{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:M6KBUVE33VQQIHAQLNBI6REHBK","short_pith_number":"pith:M6KBUVE3","canonical_record":{"source":{"id":"2607.27474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-29T21:27:17Z","cross_cats_sorted":[],"title_canon_sha256":"b8ef00da739b45410bb3cb95db356d6d71ba339a5ea53dee8b716ea7055b3595","abstract_canon_sha256":"748d3e3236c20866dc1d9f8e32006e754d6b18532d8b0beb14026e10fadb3057"},"schema_version":"1.0"},"canonical_sha256":"67941a549bdd61041c105b428f44870aa338ed3ef1f9601587c5696112de5fd4","source":{"kind":"arxiv","id":"2607.27474","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27474","created_at":"2026-07-31T01:23:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27474v1","created_at":"2026-07-31T01:23:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27474","created_at":"2026-07-31T01:23:51Z"},{"alias_kind":"pith_short_12","alias_value":"M6KBUVE33VQQ","created_at":"2026-07-31T01:23:51Z"},{"alias_kind":"pith_short_16","alias_value":"M6KBUVE33VQQIHAQ","created_at":"2026-07-31T01:23:51Z"},{"alias_kind":"pith_short_8","alias_value":"M6KBUVE3","created_at":"2026-07-31T01:23:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:M6KBUVE33VQQIHAQLNBI6REHBK","target":"record","payload":{"canonical_record":{"source":{"id":"2607.27474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-29T21:27:17Z","cross_cats_sorted":[],"title_canon_sha256":"b8ef00da739b45410bb3cb95db356d6d71ba339a5ea53dee8b716ea7055b3595","abstract_canon_sha256":"748d3e3236c20866dc1d9f8e32006e754d6b18532d8b0beb14026e10fadb3057"},"schema_version":"1.0"},"canonical_sha256":"67941a549bdd61041c105b428f44870aa338ed3ef1f9601587c5696112de5fd4","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67941a549bdd61041c105b428f44870aa338ed3ef1f9601587c5696112de5fd4","last_reissued_at":"2026-07-31T01:23:51.195116Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:23:51.195116Z"},"source_kind":"arxiv","source_id":"2607.27474","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":"2026-07-31T01:23:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S5AP1dkIXMn/OilD7y+gg31FXjvic+VZ6s3nQj5mSRcGFu66VtonyLKq3eiSbaE2DQ2m1coOAI4c8hVtIZDxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T08:14:34.384615Z"},"content_sha256":"902e4b8600ed8c9fb685f12774bcf524ccef706caafa0d6685a7e1f1817b3d07","schema_version":"1.0","event_id":"sha256:902e4b8600ed8c9fb685f12774bcf524ccef706caafa0d6685a7e1f1817b3d07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:M6KBUVE33VQQIHAQLNBI6REHBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Co-clustering of Response and Covariate Variables by Tri-Factorizing Their Non-negative Regression Coefficient Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"(2) Faculty of Education, Kenichi Satoh (1), Shiga University, Shiga University), Yomei Tokuda (2) ((1) Faculty of Data Science","submitted_at":"2026-07-29T21:27:17Z","abstract_excerpt":"Two-block data---two sets of variables measured on the same individuals, such as microbial taxa and metabolites---raise the question of how \\emph{groups} of covariate variables relate to \\emph{groups} of response variables. Co-clustering answers this for a single matrix, not for two variable blocks; existing two-block methods either cluster only one side or return signed factors rather than clusters. Starting from the multivariate linear regression $Y_1\\approx M Y_2$, we give its non-negative coefficient matrix a tri-factorization $M=X_1\\Theta X_2$ (a tri-NMF), so that $X_1$ softly clusters th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27474","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/2607.27474/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":"2026-07-31T01:23:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wHE83q5j1Gl4bz2prUUnrGJtxTS16M7Ag8MDGJE3eqdnjXFuneH46dfBjrvhYbR8oKEAZP4oea94uYJDSQELCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T08:14:34.385120Z"},"content_sha256":"93cf0b2ee9697929f2637069b963f10029422e07426569f803fcb16276333bb2","schema_version":"1.0","event_id":"sha256:93cf0b2ee9697929f2637069b963f10029422e07426569f803fcb16276333bb2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6KBUVE33VQQIHAQLNBI6REHBK/bundle.json","state_url":"https