{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DK6AVH6BMCXCPKHB23AIWLYGS4","short_pith_number":"pith:DK6AVH6B","canonical_record":{"source":{"id":"1206.5292","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-06-20T15:18:47Z","cross_cats_sorted":[],"title_canon_sha256":"a2cc4a84e8dbf417ba43f250827169a8cd48b49b20e6c65dfd70ede105c6aafc","abstract_canon_sha256":"dd6ad602a8590a9ab35f4a6e3704e1f0b1f78d1a279171676989a2306d8e72c7"},"schema_version":"1.0"},"canonical_sha256":"1abc0a9fc160ae27a8e1d6c08b2f06970b936f2f119452465f6f714aa653e3ac","source":{"kind":"arxiv","id":"1206.5292","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5292","created_at":"2026-05-18T03:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5292v1","created_at":"2026-05-18T03:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5292","created_at":"2026-05-18T03:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"DK6AVH6BMCXC","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DK6AVH6BMCXCPKHB","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DK6AVH6B","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DK6AVH6BMCXCPKHB23AIWLYGS4","target":"record","payload":{"canonical_record":{"source":{"id":"1206.5292","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-06-20T15:18:47Z","cross_cats_sorted":[],"title_canon_sha256":"a2cc4a84e8dbf417ba43f250827169a8cd48b49b20e6c65dfd70ede105c6aafc","abstract_canon_sha256":"dd6ad602a8590a9ab35f4a6e3704e1f0b1f78d1a279171676989a2306d8e72c7"},"schema_version":"1.0"},"canonical_sha256":"1abc0a9fc160ae27a8e1d6c08b2f06970b936f2f119452465f6f714aa653e3ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:40.497666Z","signature_b64":"ZNaghxYKxOc0/lUf9sv0O72vx2A9RbzKQWPMsFadzFF/AJgRNQg46iDZhccfGbKJQsOJ3hsZ3p0NMhzM/5DrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1abc0a9fc160ae27a8e1d6c08b2f06970b936f2f119452465f6f714aa653e3ac","last_reissued_at":"2026-05-18T03:52:40.497071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:40.497071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.5292","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":"2026-05-18T03:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IBNha9A8cfWVlBzmK/zFE/+XUuFJVJDjsNjqDeFymGKh3f2zTac0f6FVovcbozOx7q4zEYvkHfjUMx/54ilADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:58:02.383631Z"},"content_sha256":"b95838ab2a0fe15ade0d2b2820ad6c147a6da39a2946e64349cc26b285db1d31","schema_version":"1.0","event_id":"sha256:b95838ab2a0fe15ade0d2b2820ad6c147a6da39a2946e64349cc26b285db1d31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DK6AVH6BMCXCPKHB23AIWLYGS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Markov Logic in Infinite Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Parag Singla, Pedro Domingos","submitted_at":"2012-06-20T15:18:47Z","abstract_excerpt":"Combining first-order logic and probability has long been a goal of AI. Markov logic (Richardson & Domingos, 2006) accomplishes this by attaching weights to first-order formulas and viewing them as templates for features of Markov networks. Unfortunately, it does not have the full power of first-order logic, because it is only defined for finite domains. This paper extends Markov logic to infinite domains, by casting it in the framework of Gibbs measures (Georgii, 1988). We show that a Markov logic network (MLN) admits a Gibbs measure as long as each ground atom has a finite number of neighbor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5292","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":"2026-05-18T03:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Gk9IQKz1lzZikXvLuwPB5tTa5QP2Lf9pzPvmb2rNF943CGXviWG/SpEutyXgABX1yF6zul1lya+CwaPXWJgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:58:02.384296Z"},"content_sha256":"f7412550fe9b30f04627ce3b0787c0307509949bdbb8faa2643ceffc61b25793","schema_version":"1.0","event_id":"sha256:f7412550fe9b30f04627ce3b0787c0307509949bdbb8faa2643ceffc61b25793"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DK6AVH6BMCXCPKHB23AIWLYGS4/bundle.json","state_url":"https://pith.science