{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:644INTVNIIJGY6GVJXKWSQ5FLD","short_pith_number":"pith:644INTVN","canonical_record":{"source":{"id":"2501.04562","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-01-08T15:21:00Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"9b35edc318538fbb479c31aaee5bc8fbb04119a76dcb4398fe4455f1daf09285","abstract_canon_sha256":"b8e0dd39a7f183d3af3636b73c4e19e77f29c604b34ee2eded0839cde9154620"},"schema_version":"1.0"},"canonical_sha256":"f73886cead42126c78d54dd56943a558efee053e463856fb586f0d5aa18a573b","source":{"kind":"arxiv","id":"2501.04562","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04562","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04562v3","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04562","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_12","alias_value":"644INTVNIIJG","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_16","alias_value":"644INTVNIIJGY6GV","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_8","alias_value":"644INTVN","created_at":"2026-07-05T10:18:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:644INTVNIIJGY6GVJXKWSQ5FLD","target":"record","payload":{"canonical_record":{"source":{"id":"2501.04562","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-01-08T15:21:00Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"9b35edc318538fbb479c31aaee5bc8fbb04119a76dcb4398fe4455f1daf09285","abstract_canon_sha256":"b8e0dd39a7f183d3af3636b73c4e19e77f29c604b34ee2eded0839cde9154620"},"schema_version":"1.0"},"canonical_sha256":"f73886cead42126c78d54dd56943a558efee053e463856fb586f0d5aa18a573b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:18:12.296139Z","signature_b64":"NacafzDOfkIqa8RNjCxSUvgaeVWgKuNcgFLir1/aSzp21NNWNVJdzVKGKNtPD3Nlzb8DtKoUoj3LyqRc5ghvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f73886cead42126c78d54dd56943a558efee053e463856fb586f0d5aa18a573b","last_reissued_at":"2026-07-05T10:18:12.295676Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:18:12.295676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.04562","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:18:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7A+s+HO6/0efXghr/7O7k3/TaLHKW/NpeatXX5Qj6x/Cw71g1jMNnMSgwj6ScWJFcDAJB5elZOw38Vp2tHEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:26:19.702881Z"},"content_sha256":"8f9d51968f907a94eea9d2e4f53395b587d3cba3640fbfbd8d4d442f7cac252e","schema_version":"1.0","event_id":"sha256:8f9d51968f907a94eea9d2e4f53395b587d3cba3640fbfbd8d4d442f7cac252e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:644INTVNIIJGY6GVJXKWSQ5FLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical Double K-Means: a co-clustering approach for text data analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"stat.ME","authors_text":"Domenica Fioredistella Iezzi, Emiliano Seri, Ilaria Bombelli, Maurizio Vichi","submitted_at":"2025-01-08T15:21:00Z","abstract_excerpt":"In text analysis, Spherical K-means (SKM) is a specialized k-means clustering algorithm widely utilized for grouping documents represented in high-dimensional, sparse term-document matrices, often normalized using techniques like TF-IDF. Researchers frequently seek to cluster not only documents but also the terms associated with them into coherent groups. To address this dual clustering requirement, we introduce Spherical Double K-Means (SDKM), a novel methodology that simultaneously clusters documents and terms. This approach offers several advantages: first, by integrating the clustering of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04562","kind":"arxiv","version":3},"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/2501.04562/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":"2026-07-05T10:18:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CYR62VGxy916jMinm9GqaY7awVrYdgBQiSkC/PZbaAFLFxvkssqENhK5Ni3vXwEBkNn6UDrBCJf8bQIxLBinDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T06:26:19.703487Z"},"content_sha256":"6c3e1e6ebefaaa04beb028e166df02ca3416c3e363ec89892e54b6f86ec08ac8","schema_version":"1.0","event_id":"sha256:6c3e1e6ebefaaa04beb028e166df02ca3416c3e363ec89892e54b6f86ec08ac8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/644INTVNIIJGY6GVJXKWSQ5FLD/bundle.json","state_url":"https://pith.science/pith/644INTVNIIJGY6GVJXKWSQ5FLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/644INTVNIIJGY6GVJXKWSQ5FLD/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":"2026-08-06T06:26:19Z","links":{"resolver":"https://pith.science/pith/644INTVNIIJGY6GVJXKWSQ5FLD","bundle":"https://pith.science/pith/644INTVNIIJGY6GVJXKWSQ5FLD/bundle.json","state":"https://pith.science/pith/644INTVNIIJGY6GVJXKWSQ5FLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/644INTVNIIJGY6GVJXKWSQ5FLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:644INTVNIIJGY6GVJXKWSQ5FLD","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":"b8e0dd39a7f183d3af3636b73c4e19e77f29c604b34ee2eded0839cde9154620","cross_cats_sorted":["stat.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-01-08T15:21:00Z","title_canon_sha256":"9b35edc318538fbb479c31aaee5bc8fbb04119a76dcb4398fe4455f1daf09285"},"schema_version":"1.0","source":{"id":"2501.04562","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04562","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04562v3","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04562","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_12","alias_value":"644INTVNIIJG","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_16","alias_value":"644INTVNIIJGY6GV","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_8","alias_value":"644INTVN","created_at":"2026-07-05T10:18:12Z"}],"graph_snapshots":[{"event_id":"sha256:6c3e1e6ebefaaa04beb028e166df02ca3416c3e363ec89892e54b6f86ec08ac8","target":"graph","created_at":"2026-07-05T10:18:12Z","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/2501.04562/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In text analysis, Spherical K-means (SKM) is a specialized k-means clustering algorithm widely utilized for grouping documents represented in high-dimensional, sparse term-document matrices, often normalized using techniques like TF-IDF. Researchers frequently seek to cluster not only documents but also the terms associated with them into coherent groups. To address this dual clustering requirement, we introduce Spherical Double K-Means (SDKM), a novel methodology that simultaneously clusters documents and terms. This approach offers several advantages: first, by integrating the clustering of ","authors_text":"Domenica Fioredistella Iezzi, Emiliano Seri, Ilaria Bombelli, Maurizio Vichi","cross_cats":["stat.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-01-08T15:21:00Z","title":"Spherical Double K-Means: a co-clustering approach for text data analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04562","kind":"arxiv","version":3},"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":"sha256:8f9d51968f907a94eea9d2e4f53395b587d3cba3640fbfbd8d4d442f7cac252e","target":"record","created_at":"2026-07-05T10:18:12Z","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":"b8e0dd39a7f183d3af3636b73c4e19e77f29c604b34ee2eded0839cde9154620","cross_cats_sorted":["stat.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-01-08T15:21:00Z","title_canon_sha256":"9b35edc318538fbb479c31aaee5bc8fbb04119a76dcb4398fe4455f1daf09285"},"schema_version":"1.0","source":{"id":"2501.04562","kind":"arxiv","version":3}},"canonical_sha256":"f73886cead42126c78d54dd56943a558efee053e463856fb586f0d5aa18a573b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f73886cead42126c78d54dd56943a558efee053e463856fb586f0d5aa18a573b","first_computed_at":"2026-07-05T10:18:12.295676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:18:12.295676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NacafzDOfkIqa8RNjCxSUvgaeVWgKuNcgFLir1/aSzp21NNWNVJdzVKGKNtPD3Nlzb8DtKoUoj3LyqRc5ghvCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:18:12.296139Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.04562","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f9d51968f907a94eea9d2e4f53395b587d3cba3640fbfbd8d4d442f7cac252e","sha256:6c3e1e6ebefaaa04beb028e166df02ca3416c3e363ec89892e54b6f86ec08ac8"],"state_sha256":"13ff35ba9743587383ddd537d33867b2773a11e8d5261d575f04f4966905675e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Su+8/jGNuUQK09BmOqdMwzKofQiUs4qgbDH58Xt+bD7j8wjX/hRxSjYAgtPWtcL64DQA9xDeOhcP32xMODg6Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T06:26:19.708767Z","bundle_sha256":"e6ddb0c64b1fca1247569b9bf3027e4436c26fef01454b7888c670cfa34c3f60"}}