://pith.science/pith/M6KBUVE33VQQIHAQLNBI6REHBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6KBUVE33VQQIHAQLNBI6REHBK/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":"2026-08-21T08:14:34Z","links":{"resolver":"https://pith.science/pith/M6KBUVE33VQQIHAQLNBI6REHBK","bundle":"https://pith.science/pith/M6KBUVE33VQQIHAQLNBI6REHBK/bundle.json","state":"https://pith.science/pith/M6KBUVE33VQQIHAQLNBI6REHBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6KBUVE33VQQIHAQLNBI6REHBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:M6KBUVE33VQQIHAQLNBI6REHBK","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":"748d3e3236c20866dc1d9f8e32006e754d6b18532d8b0beb14026e10fadb3057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-29T21:27:17Z","title_canon_sha256":"b8ef00da739b45410bb3cb95db356d6d71ba339a5ea53dee8b716ea7055b3595"},"schema_version":"1.0","source":{"id":"2607.27474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27474","created_at":"2026-07-31T01:23:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27474v1","created_at":"2026-07-31T01:23:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27474","created_at":"2026-07-31T01:23:51Z"},{"alias_kind":"pith_short_12","alias_value":"M6KBUVE33VQQ","created_at":"2026-07-31T01:23:51Z"},{"alias_kind":"pith_short_16","alias_value":"M6KBUVE33VQQIHAQ","created_at":"2026-07-31T01:23:51Z"},{"alias_kind":"pith_short_8","alias_value":"M6KBUVE3","created_at":"2026-07-31T01:23:51Z"}],"graph_snapshots":[{"event_id":"sha256:93cf0b2ee9697929f2637069b963f10029422e07426569f803fcb16276333bb2","target":"graph","created_at":"2026-07-31T01:23:51Z","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/2607.27474/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two-block data---two sets of variables measured on the same individuals, such as microbial taxa and metabolites---raise the question of how \\emph{groups} of covariate variables relate to \\emph{groups} of response variables. Co-clustering answers this for a single matrix, not for two variable blocks; existing two-block methods either cluster only one side or return signed factors rather than clusters. Starting from the multivariate linear regression $Y_1\\approx M Y_2$, we give its non-negative coefficient matrix a tri-factorization $M=X_1\\Theta X_2$ (a tri-NMF), so that $X_1$ softly clusters th","authors_text":"(2) Faculty of Education, Kenichi Satoh (1), Shiga University, Shiga University), Yomei Tokuda (2) ((1) Faculty of Data Science","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-29T21:27:17Z","title":"Co-clustering of Response and Covariate Variables by Tri-Factorizing Their Non-negative Regression Coefficient Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27474","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":"sha256:902e4b8600ed8c9fb685f12774bcf524ccef706caafa0d6685a7e1f1817b3d07","target":"record","created_at":"2026-07-31T01:23:51Z","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":"748d3e3236c20866dc1d9f8e32006e754d6b18532d8b0beb14026e10fadb3057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-07-29T21:27:17Z","title_canon_sha256":"b8ef00da739b45410bb3cb95db356d6d71ba339a5ea53dee8b716ea7055b3595"},"schema_version":"1.0","source":{"id":"2607.27474","kind":"arxiv","version":1}},"canonical_sha256":"67941a549bdd61041c105b428f44870aa338ed3ef1f9601587c5696112de5fd4","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67941a549bdd61041c105b428f44870aa338ed3ef1f9601587c5696112de5fd4","first_computed_at":"2026-07-31T01:23:51.195116Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:23:51.195116Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.27474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:902e4b8600ed8c9fb685f12774bcf524ccef706caafa0d6685a7e1f1817b3d07","sha256:93cf0b2ee9697929f2637069b963f10029422e07426569f803fcb16276333bb2"],"state_sha256":"04f213e7d92286a9a1436d3d3a1306d388839be155839dd05c2fa119d2564cd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3xDXOhFLll4qMegnjm4tkVFfABTOr5tc4hyjs4h59gxWy0jkb1LtBHHL0DDf6nasnDz/eisdc7U7WTrYPzl8AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T08:14:34.388909Z","bundle_sha256":"9b594128040c108ae730129415d8be4ced4bd041f6556a945a093191352d5ef0"}}