{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YN2NU72EJH3WXGDSESZZ2WLIKN","short_pith_number":"pith:YN2NU72E","canonical_record":{"source":{"id":"1601.00736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-01-05T05:08:33Z","cross_cats_sorted":[],"title_canon_sha256":"b544d58cb0e9f49c41b9d679b21b531170e9aca44ad16730a88c32397c8c5524","abstract_canon_sha256":"30e301da5c49c174f625a10a7db39f6a6ea889e9abde06a6be5408af20e5f0d4"},"schema_version":"1.0"},"canonical_sha256":"c374da7f4449f76b987224b39d5968537467bef37a84a6e68fb3922fb8e317de","source":{"kind":"arxiv","id":"1601.00736","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00736","created_at":"2026-05-18T01:23:22Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00736v1","created_at":"2026-05-18T01:23:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00736","created_at":"2026-05-18T01:23:22Z"},{"alias_kind":"pith_short_12","alias_value":"YN2NU72EJH3W","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YN2NU72EJH3WXGDS","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YN2NU72E","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YN2NU72EJH3WXGDSESZZ2WLIKN","target":"record","payload":{"canonical_record":{"source":{"id":"1601.00736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-01-05T05:08:33Z","cross_cats_sorted":[],"title_canon_sha256":"b544d58cb0e9f49c41b9d679b21b531170e9aca44ad16730a88c32397c8c5524","abstract_canon_sha256":"30e301da5c49c174f625a10a7db39f6a6ea889e9abde06a6be5408af20e5f0d4"},"schema_version":"1.0"},"canonical_sha256":"c374da7f4449f76b987224b39d5968537467bef37a84a6e68fb3922fb8e317de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:22.026232Z","signature_b64":"GxU1RjDoUg7M5npVOMcoaruJ8tB4cC5zK/1o8A+V/ua3jgNPYR32T0ByVx8BOqjDydFPedaO0nBmIfbOK4nuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c374da7f4449f76b987224b39d5968537467bef37a84a6e68fb3922fb8e317de","last_reissued_at":"2026-05-18T01:23:22.025456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:22.025456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.00736","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":"2026-05-18T01:23:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/yoQvYh8YgcOWQzv8ipKuwK0xDDqcijAhJ8yB8oTEYIME2i/l14I85koh/p1phKtSLixO0qK+5sLxGXgPBPPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:12:32.620620Z"},"content_sha256":"027905822e017ff277e6df5a01cf2a1c119b9c3bfd626f50682eb26c0554da25","schema_version":"1.0","event_id":"sha256:027905822e017ff277e6df5a01cf2a1c119b9c3bfd626f50682eb26c0554da25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YN2NU72EJH3WXGDSESZZ2WLIKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Penalized Maximum Likelihood Estimation of Multi-layered Gaussian Graphical Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"George Michailidis, Jiahe Lin, Moulinath Banerjee, Sumanta Basu","submitted_at":"2016-01-05T05:08:33Z","abstract_excerpt":"Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum likelihood estimator for Gaussian multi-layered graphical models, based on a computational approach involving screening of variables, iterative estimation of the directed edges between layers and undirected edges within layers and a final refitting and stability selection step that provides improved performance in finite sample settings. We establish the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00736","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":"2026-05-18T01:23:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tFRTXdflD41A3gOzAdo/fJWhuYlwaxnCFo+vAZpmEz0HYKWFABdJpV95mVTmkspdlMqwErQqfIH/Ubb+x8j0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:12:32.620969Z"},"content_sha256":"824ced41d0aa6f50c4ea81bde74590200fdc2538c67eb8082f689e0770f9d1f3","schema_version":"1.0","event_id":"sha256:824ced41d0aa6f50c4ea81bde74590200fdc2538c67eb8082f689e0770f9d1f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YN2NU72EJH3WXGDSESZZ2WLIKN/bundle.json","state_url":"https://pith.science/pith/YN2NU72EJH3WXGDSESZZ2WLIKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YN2NU72EJH3WXGDSESZZ2WLIKN/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":"2026-06-02T23:12:32Z","links":{"resolver":"https://pith.science/pith/YN2NU72EJH3WXGDSESZZ2WLIKN","bundle":"https://pith.science/pith/YN2NU72EJH3WXGDSESZZ2WLIKN/bundle.json","state":"https://pith.science/pith/YN2NU72EJH3WXGDSESZZ2WLIKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YN2NU72EJH3WXGDSESZZ2WLIKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YN2NU72EJH3WXGDSESZZ2WLIKN","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":"30e301da5c49c174f625a10a7db39f6a6ea889e9abde06a6be5408af20e5f0d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-01-05T05:08:33Z","title_canon_sha256":"b544d58cb0e9f49c41b9d679b21b531170e9aca44ad16730a88c32397c8c5524"},"schema_version":"1.0","source":{"id":"1601.00736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00736","created_at":"2026-05-18T01:23:22Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00736v1","created_at":"2026-05-18T01:23:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00736","created_at":"2026-05-18T01:23:22Z"},{"alias_kind":"pith_short_12","alias_value":"YN2NU72EJH3W","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YN2NU72EJH3WXGDS","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YN2NU72E","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:824ced41d0aa6f50c4ea81bde74590200fdc2538c67eb8082f689e0770f9d1f3","target":"graph","created_at":"2026-05-18T01:23:22Z","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":"Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum likelihood estimator for Gaussian multi-layered graphical models, based on a computational approach involving screening of variables, iterative estimation of the directed edges between layers and undirected edges within layers and a final refitting and stability selection step that provides improved performance in finite sample settings. We establish the co","authors_text":"George Michailidis, Jiahe Lin, Moulinath Banerjee, Sumanta Basu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-01-05T05:08:33Z","title":"Penalized Maximum Likelihood Estimation of Multi-layered Gaussian Graphical Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00736","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":"sha256:027905822e017ff277e6df5a01cf2a1c119b9c3bfd626f50682eb26c0554da25","target":"record","created_at":"2026-05-18T01:23:22Z","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":"30e301da5c49c174f625a10a7db39f6a6ea889e9abde06a6be5408af20e5f0d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-01-05T05:08:33Z","title_canon_sha256":"b544d58cb0e9f49c41b9d679b21b531170e9aca44ad16730a88c32397c8c5524"},"schema_version":"1.0","source":{"id":"1601.00736","kind":"arxiv","version":1}},"canonical_sha256":"c374da7f4449f76b987224b39d5968537467bef37a84a6e68fb3922fb8e317de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c374da7f4449f76b987224b39d5968537467bef37a84a6e68fb3922fb8e317de","first_computed_at":"2026-05-18T01:23:22.025456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:22.025456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GxU1RjDoUg7M5npVOMcoaruJ8tB4cC5zK/1o8A+V/ua3jgNPYR32T0ByVx8BOqjDydFPedaO0nBmIfbOK4nuDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:22.026232Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:027905822e017ff277e6df5a01cf2a1c119b9c3bfd626f50682eb26c0554da25","sha256:824ced41d0aa6f50c4ea81bde74590200fdc2538c67eb8082f689e0770f9d1f3"],"state_sha256":"525f28753205df98ff04bfccc23bcc68a0718d7f791de39e5df3a3ed9faee5fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+Z+aAhOQ7tK8Qp+NK+WHNU49a8e7V0jfCT/RRpAl0jkJV9pgya1GM4ngGtnEKs8JsSXwu9PmqB9cORLFEmIAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:12:32.622898Z","bundle_sha256":"c674f357439cbd08ef39364150224554ea0de30855783fc197a3cc6aa65fd7dd"}}