{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:K56STSD3TEJ54YQJQ6BF2FFLJE","short_pith_number":"pith:K56STSD3","canonical_record":{"source":{"id":"1405.3250","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-05-13T18:39:11Z","cross_cats_sorted":["cs.DB","cs.LO"],"title_canon_sha256":"205b8cb63345c77c60e8c5781029752be5143bc04b47af893e2d480a77219d9b","abstract_canon_sha256":"aea39e2bb106c380393831835649cc805a5a5dffb96601e94043a21a3d2a34a3"},"schema_version":"1.0"},"canonical_sha256":"577d29c87b9913de620987825d14ab4903bbe6ab7c2a30412fec921a66db701f","source":{"kind":"arxiv","id":"1405.3250","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3250","created_at":"2026-07-05T00:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3250v2","created_at":"2026-07-05T00:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3250","created_at":"2026-07-05T00:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"K56STSD3TEJ5","created_at":"2026-07-05T00:18:25Z"},{"alias_kind":"pith_short_16","alias_value":"K56STSD3TEJ54YQJ","created_at":"2026-07-05T00:18:25Z"},{"alias_kind":"pith_short_8","alias_value":"K56STSD3","created_at":"2026-07-05T00:18:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:K56STSD3TEJ54YQJQ6BF2FFLJE","target":"record","payload":{"canonical_record":{"source":{"id":"1405.3250","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-05-13T18:39:11Z","cross_cats_sorted":["cs.DB","cs.LO"],"title_canon_sha256":"205b8cb63345c77c60e8c5781029752be5143bc04b47af893e2d480a77219d9b","abstract_canon_sha256":"aea39e2bb106c380393831835649cc805a5a5dffb96601e94043a21a3d2a34a3"},"schema_version":"1.0"},"canonical_sha256":"577d29c87b9913de620987825d14ab4903bbe6ab7c2a30412fec921a66db701f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:18:25.844145Z","signature_b64":"ZfWpVUCXfsEdRxL8zLl8Z5Ti0JIAardavEtGtj9sZieR6IcLIF8BywazUv0brd/Hp2RdQC1RycwtLftDYTtDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"577d29c87b9913de620987825d14ab4903bbe6ab7c2a30412fec921a66db701f","last_reissued_at":"2026-07-05T00:18:25.843808Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:18:25.843808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.3250","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":"2026-07-05T00:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5ZkuMTTk+7RyKH2k/unDW7fLxBaTZpZu1smBMjINeBuL5nHfCumiR+BmQLbpJ75GvAFlRN8kmsGDZd+KdFHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T09:54:54.884335Z"},"content_sha256":"95c7b2ab4aab0c4dd375c13e7b447da6fb20f2c5e6cf996586e8566392e69537","schema_version":"1.0","event_id":"sha256:95c7b2ab4aab0c4dd375c13e7b447da6fb20f2c5e6cf996586e8566392e69537"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:K56STSD3TEJ54YQJQ6BF2FFLJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DB","cs.LO"],"primary_cat":"cs.AI","authors_text":"Dan Suciu, Eric Gribkoff, Guy Van den Broeck","submitted_at":"2014-05-13T18:39:11Z","abstract_excerpt":"In this paper we study lifted inference for the Weighted First-Order Model Counting problem (WFOMC), which counts the assignments that satisfy a given sentence in first-order logic (FOL); it has applications in Statistical Relational Learning (SRL) and Probabilistic Databases (PDB). We present several results. First, we describe a lifted inference algorithm that generalizes prior approaches in SRL and PDB. Second, we provide a novel dichotomy result for a non-trivial fragment of FO CNF sentences, showing that for each sentence the WFOMC problem is either in PTIME or #P-hard in the size of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3250","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/1405.3250/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":"2026-07-05T00:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ZlpjItdvXNlE6LukEF2WfgtStKQFTsd7q0fcTRdRF8OJkZPv9yhfR/CMAyrctMV4oe1bpLsGkOq7TsnCExrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T09:54:54.885256Z"},"content_sha256":"8a8d82362c4d75660e411b7e94d4acdf2ca7ee874117ed90d832af9d13bada6f","schema_version":"1.0","event_id":"sha256:8a8d82362c4d75660e411b7e94d4acdf2ca7ee874117ed90d832af9d13bada6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K56STSD3TEJ54YQJQ6BF2FFLJE/bundle.json","state_url":"https://pith.science/pith/K56STSD3TEJ54YQJQ6