{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6K2TGWMD7H4SBIYDP3GBO6J2QE","short_pith_number":"pith:6K2TGWMD","canonical_record":{"source":{"id":"2605.21304","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-20T15:33:59Z","cross_cats_sorted":[],"title_canon_sha256":"2696c40b70e5a55a746c6c1b2c85ee157f09fa0e351c23f0b50fd1b4496abc56","abstract_canon_sha256":"be3698399f78aa5754ee3c070245c21d31b25bb76a31ab423bca80cff4da8e28"},"schema_version":"1.0"},"canonical_sha256":"f2b5335983f9f920a3037ecc17793a8121a77d39f3dcc640e056be5df1089b49","source":{"kind":"arxiv","id":"2605.21304","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21304","created_at":"2026-05-21T02:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21304v1","created_at":"2026-05-21T02:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21304","created_at":"2026-05-21T02:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"6K2TGWMD7H4S","created_at":"2026-05-21T02:05:28Z"},{"alias_kind":"pith_short_16","alias_value":"6K2TGWMD7H4SBIYD","created_at":"2026-05-21T02:05:28Z"},{"alias_kind":"pith_short_8","alias_value":"6K2TGWMD","created_at":"2026-05-21T02:05:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6K2TGWMD7H4SBIYDP3GBO6J2QE","target":"record","payload":{"canonical_record":{"source":{"id":"2605.21304","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-20T15:33:59Z","cross_cats_sorted":[],"title_canon_sha256":"2696c40b70e5a55a746c6c1b2c85ee157f09fa0e351c23f0b50fd1b4496abc56","abstract_canon_sha256":"be3698399f78aa5754ee3c070245c21d31b25bb76a31ab423bca80cff4da8e28"},"schema_version":"1.0"},"canonical_sha256":"f2b5335983f9f920a3037ecc17793a8121a77d39f3dcc640e056be5df1089b49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T02:05:28.248389Z","signature_b64":"r/r5Q6Uks8WdBzDHN9uZpjdeTOuxLELeNnSbeFwxpl8IhIGMiZ4sTTmfnvhy5Lqp7ow3OJYpPnQCKjF+X7NtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2b5335983f9f920a3037ecc17793a8121a77d39f3dcc640e056be5df1089b49","last_reissued_at":"2026-05-21T02:05:28.247663Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T02:05:28.247663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.21304","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":"2026-05-21T02:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zzs/Kqh+As87dBD7USKY016+AVzbcD3HUmQKljCDl35Ybn41N0fe/0bYSmzUp90K0KpdWDueuxs3+9KqqpYSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T15:46:31.668549Z"},"content_sha256":"798cce26aa325ebaf9f3a260aaaf558b5c974c2ae3d83347e68ad69ef6879a16","schema_version":"1.0","event_id":"sha256:798cce26aa325ebaf9f3a260aaaf558b5c974c2ae3d83347e68ad69ef6879a16"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6K2TGWMD7H4SBIYDP3GBO6J2QE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How does limma-trend work? An empirical partially Bayes perspective","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Nikolaos Ignatiadis, Sagnik Nandy, Wanyi Ling","submitted_at":"2026-05-20T15:33:59Z","abstract_excerpt":"In high-throughput biology, it is common to fit thousands of linear regressions -- one per gene, protein, or other unit -- with very few samples per unit. Limma-trend, one of the most widely used methods in this setting, improves power by shrinking variance estimates parametrically toward a fitted curve (the trend) relating variance to a unit-level summary (e.g., average intensity, peptide count), before computing p-values and applying the Benjamini-Hochberg procedure to control the false discovery rate (FDR). We study limma-trend through the lens of empirical partially Bayes inference, a para"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21304","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.21304/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-21T02:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ELAEXHPoqxp2SE0vQ/pCl2yTPP64KDKI/W5UaYr5M9pVC6wbRBHK9Uo7rzET06rvEmGR0RsDxRlSu9mZhENDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T15:46:31.668932Z"},"content_sha256":"547472ab52773b85b460c5aa87f8e1cfed79186358162b971644a54c9ca99cfb","schema_version":"1.0","event_id":"sha256:547472ab52773b85b460c5aa87f8e1cfed79186358162b971644a54c9ca99cfb"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:6K2TGWMD7H4SBIYDP3GBO6J2QE","target":"integrity","payload":{"note":"URL 