{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LEBD7NAOT7W72M6IDRB2VX7R4I","short_pith_number":"pith:LEBD7NAO","canonical_record":{"source":{"id":"1103.1472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-08T09:18:00Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"046daae4466aa5219ef8e74ce962ec59a8fef6a6e4982cb029cc6bc4f9ccc641","abstract_canon_sha256":"08057dd77ef3574f56e4b7a2609e1bf7b0a83fa96130aec1c2f97567950d5efc"},"schema_version":"1.0"},"canonical_sha256":"59023fb40e9fedfd33c81c43aadff1e20c9dac3fbaadf10cae65f54ce54f62fa","source":{"kind":"arxiv","id":"1103.1472","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1472","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1472v1","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1472","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"LEBD7NAOT7W7","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LEBD7NAOT7W72M6I","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LEBD7NAO","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LEBD7NAOT7W72M6IDRB2VX7R4I","target":"record","payload":{"canonical_record":{"source":{"id":"1103.1472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-08T09:18:00Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"046daae4466aa5219ef8e74ce962ec59a8fef6a6e4982cb029cc6bc4f9ccc641","abstract_canon_sha256":"08057dd77ef3574f56e4b7a2609e1bf7b0a83fa96130aec1c2f97567950d5efc"},"schema_version":"1.0"},"canonical_sha256":"59023fb40e9fedfd33c81c43aadff1e20c9dac3fbaadf10cae65f54ce54f62fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:15.801721Z","signature_b64":"DYuknq2DoCZlkROOfiNWXYeBQF9w/niKSedtV5bqJRLb1RRkz0IN1PVS6fse9RdzkAcLvf3sLg8V5sHw2o+9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59023fb40e9fedfd33c81c43aadff1e20c9dac3fbaadf10cae65f54ce54f62fa","last_reissued_at":"2026-05-18T04:27:15.801188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:15.801188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.1472","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":"2026-05-18T04:27:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8kcEIPSmKaIje13EmMIXv+35OS+jrP2D8lLKN7eVc2LsPqjv6kkkPdDu1cmSjf0NlX1IUrPZ62uGq2P5h1oDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T13:49:15.999543Z"},"content_sha256":"a67ea4a146948ff9bae588920cfae19b733c8f97068ecfac2be33bcc7ba43a26","schema_version":"1.0","event_id":"sha256:a67ea4a146948ff9bae588920cfae19b733c8f97068ecfac2be33bcc7ba43a26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LEBD7NAOT7W72M6IDRB2VX7R4I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Causal inference for continuous-time processes when covariates are observed only at discrete times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dylan S. Small, Marshall M. Joffe, Mingyuan Zhang","submitted_at":"2011-03-08T09:18:00Z","abstract_excerpt":"Most of the work on the structural nested model and g-estimation for causal inference in longitudinal data assumes a discrete-time underlying data generating process. However, in some observational studies, it is more reasonable to assume that the data are generated from a continuous-time process and are only observable at discrete time points. When these circumstances arise, the sequential randomization assumption in the observed discrete-time data, which is essential in justifying discrete-time g-estimation, may not be reasonable. Under a deterministic model, we discuss other useful assumpti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1472","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":"2026-05-18T04:27:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hzAvFykqNOVzLFliXTFvl6shLFHS+zUVBfrFJbEZENdqK2UDqr0KTfHKbXrm6gUPmO3Wvn4dp2V6h5KTIME2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T13:49:16.000226Z"},"content_sha256":"b646210800f5e4527e020764e8381a2645ed13c12ae6921138efbd16089e208a","schema_version":"1.0","event_id":"sha256:b646210800f5e4527e020764e8381a2645ed13c12ae6921138efbd16089e208a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LEBD7NAOT7W72M6IDRB2VX7R4I/bundle.json","state_url":"https://pith.science/pith/LEBD7NAOT7W72M6IDRB2VX7R4I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LEBD7NAOT7W72M6IDRB2VX7R4I/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":"2026-05-24T13:49:16Z","links":{"resolver":"https://pith.science/pith/LEBD7NAOT7W72M6IDRB2VX7R4I","bundle":"https://pith.science/pith/LEBD7NAOT7W72M6IDRB2VX7R4I/bundle.json","state":"https://pith.science/pith/LEBD7NAOT7W72M6IDRB2VX7R4I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LEBD7NAOT7W72M6IDRB2VX7R4I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LEBD7NAOT7W72M6IDRB2VX7R4I","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":"08057dd77ef3574f56e4b7a2609e1bf7b0a83fa96130aec1c2f97567950d5efc","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-08T09:18:00Z","title_canon_sha256":"046daae4466aa5219ef8e74ce962ec59a8fef6a6e4982cb029cc6bc4f9ccc641"},"schema_version":"1.0","source":{"id":"1103.1472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1472","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1472v1","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1472","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"LEBD7NAOT7W7","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LEBD7NAOT7W72M6I","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LEBD7NAO","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:b646210800f5e4527e020764e8381a2645ed13c12ae6921138efbd16089e208a","target":"graph","created_at":"2026-05-18T04:27:15Z","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":"Most of the work on the structural nested model and g-estimation for causal inference in longitudinal data assumes a discrete-time underlying data generating process. However, in some observational studies, it is more reasonable to assume that the data are generated from a continuous-time process and are only observable at discrete time points. When these circumstances arise, the sequential randomization assumption in the observed discrete-time data, which is essential in justifying discrete-time g-estimation, may not be reasonable. Under a deterministic model, we discuss other useful assumpti","authors_text":"Dylan S. Small, Marshall M. Joffe, Mingyuan Zhang","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-08T09:18:00Z","title":"Causal inference for continuous-time processes when covariates are observed only at discrete times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1472","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:a67ea4a146948ff9bae588920cfae19b733c8f97068ecfac2be33bcc7ba43a26","target":"record","created_at":"2026-05-18T04:27:15Z","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":"08057dd77ef3574f56e4b7a2609e1bf7b0a83fa96130aec1c2f97567950d5efc","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-08T09:18:00Z","title_canon_sha256":"046daae4466aa5219ef8e74ce962ec59a8fef6a6e4982cb029cc6bc4f9ccc641"},"schema_version":"1.0","source":{"id":"1103.1472","kind":"arxiv","version":1}},"canonical_sha256":"59023fb40e9fedfd33c81c43aadff1e20c9dac3fbaadf10cae65f54ce54f62fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59023fb40e9fedfd33c81c43aadff1e20c9dac3fbaadf10cae65f54ce54f62fa","first_computed_at":"2026-05-18T04:27:15.801188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:15.801188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DYuknq2DoCZlkROOfiNWXYeBQF9w/niKSedtV5bqJRLb1RRkz0IN1PVS6fse9RdzkAcLvf3sLg8V5sHw2o+9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:15.801721Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a67ea4a146948ff9bae588920cfae19b733c8f97068ecfac2be33bcc7ba43a26","sha256:b646210800f5e4527e020764e8381a2645ed13c12ae6921138efbd16089e208a"],"state_sha256":"28c654ef2e2c7637f8d85590c2c2ae5a255bcaa2422ba09dd16e6c9cc88ef5c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I8S12F5LeYWoJYVjOXjcxhHsPwavYMfueJxCPlaeLTrtwha7EpeVuczbUSYYp6o9D1UyJ8zZvk8jt+M5j5QHDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T13:49:16.003668Z","bundle_sha256":"37bafdf912e36f6bf59097517dbb609759f5f85ce4664667d34dc63271db790d"}}