BF2FFLJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K56STSD3TEJ54YQJQ6BF2FFLJE/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":"2026-08-05T09:54:54Z","links":{"resolver":"https://pith.science/pith/K56STSD3TEJ54YQJQ6BF2FFLJE","bundle":"https://pith.science/pith/K56STSD3TEJ54YQJQ6BF2FFLJE/bundle.json","state":"https://pith.science/pith/K56STSD3TEJ54YQJQ6BF2FFLJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K56STSD3TEJ54YQJQ6BF2FFLJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:K56STSD3TEJ54YQJQ6BF2FFLJE","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":"aea39e2bb106c380393831835649cc805a5a5dffb96601e94043a21a3d2a34a3","cross_cats_sorted":["cs.DB","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-05-13T18:39:11Z","title_canon_sha256":"205b8cb63345c77c60e8c5781029752be5143bc04b47af893e2d480a77219d9b"},"schema_version":"1.0","source":{"id":"1405.3250","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3250","created_at":"2026-07-05T00:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3250v2","created_at":"2026-07-05T00:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3250","created_at":"2026-07-05T00:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"K56STSD3TEJ5","created_at":"2026-07-05T00:18:25Z"},{"alias_kind":"pith_short_16","alias_value":"K56STSD3TEJ54YQJ","created_at":"2026-07-05T00:18:25Z"},{"alias_kind":"pith_short_8","alias_value":"K56STSD3","created_at":"2026-07-05T00:18:25Z"}],"graph_snapshots":[{"event_id":"sha256:8a8d82362c4d75660e411b7e94d4acdf2ca7ee874117ed90d832af9d13bada6f","target":"graph","created_at":"2026-07-05T00:18:25Z","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/1405.3250/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study lifted inference for the Weighted First-Order Model Counting problem (WFOMC), which counts the assignments that satisfy a given sentence in first-order logic (FOL); it has applications in Statistical Relational Learning (SRL) and Probabilistic Databases (PDB). We present several results. First, we describe a lifted inference algorithm that generalizes prior approaches in SRL and PDB. Second, we provide a novel dichotomy result for a non-trivial fragment of FO CNF sentences, showing that for each sentence the WFOMC problem is either in PTIME or #P-hard in the size of the ","authors_text":"Dan Suciu, Eric Gribkoff, Guy Van den Broeck","cross_cats":["cs.DB","cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-05-13T18:39:11Z","title":"Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3250","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":"sha256:95c7b2ab4aab0c4dd375c13e7b447da6fb20f2c5e6cf996586e8566392e69537","target":"record","created_at":"2026-07-05T00:18:25Z","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":"aea39e2bb106c380393831835649cc805a5a5dffb96601e94043a21a3d2a34a3","cross_cats_sorted":["cs.DB","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2014-05-13T18:39:11Z","title_canon_sha256":"205b8cb63345c77c60e8c5781029752be5143bc04b47af893e2d480a77219d9b"},"schema_version":"1.0","source":{"id":"1405.3250","kind":"arxiv","version":2}},"canonical_sha256":"577d29c87b9913de620987825d14ab4903bbe6ab7c2a30412fec921a66db701f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"577d29c87b9913de620987825d14ab4903bbe6ab7c2a30412fec921a66db701f","first_computed_at":"2026-07-05T00:18:25.843808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:18:25.843808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZfWpVUCXfsEdRxL8zLl8Z5Ti0JIAardavEtGtj9sZieR6IcLIF8BywazUv0brd/Hp2RdQC1RycwtLftDYTtDCg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:18:25.844145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3250","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95c7b2ab4aab0c4dd375c13e7b447da6fb20f2c5e6cf996586e8566392e69537","sha256:8a8d82362c4d75660e411b7e94d4acdf2ca7ee874117ed90d832af9d13bada6f"],"state_sha256":"787544fceb6b45ebe4a165226114bb390d14c7550f043689529b10a93dd7ec67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5Vku2T1KT5bDzGL8LDVk9JV34YpL82IlJT0qAXPeSTZkuCjTEDTjNXyUv+VB2PQ5VLvkvaieoWd0kjoOmnVCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T09:54:54.904035Z","bundle_sha256":"954caa436b18022dc4491612b76e7c10e4fed90eaf5d294dd92d892083e5d704"}}