{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VC2TDGZJZAV4BOPJFFVX6WHN35","short_pith_number":"pith:VC2TDGZJ","canonical_record":{"source":{"id":"1402.0558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-02-04T01:33:50Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"8aee6d95dbe205a20d3925827619f143b618392208b38e37aa6870ca0936ea21","abstract_canon_sha256":"32ca0c5d8365520de7fe5d93753928967ae301740959c82cf75d6075b3550cd1"},"schema_version":"1.0"},"canonical_sha256":"a8b5319b29c82bc0b9e9296b7f58eddf6f280cf5cf4d46946ab7bfc2d6b8924a","source":{"kind":"arxiv","id":"1402.0558","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0558","created_at":"2026-05-18T03:00:13Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0558v1","created_at":"2026-05-18T03:00:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0558","created_at":"2026-05-18T03:00:13Z"},{"alias_kind":"pith_short_12","alias_value":"VC2TDGZJZAV4","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VC2TDGZJZAV4BOPJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VC2TDGZJ","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VC2TDGZJZAV4BOPJFFVX6WHN35","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-02-04T01:33:50Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"8aee6d95dbe205a20d3925827619f143b618392208b38e37aa6870ca0936ea21","abstract_canon_sha256":"32ca0c5d8365520de7fe5d93753928967ae301740959c82cf75d6075b3550cd1"},"schema_version":"1.0"},"canonical_sha256":"a8b5319b29c82bc0b9e9296b7f58eddf6f280cf5cf4d46946ab7bfc2d6b8924a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:13.965203Z","signature_b64":"32WBPDj04DLWnKTK7xoqI3EQYjVrQ7xUxTHxxeQz9cthCCI8ZiNvVK4BZNlEjG7iX/ozfF2gmuvdgPz4jhfhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8b5319b29c82bc0b9e9296b7f58eddf6f280cf5cf4d46946ab7bfc2d6b8924a","last_reissued_at":"2026-05-18T03:00:13.964404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:13.964404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0558","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":"2026-05-18T03:00:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1eCKMqG/tAk4wQJyUDSys8lDXbEkhDMkZT0fRDX3aN9xesQ0YXmEH72Oj2nhlFxmzIBb2wnyt8hMoY/AJAj6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:57:25.444336Z"},"content_sha256":"2dacd085bb1818c6746823bdded2398e5224c455cb83c3871e65ecb3e16b7e41","schema_version":"1.0","event_id":"sha256:2dacd085bb1818c6746823bdded2398e5224c455cb83c3871e65ecb3e16b7e41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VC2TDGZJZAV4BOPJFFVX6WHN35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parameterized Complexity Results for Exact Bayesian Network Structure Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.AI","authors_text":"Sebastian Ordyniak, Stefan Szeider","submitted_at":"2014-02-04T01:33:50Z","abstract_excerpt":"Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data.  In this paper we study the computational worst-case complexity of exact Bayesian network structure learning under graph theoretic restrictions on the (directed) super-structure.  The super-structure is an undirected graph that contains as subgraphs the skeletons of solution networks. We introduce the directed super-structure as a natural generalization of its undirected counterpart. Our results apply to several variants of score-bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0558","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":"2026-05-18T03:00:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMPyCvpOOC2sPIe7h8b+8BUkM+rnlvDUd0h3lOE1WfA9q4IGt/bsm+qGa+/JVI0VTDEuI75o52Q/XUQZlGylAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:57:25.445032Z"},"content_sha256":"95d21862abc71c43627cbc14f2056348d2cf81af740fd3ee8db4467ea57143f7","schema_version":"1.0","event_id":"sha256:95d21862abc71c43627cbc14f2056348d2cf81af740fd3ee8db4467ea57143f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VC2TDGZJZAV4BOPJFFVX6WHN35/bundle.json","state_url":"https://pith.science/pith/VC2TDGZJZAV4BOPJFFVX6WHN35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VC2TDGZJZAV4BOPJFFVX6WHN35/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":"2026-05-28T21:57:25Z","links":{"resolver":"https://pith.science/pith/VC2TDGZJZAV4BOPJFFVX6WHN35","bundle":"https://pith.science/pith/VC2TDGZJZAV4BOPJFFVX6WHN35/bundle.json","state":"https://pith.science/pith/VC2TDGZJZAV4BOPJFFVX6WHN35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VC2TDGZJZAV4BOPJFFVX6WHN35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VC2TDGZJZAV4BOPJFFVX6WHN35","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":"32ca0c5d8365520de7fe5d93753928967ae301740959c82cf75d6075b3550cd1","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-02-04T01:33:50Z","title_canon_sha256":"8aee6d95dbe205a20d3925827619f143b618392208b38e37aa6870ca0936ea21"},"schema_version":"1.0","source":{"id":"1402.0558","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0558","created_at":"2026-05-18T03:00:13Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0558v1","created_at":"2026-05-18T03:00:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0558","created_at":"2026-05-18T03:00:13Z"},{"alias_kind":"pith_short_12","alias_value":"VC2TDGZJZAV4","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VC2TDGZJZAV4BOPJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VC2TDGZJ","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:95d21862abc71c43627cbc14f2056348d2cf81af740fd3ee8db4467ea57143f7","target":"graph","created_at":"2026-05-18T03:00:13Z","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":"Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data.  In this paper we study the computational worst-case complexity of exact Bayesian network structure learning under graph theoretic restrictions on the (directed) super-structure.  The super-structure is an undirected graph that contains as subgraphs the skeletons of solution networks. We introduce the directed super-structure as a natural generalization of its undirected counterpart. Our results apply to several variants of score-bas","authors_text":"Sebastian Ordyniak, Stefan Szeider","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-02-04T01:33:50Z","title":"Parameterized Complexity Results for Exact Bayesian Network Structure Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0558","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":"sha256:2dacd085bb1818c6746823bdded2398e5224c455cb83c3871e65ecb3e16b7e41","target":"record","created_at":"2026-05-18T03:00:13Z","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":"32ca0c5d8365520de7fe5d93753928967ae301740959c82cf75d6075b3550cd1","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-02-04T01:33:50Z","title_canon_sha256":"8aee6d95dbe205a20d3925827619f143b618392208b38e37aa6870ca0936ea21"},"schema_version":"1.0","source":{"id":"1402.0558","kind":"arxiv","version":1}},"canonical_sha256":"a8b5319b29c82bc0b9e9296b7f58eddf6f280cf5cf4d46946ab7bfc2d6b8924a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8b5319b29c82bc0b9e9296b7f58eddf6f280cf5cf4d46946ab7bfc2d6b8924a","first_computed_at":"2026-05-18T03:00:13.964404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:13.964404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"32WBPDj04DLWnKTK7xoqI3EQYjVrQ7xUxTHxxeQz9cthCCI8ZiNvVK4BZNlEjG7iX/ozfF2gmuvdgPz4jhfhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:13.965203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0558","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dacd085bb1818c6746823bdded2398e5224c455cb83c3871e65ecb3e16b7e41","sha256:95d21862abc71c43627cbc14f2056348d2cf81af740fd3ee8db4467ea57143f7"],"state_sha256":"5eaf27b594d92924935e1eae8ce0788c338b90351ec36885b8b54eaeda3742c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/dGP5Df8j7hv5CMAmumGd/IvQWvky1d0jylhuv4JFSgNXSGkiY50gvAostCuBi0AIeh7g8kVh3e60QNQpULBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:57:25.448358Z","bundle_sha256":"72ec2d5643fe9d1ad4bda5eda087d7ba341aa57135527f22f1eb3acce115c3ab"}}