'http://www.ncbi.nlm' returned status transport error (transport error: [Errno -2] Name or service not known) at last check.","snippet":null,"arxiv_id":"2605.21304","detector":"external_links","evidence":{"url":"http://www.ncbi.nlm","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -2] Name or service not known","verdict_class":"incontrovertible","checked_at_unix":1779406573.3840091},"severity":"advisory","ref_index":null,"audited_at":"2026-05-21T23:36:13.395074Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"http://www.ncbi.nlm","finding_type":"dead_url","evidence_hash":"d4402188eae5792084ad2042b61b617ebc5530db6a9b74e241f38c3b737b5851","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":6109,"payload_sha256":"688dd8a2a78becfec5e94796f2c444cbe3b8f441a87d1f1d227c3d712f2b3250","signature_b64":"plwUsuEumIPS1WHekn6+FW3jYsT33rmlFCM/VpIulZwc9g0AkdWW+ygXVoVl4ltfXTFZJHYUJy6tW7qmuIxNCQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T23:40:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I8PJTmrSrxNO1VMMbreR9UVifQQuucpSHLoGXE2YmUv2KG/9bU8tW1sWYj+6x9scwDV2ZB1Oqed/yKsvxv+ECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T15:46:31.669836Z"},"content_sha256":"fe12cc605b79b651b76c46b8ae447a2b61763114f456dbe4acc60a0bf9acb7a5","schema_version":"1.0","event_id":"sha256:fe12cc605b79b651b76c46b8ae447a2b61763114f456dbe4acc60a0bf9acb7a5"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:6K2TGWMD7H4SBIYDP3GBO6J2QE","target":"integrity","payload":{"note":"URL 'http://www.ncbi.nlm' returned status transport error (transport error: [Errno -2] Name or service not known) at last check.","snippet":null,"arxiv_id":"2605.21304","detector":"external_links","evidence":{"url":"http://www.ncbi.nlm","final_url":null,"host_kind":"website","status_code":0,"status_text":"transport error: [Errno -2] Name or service not known","verdict_class":"incontrovertible","checked_at_unix":1779363372.599138},"severity":"advisory","ref_index":null,"audited_at":"2026-05-21T11:36:12.638090Z","event_type":"pith.integrity.v1","detected_doi":null,"detector_url":"https://pith.science/pith-integrity-protocol#external_links","external_url":"http://www.ncbi.nlm","finding_type":"dead_url","evidence_hash":"bf815705d39a2ee9caa8a01f22a7bfbfd28ce8d03e3d6c75ee4ad93995887702","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":5943,"payload_sha256":"ab18ae529fb59781e7f1e9b734bec8c44ec2d69774d8d8382dea85224627c21a","signature_b64":"l8hXU+VaYcVtyR/0jGM4BXf/YPNUJ5cR6dYwgwyaSyRC0727XwNZwqbFHr9z5sFGBJf6WAfw8n5vMyxL9IlqCw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T11:39:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9l3q72PEdK62kZiT38v0w8DbdSnHIUNUOZ66acCc1zIxsNlmQYCs1+CpYzoJz0hQhNfk/dcPIPdZFB1tDAiEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T15:46:31.670113Z"},"content_sha256":"a332ee446da78981910174ac8be2b711c0f373dd8fe6d2873ee27cdf6c4a06c1","schema_version":"1.0","event_id":"sha256:a332ee446da78981910174ac8be2b711c0f373dd8fe6d2873ee27cdf6c4a06c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6K2TGWMD7H4SBIYDP3GBO6J2QE/bundle.json","state_url":"https://pith.science/pith/6K2TGWMD7H4SBIYDP3GBO6J2QE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6K2TGWMD7H4SBIYDP3GBO6J2QE/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":"2026-06-21T15:46:31Z","links":{"resolver":"https://pith.science/pith/6K2TGWMD7H4SBIYDP3GBO6J2QE","bundle":"https://pith.science/pith/6K2TGWMD7H4SBIYDP3GBO6J2QE/bundle.json","state":"https://pith.science/pith/6K2TGWMD7H4SBIYDP3GBO6J2QE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6K2TGWMD7H4SBIYDP3GBO6J2QE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6K2TGWMD7H4SBIYDP3GBO6J2QE","merge_version