/pith/DK6AVH6BMCXCPKHB23AIWLYGS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DK6AVH6BMCXCPKHB23AIWLYGS4/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":"2026-05-26T04:58:02Z","links":{"resolver":"https://pith.science/pith/DK6AVH6BMCXCPKHB23AIWLYGS4","bundle":"https://pith.science/pith/DK6AVH6BMCXCPKHB23AIWLYGS4/bundle.json","state":"https://pith.science/pith/DK6AVH6BMCXCPKHB23AIWLYGS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DK6AVH6BMCXCPKHB23AIWLYGS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DK6AVH6BMCXCPKHB23AIWLYGS4","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":"dd6ad602a8590a9ab35f4a6e3704e1f0b1f78d1a279171676989a2306d8e72c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-06-20T15:18:47Z","title_canon_sha256":"a2cc4a84e8dbf417ba43f250827169a8cd48b49b20e6c65dfd70ede105c6aafc"},"schema_version":"1.0","source":{"id":"1206.5292","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5292","created_at":"2026-05-18T03:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5292v1","created_at":"2026-05-18T03:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5292","created_at":"2026-05-18T03:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"DK6AVH6BMCXC","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DK6AVH6BMCXCPKHB","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DK6AVH6B","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:f7412550fe9b30f04627ce3b0787c0307509949bdbb8faa2643ceffc61b25793","target":"graph","created_at":"2026-05-18T03:52:40Z","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":"Combining first-order logic and probability has long been a goal of AI. Markov logic (Richardson & Domingos, 2006) accomplishes this by attaching weights to first-order formulas and viewing them as templates for features of Markov networks. Unfortunately, it does not have the full power of first-order logic, because it is only defined for finite domains. This paper extends Markov logic to infinite domains, by casting it in the framework of Gibbs measures (Georgii, 1988). We show that a Markov logic network (MLN) admits a Gibbs measure as long as each ground atom has a finite number of neighbor","authors_text":"Parag Singla, Pedro Domingos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-06-20T15:18:47Z","title":"Markov Logic in Infinite Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5292","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:b95838ab2a0fe15ade0d2b2820ad6c147a6da39a2946e64349cc26b285db1d31","target":"record","created_at":"2026-05-18T03:52:40Z","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":"dd6ad602a8590a9ab35f4a6e3704e1f0b1f78d1a279171676989a2306d8e72c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2012-06-20T15:18:47Z","title_canon_sha256":"a2cc4a84e8dbf417ba43f250827169a8cd48b49b20e6c65dfd70ede105c6aafc"},"schema_version":"1.0","source":{"id":"1206.5292","kind":"arxiv","version":1}},"canonical_sha256":"1abc0a9fc160ae27a8e1d6c08b2f06970b936f2f119452465f6f714aa653e3ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1abc0a9fc160ae27a8e1d6c08b2f06970b936f2f119452465f6f714aa653e3ac","first_computed_at":"2026-05-18T03:52:40.497071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:40.497071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZNaghxYKxOc0/lUf9sv0O72vx2A9RbzKQWPMsFadzFF/AJgRNQg46iDZhccfGbKJQsOJ3hsZ3p0NMhzM/5DrAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:40.497666Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5292","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b95838ab2a0fe15ade0d2b2820ad6c147a6da39a2946e64349cc26b285db1d31","sha256:f7412550fe9b30f04627ce3b0787c0307509949bdbb8faa2643ceffc61b25793"],"state_sha256":"5f75b52f93afae83a7c9334318102d0d29c750e6fd19e4d53a02a1d9e9578de3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6QqtaFplcqJnK223wy+0HoHUgv6x5gHSsgj/YdsdTuqVX6qAg3Nftv6qVKbDHTcdEm22Cri1iLu+h6R3IavuCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:58:02.387424Z","bundle_sha256":"17a1aaae9e2deed41cd9fd615dce3e4f0dc357a7e6b1589ad6b31cf435a3afca"}}