{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RL5IEMCO2HAPRB7GL3EPTEBFVV","short_pith_number":"pith:RL5IEMCO","canonical_record":{"source":{"id":"1804.07919","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-04-21T08:55:41Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1804d777ffb896b366edc64dacfdd926315eaa6963c30b7484ed175afaf21b30","abstract_canon_sha256":"278d0f28dd776bbbb35d23fbaa3f88e74e3286cded0fecb400277b1134bd43f6"},"schema_version":"1.0"},"canonical_sha256":"8afa82304ed1c0f887e65ec8f99025ad7caccd31d5a2ba708ed1d71c796b2393","source":{"kind":"arxiv","id":"1804.07919","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07919","created_at":"2026-05-18T00:17:50Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07919v1","created_at":"2026-05-18T00:17:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07919","created_at":"2026-05-18T00:17:50Z"},{"alias_kind":"pith_short_12","alias_value":"RL5IEMCO2HAP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RL5IEMCO2HAPRB7G","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RL5IEMCO","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RL5IEMCO2HAPRB7GL3EPTEBFVV","target":"record","payload":{"canonical_record":{"source":{"id":"1804.07919","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-04-21T08:55:41Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1804d777ffb896b366edc64dacfdd926315eaa6963c30b7484ed175afaf21b30","abstract_canon_sha256":"278d0f28dd776bbbb35d23fbaa3f88e74e3286cded0fecb400277b1134bd43f6"},"schema_version":"1.0"},"canonical_sha256":"8afa82304ed1c0f887e65ec8f99025ad7caccd31d5a2ba708ed1d71c796b2393","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:50.201293Z","signature_b64":"/8m67UzNUTYt32EBBwl0KSS+iDr/RQDa2FXhhahSMfNo6jgU/BwfNiRDEPCRnR0g69ZHy0Usgy/XYFXzfEoXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8afa82304ed1c0f887e65ec8f99025ad7caccd31d5a2ba708ed1d71c796b2393","last_reissued_at":"2026-05-18T00:17:50.200586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:50.200586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.07919","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":"2026-05-18T00:17:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p2g/A2WhsWqkLiIMHLp1eP++cM3Ww7jebz8a3QMeZIq3i76aRSv9Ql3yjn5JZ9vif/iWrDyN8LiZDcb+3/zSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T23:17:45.948024Z"},"content_sha256":"631516f7a0c18a068745a1f981ad97c8ce464bafde6c33b937286974d3d75909","schema_version":"1.0","event_id":"sha256:631516f7a0c18a068745a1f981ad97c8ce464bafde6c33b937286974d3d75909"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RL5IEMCO2HAPRB7GL3EPTEBFVV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Probabilistic Analysis of Balancing Scores for Causal Inference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Priyantha Wijayatunga","submitted_at":"2018-04-21T08:55:41Z","abstract_excerpt":"Propensity scores are often used for stratification of treatment and control groups of subjects in observational data to remove confounding bias when estimating of causal effect of the treatment on an outcome in so-called potential outcome causal modeling framework. In this article, we try to get some insights into basic behavior of the propensity scores in a probabilistic sense. We do a simple analysis of their usage confining to the case of discrete confounding covariates and outcomes. While making clear about behavior of the propensity score our analysis shows how the so-called prognostic s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07919","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":"2026-05-18T00:17:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EtvxrN8vO8c7mdLmqtcnd0fLadt2fjjZKzKD0xTxpNdqO2bY4FGQxd2LtP8Jhqj7dxkqPrZHoNKUzawCYHG5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T23:17:45.948383Z"},"content_sha256":"50d65108225e95d5f906769d7a27086543a8ba298040bc28b4713e4286426408","schema_version":"1.0","event_id":"sha256:50d65108225e95d5f906769d7a27086543a8ba298040bc28b4713e4286426408"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RL5IEMCO2HAPRB7GL3EPTEBFVV/bundle.json","state_url":"https://pith.science