":"pith-open-graph-merge-v1","event_count":4,"valid_event_count":4,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"be3698399f78aa5754ee3c070245c21d31b25bb76a31ab423bca80cff4da8e28","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-20T15:33:59Z","title_canon_sha256":"2696c40b70e5a55a746c6c1b2c85ee157f09fa0e351c23f0b50fd1b4496abc56"},"schema_version":"1.0","source":{"id":"2605.21304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21304","created_at":"2026-05-21T02:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21304v1","created_at":"2026-05-21T02:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21304","created_at":"2026-05-21T02:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"6K2TGWMD7H4S","created_at":"2026-05-21T02:05:28Z"},{"alias_kind":"pith_short_16","alias_value":"6K2TGWMD7H4SBIYD","created_at":"2026-05-21T02:05:28Z"},{"alias_kind":"pith_short_8","alias_value":"6K2TGWMD","created_at":"2026-05-21T02:05:28Z"}],"graph_snapshots":[{"event_id":"sha256:547472ab52773b85b460c5aa87f8e1cfed79186358162b971644a54c9ca99cfb","target":"graph","created_at":"2026-05-21T02:05:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.21304/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In high-throughput biology, it is common to fit thousands of linear regressions -- one per gene, protein, or other unit -- with very few samples per unit. Limma-trend, one of the most widely used methods in this setting, improves power by shrinking variance estimates parametrically toward a fitted curve (the trend) relating variance to a unit-level summary (e.g., average intensity, peptide count), before computing p-values and applying the Benjamini-Hochberg procedure to control the false discovery rate (FDR). We study limma-trend through the lens of empirical partially Bayes inference, a para","authors_text":"Nikolaos Ignatiadis, Sagnik Nandy, Wanyi Ling","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-20T15:33:59Z","title":"How does limma-trend work? An empirical partially Bayes perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21304","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":"sha256:798cce26aa325ebaf9f3a260aaaf558b5c974c2ae3d83347e68ad69ef6879a16","target":"record","created_at":"2026-05-21T02:05:28Z","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":"be3698399f78aa5754ee3c070245c21d31b25bb76a31ab423bca80cff4da8e28","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-20T15:33:59Z","title_canon_sha256":"2696c40b70e5a55a746c6c1b2c85ee157f09fa0e351c23f0b50fd1b4496abc56"},"schema_version":"1.0","source":{"id":"2605.21304","kind":"arxiv","version":1}},"canonical_sha256":"f2b5335983f9f920a3037ecc17793a8121a77d39f3dcc640e056be5df1089b49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2b5335983f9f920a3037ecc17793a8121a77d39f3dcc640e056be5df1089b49","first_computed_at":"2026-05-21T02:05:28.247663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T02:05:28.247663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r/r5Q6Uks8WdBzDHN9uZpjdeTOuxLELeNnSbeFwxpl8IhIGMiZ4sTTmfnvhy5Lqp7ow3OJYpPnQCKjF+X7NtAA==","signature_status":"signed_v1","signed_at":"2026-05-21T02:05:28.248389Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.21304","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:a332ee446da78981910174ac8be2b711c0f373dd8fe6d2873ee27cdf6c4a06c1","sha256:fe12cc605b79b651b76c46b8ae447a2b61763114f456dbe4acc60a0bf9acb7a5"]}],"invalid_events":[],"applied_event_ids":["sha256:798cce26aa325ebaf9f3a260aaaf558b5c974c2ae3d83347e68ad69ef6879a16","sha256:547472ab52773b85b460c5aa87f8e1cfed79186358162b971644a54c9ca99cfb"],"state_sha256":"1cc454f50dd4ab5c076f2b4d77a57108edaf3d3d8645eb389483c0002b19a600"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8GRJ8lE7mKcm5FZCGhNFEaaoayXwsAQrWB2YcRbSi+T6VwK2o8JFf79jZgl4dL311h2v4UzRJJE+6A3AXG6KDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T15:46:31.672140Z","bundle_sha256":"47b9af217d59c6973d9c8b9fe6cbec9c953bf2d906911ccc8aaf00c61050b9c0"}}