{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XG6QXKEBT2BQ4OHCMF4R6HO3IG","short_pith_number":"pith:XG6QXKEB","canonical_record":{"source":{"id":"1805.05485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-14T22:45:13Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"d47efcb8f1628bcf1b169b9b0e6cda7e6b1b06e97816bae1990cdf9028d9cacb","abstract_canon_sha256":"8160af28f8e7026c7c1c4405897a888ddf3388c6f340e089ac7ee9ef8f71f6af"},"schema_version":"1.0"},"canonical_sha256":"b9bd0ba8819e830e38e261791f1ddb419a5fe93c24ef1b1c091154ca3e25e1a7","source":{"kind":"arxiv","id":"1805.05485","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05485","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05485v1","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05485","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"pith_short_12","alias_value":"XG6QXKEBT2BQ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XG6QXKEBT2BQ4OHC","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XG6QXKEB","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XG6QXKEBT2BQ4OHCMF4R6HO3IG","target":"record","payload":{"canonical_record":{"source":{"id":"1805.05485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-14T22:45:13Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"d47efcb8f1628bcf1b169b9b0e6cda7e6b1b06e97816bae1990cdf9028d9cacb","abstract_canon_sha256":"8160af28f8e7026c7c1c4405897a888ddf3388c6f340e089ac7ee9ef8f71f6af"},"schema_version":"1.0"},"canonical_sha256":"b9bd0ba8819e830e38e261791f1ddb419a5fe93c24ef1b1c091154ca3e25e1a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:00.484602Z","signature_b64":"rgsvPYDLYgniz6v0QZt+niQavhQWqX4GxEokjmKX2KhPZIagwv2bzpjDZ+YkiuRzrBflUhS7amvxmUvAkJCbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9bd0ba8819e830e38e261791f1ddb419a5fe93c24ef1b1c091154ca3e25e1a7","last_reissued_at":"2026-05-18T00:16:00.484098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:00.484098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.05485","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":"2026-05-18T00:16:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cZKarIT5OwuSK1ex6Yx2owMbzPT1SUpTuc20V0NhDPAprX5kp7uXPfXFULMQKoaep+NK4s5jZqM3LU1SMCGpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:29:51.861958Z"},"content_sha256":"d37c9a64bf562979499d3759b914da89ba7ece429f89607bae5e6fdeda8b8abc","schema_version":"1.0","event_id":"sha256:d37c9a64bf562979499d3759b914da89ba7ece429f89607bae5e6fdeda8b8abc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XG6QXKEBT2BQ4OHCMF4R6HO3IG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Maximum Likelihood Threshold of a Path Diagram","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andreas K\\\"aufl, Christopher Fox, Guillaume Pouliot, Mathias Drton","submitted_at":"2018-05-14T22:45:13Z","abstract_excerpt":"Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and bidirected edges that indicate possible correlations among noise terms. Using this graphical representation, we determine the maximum likelihood threshold, that is, the minimum sample size at which the likelihood function of a Gaussian structural equation model is almost surely bounded. Our result allows the model to have feedback loops and is based on decomp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05485","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":"2026-05-18T00:16:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UrpzmFZK4oPavcpYNfzaiSNcyWoC6VZGdhOguDbqFIi4/CITVT2NIfLLAyGqnesoF5Ae65riV/Wu1MOgvejaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:29:51.862688Z"},"content_sha256":"68783b22cda2b48080243075083c852857b00f4bf8c21ca3f7dd451042470546","schema_version":"1.0","event_id":"sha256:68783b22cda2b48080243075083c852857b00f4bf8c21ca3f7dd451042470546"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XG6QXKEBT2BQ4OHCMF4R6HO3IG/bundle.json","state_url":"https://pith.science/pith/XG6QXKEBT2BQ4OHCMF4R6HO3IG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XG6QXKEBT2BQ4OHCMF4R6HO3IG/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":"2026-06-10T10:29:51Z","links":{"resolver":"https://pith.science/pith/XG6QXKEBT2BQ4OHCMF4R6HO3IG","bundle":"https://pith.science/pith/XG6QXKEBT2BQ4OHCMF4R6HO3IG/bundle.json","state":"https://pith.science/pith/XG6QXKEBT2BQ4OHCMF4R6HO3IG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XG6QXKEBT2BQ4OHCMF4R6HO3IG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XG6QXKEBT2BQ4OHCMF4R6HO3IG","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":"8160af28f8e7026c7c1c4405897a888ddf3388c6f340e089ac7ee9ef8f71f6af","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-14T22:45:13Z","title_canon_sha256":"d47efcb8f1628bcf1b169b9b0e6cda7e6b1b06e97816bae1990cdf9028d9cacb"},"schema_version":"1.0","source":{"id":"1805.05485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05485","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05485v1","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05485","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"pith_short_12","alias_value":"XG6QXKEBT2BQ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XG6QXKEBT2BQ4OHC","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XG6QXKEB","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:68783b22cda2b48080243075083c852857b00f4bf8c21ca3f7dd451042470546","target":"graph","created_at":"2026-05-18T00:16:00Z","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":"Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and bidirected edges that indicate possible correlations among noise terms. Using this graphical representation, we determine the maximum likelihood threshold, that is, the minimum sample size at which the likelihood function of a Gaussian structural equation model is almost surely bounded. Our result allows the model to have feedback loops and is based on decomp","authors_text":"Andreas K\\\"aufl, Christopher Fox, Guillaume Pouliot, Mathias Drton","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-14T22:45:13Z","title":"The Maximum Likelihood Threshold of a Path Diagram"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05485","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:d37c9a64bf562979499d3759b914da89ba7ece429f89607bae5e6fdeda8b8abc","target":"record","created_at":"2026-05-18T00:16:00Z","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":"8160af28f8e7026c7c1c4405897a888ddf3388c6f340e089ac7ee9ef8f71f6af","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-14T22:45:13Z","title_canon_sha256":"d47efcb8f1628bcf1b169b9b0e6cda7e6b1b06e97816bae1990cdf9028d9cacb"},"schema_version":"1.0","source":{"id":"1805.05485","kind":"arxiv","version":1}},"canonical_sha256":"b9bd0ba8819e830e38e261791f1ddb419a5fe93c24ef1b1c091154ca3e25e1a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9bd0ba8819e830e38e261791f1ddb419a5fe93c24ef1b1c091154ca3e25e1a7","first_computed_at":"2026-05-18T00:16:00.484098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:00.484098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rgsvPYDLYgniz6v0QZt+niQavhQWqX4GxEokjmKX2KhPZIagwv2bzpjDZ+YkiuRzrBflUhS7amvxmUvAkJCbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:00.484602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.05485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d37c9a64bf562979499d3759b914da89ba7ece429f89607bae5e6fdeda8b8abc","sha256:68783b22cda2b48080243075083c852857b00f4bf8c21ca3f7dd451042470546"],"state_sha256":"7eaf72539cd4e334208b7db1cbfb3f3bee0ce4bbcd8ce6eb2f82048a9a47d09a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfHNS7YMlh2h9i7cWqujgK3Vj8sW/GgKC/z6Cx0sKc12E9wsNLPYbY8JBthXQOlzOBgUt3vPsaStExeKfUYnCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:29:51.865645Z","bundle_sha256":"d40f614d295d66ba19554f4b1136b51f374fe601cd87fdb751918d9e3c1e04af"}}