/pith/RL5IEMCO2HAPRB7GL3EPTEBFVV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RL5IEMCO2HAPRB7GL3EPTEBFVV/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":"2026-06-27T23:17:45Z","links":{"resolver":"https://pith.science/pith/RL5IEMCO2HAPRB7GL3EPTEBFVV","bundle":"https://pith.science/pith/RL5IEMCO2HAPRB7GL3EPTEBFVV/bundle.json","state":"https://pith.science/pith/RL5IEMCO2HAPRB7GL3EPTEBFVV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RL5IEMCO2HAPRB7GL3EPTEBFVV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RL5IEMCO2HAPRB7GL3EPTEBFVV","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":"278d0f28dd776bbbb35d23fbaa3f88e74e3286cded0fecb400277b1134bd43f6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-04-21T08:55:41Z","title_canon_sha256":"1804d777ffb896b366edc64dacfdd926315eaa6963c30b7484ed175afaf21b30"},"schema_version":"1.0","source":{"id":"1804.07919","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07919","created_at":"2026-05-18T00:17:50Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07919v1","created_at":"2026-05-18T00:17:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07919","created_at":"2026-05-18T00:17:50Z"},{"alias_kind":"pith_short_12","alias_value":"RL5IEMCO2HAP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RL5IEMCO2HAPRB7G","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RL5IEMCO","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:50d65108225e95d5f906769d7a27086543a8ba298040bc28b4713e4286426408","target":"graph","created_at":"2026-05-18T00:17:50Z","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":"Propensity scores are often used for stratification of treatment and control groups of subjects in observational data to remove confounding bias when estimating of causal effect of the treatment on an outcome in so-called potential outcome causal modeling framework. In this article, we try to get some insights into basic behavior of the propensity scores in a probabilistic sense. We do a simple analysis of their usage confining to the case of discrete confounding covariates and outcomes. While making clear about behavior of the propensity score our analysis shows how the so-called prognostic s","authors_text":"Priyantha Wijayatunga","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-04-21T08:55:41Z","title":"Probabilistic Analysis of Balancing Scores for Causal Inference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07919","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":"sha256:631516f7a0c18a068745a1f981ad97c8ce464bafde6c33b937286974d3d75909","target":"record","created_at":"2026-05-18T00:17:50Z","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":"278d0f28dd776bbbb35d23fbaa3f88e74e3286cded0fecb400277b1134bd43f6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-04-21T08:55:41Z","title_canon_sha256":"1804d777ffb896b366edc64dacfdd926315eaa6963c30b7484ed175afaf21b30"},"schema_version":"1.0","source":{"id":"1804.07919","kind":"arxiv","version":1}},"canonical_sha256":"8afa82304ed1c0f887e65ec8f99025ad7caccd31d5a2ba708ed1d71c796b2393","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8afa82304ed1c0f887e65ec8f99025ad7caccd31d5a2ba708ed1d71c796b2393","first_computed_at":"2026-05-18T00:17:50.200586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:50.200586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/8m67UzNUTYt32EBBwl0KSS+iDr/RQDa2FXhhahSMfNo6jgU/BwfNiRDEPCRnR0g69ZHy0Usgy/XYFXzfEoXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:50.201293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07919","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:631516f7a0c18a068745a1f981ad97c8ce464bafde6c33b937286974d3d75909","sha256:50d65108225e95d5f906769d7a27086543a8ba298040bc28b4713e4286426408"],"state_sha256":"d80d07e215787f37948efa682d2369de6c69659d077672dbd52444607b1d2787"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hyJy3Ke4NInmDyc8IqfRuU00cHvUpUL97Vf6668fmD7zfVJqa8+Ck2f0E8QdYafE17dSEkRoLDkefQLXaqS2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T23:17:45.950257Z","bundle_sha256":"4173c33bb6b8c26419898c5b68cc4bbbece4c6c08fe5ce9e86aa1c917c4f8729"}}