce both computational and space requirements when making queries on mixed stochastic/deterministic graphical models. We demonstrate that many of these large-clique triangulations are non-minimal and are thus unattainable via the variable elimination algorithm. We introduce ancestral pairs as the basis for novel triangulation heuristics and prove that no more than the addition of edges between ancestral pairs need be considered when searching for state space optimal triangulations in such graphs. Empirical results on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6825","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":"2026-05-18T03:52:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oIJh8OWLkSHbT6EZnIaj6pwiR4ecZdGUQhaXjH1lNVza8RTDaUqwOLnySGyyqQbjZz369ImYykY9GurORMwBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T04:29:13.332047Z"},"content_sha256":"a8f06c5ecbc96af93686019a165de59beb3c4ad5abacd7374d4fc6b856aa90c9","schema_version":"1.0","event_id":"sha256:a8f06c5ecbc96af93686019a165de59beb3c4ad5abacd7374d4fc6b856aa90c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBL4Y2W6M7RBHCGN4HSC7GVW3V/bundle.json","state_url":"https://pith.science/pith/QBL4Y2W6M7RBHCGN4HSC7GVW3V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBL4Y2W6M7RBHCGN4HSC7GVW3V/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":"2026-05-23T04:29:13Z","links":{"resolver":"https://pith.science/pith/QBL4Y2W6M7RBHCGN4HSC7GVW3V","bundle":"https://pith.science/pith/QBL4Y2W6M7RBHCGN4HSC7GVW3V/bundle.json","state":"https://pith.science/pith/QBL4Y2W6M7RBHCGN4HSC7GVW3V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBL4Y2W6M7RBHCGN4HSC7GVW3V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QBL4Y2W6M7RBHCGN4HSC7GVW3V","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":"088fdfde7a31bb6e84a98bee069075fd681f3f6c0e934273fa4bc5880df69634","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-06-27T15:41:21Z","title_canon_sha256":"4939d8b8b3ad674f7e9336e7226ae1a40a07b6a2a61202c021c2d2d4d0c40712"},"schema_version":"1.0","source":{"id":"1206.6825","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6825","created_at":"2026-05-18T03:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6825v1","created_at":"2026-05-18T03:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6825","created_at":"2026-05-18T03:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"QBL4Y2W6M7RB","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QBL4Y2W6M7RBHCGN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QBL4Y2W6","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:a8f06c5ecbc96af93686019a165de59beb3c4ad5abacd7374d4fc6b856aa90c9","target":"graph","created_at":"2026-05-18T03:52:15Z","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":"We observe that certain large-clique graph triangulations can be useful to reduce both computational and space requirements when making queries on mixed stochastic/deterministic graphical models. We demonstrate that many of these large-clique triangulations are non-minimal and are thus unattainable via the variable elimination algorithm. We introduce ancestral pairs as the basis for novel triangulation heuristics and prove that no more than the addition of edges between ancestral pairs need be considered when searching for state space optimal triangulations in such graphs. Empirical results on","authors_text":"Chris Bartels, Jeff A. Bilmes","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-06-27T15:41:21Z","title":"Non-Minimal Triangulations for Mixed Stochastic/Deterministic Graphical Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6825","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":"sha256:63f8e403dbc19df0145b9bd26f0179253bbca377d85b2a6d6ff3456b5eba41e1","target":"record","created_at":"2026-05-18T03:52:15Z","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":"088fdfde7a31bb6e84a98bee069075fd681f3f6c0e934273fa4bc5880df69634","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-06-27T15:41:21Z","title_canon_sha256":"4939d8b8b3ad674f7e9336e7226ae1a40a07b6a2a61202c021c2d2d4d0c40712"},"schema_version":"1.0","source":{"id":"1206.6825","kind":"arxiv","version":1}},"canonical_sha256":"8057cc6ade67e21388cde1e42f9ab6dd7296a230e7dc387fe1659148479ee42a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8057cc6ade67e21388cde1e42f9ab6dd7296a230e7dc387fe1659148479ee42a","first_computed_at":"2026-05-18T03:52:15.784882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:15.784882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KuhLXlH/CwBDKZDVJxrHcelSM4CEyzyEZSXs4bmvt486lhZNCR9qBv/jwvvjYMzyiPNBRYofPnkMoQp6zc4oAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:15.785459Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6825","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63f8e403dbc19df0145b9bd26f0179253bbca377d85b2a6d6ff3456b5eba41e1","sha256:a8f06c5ecbc96af93686019a165de59beb3c4ad5abacd7374d4fc6b856aa90c9"],"state_sha256":"af7b1f00314a6d1aa6650d5fabcacf0b678ccde248d1f3e77d69159c7f25e66f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7Y3bBc/gsCogIT2GHe7zjGcOq44lpnNR+usEyzLPgAHBq8JZup/0H1hnP6I/yq7onkrljgm5NnlrzWy1RhHBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T04:29:13.335413Z","bundle_sha256":"eda91930507c8ab52a4601d71044eb2be8b271432f14a422ab64681ea6bec216"}}