{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:O74HJW3J34AWIGAUDPULDGGFI6","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":"1c6fd08378f54050436e7f89cda920327575db4715a499495c01f269f402b826","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2020-10-13T12:31:13Z","title_canon_sha256":"f3066e3c200ec20e7d5d304c88f7352d7eb64caac55c532cc949a91a2768f06f"},"schema_version":"1.0","source":{"id":"2010.06333","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.06333","created_at":"2026-07-05T02:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"2010.06333v3","created_at":"2026-07-05T02:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.06333","created_at":"2026-07-05T02:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"O74HJW3J34AW","created_at":"2026-07-05T02:31:19Z"},{"alias_kind":"pith_short_16","alias_value":"O74HJW3J34AWIGAU","created_at":"2026-07-05T02:31:19Z"},{"alias_kind":"pith_short_8","alias_value":"O74HJW3J","created_at":"2026-07-05T02:31:19Z"}],"graph_snapshots":[{"event_id":"sha256:9499a034a0cea84a9b14f4e12e7a1cd1788f126fec0ec32dbbeb9afb14cc81b0","target":"graph","created_at":"2026-07-05T02:31:19Z","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/2010.06333/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Capacitated spatial clustering, a type of unsupervised machine learning method, is often used to tackle problems in compressing, classifying, logistic optimization and infrastructure optimization. Depending on the application at hand, a wide set of extensions may be necessary in clustering.\n  In this article we propose a number of novel extensions to PACK that is a novel capacitated spatial clustering method. These extensions are relocation and location preference of cluster centers, outliers, and non-spatial attributes. The strength of PACK is that it can consider all of these extensions join","authors_text":"Jukka Riekki, Lauri Lov\\'en, Leena Ruha, Markku Kuismin, Mikko J. Sillanp\\\"a\\\"a, Teemu Lepp\\\"anen, Tero L\\\"ahderanta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2020-10-13T12:31:13Z","title":"Capacitated spatial clustering with multiple constraints and attributes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.06333","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:c8af28ae704305c83a9c0e4055892f4fe4176861c3535d78a786eb23d895a9a2","target":"record","created_at":"2026-07-05T02:31:19Z","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":"1c6fd08378f54050436e7f89cda920327575db4715a499495c01f269f402b826","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2020-10-13T12:31:13Z","title_canon_sha256":"f3066e3c200ec20e7d5d304c88f7352d7eb64caac55c532cc949a91a2768f06f"},"schema_version":"1.0","source":{"id":"2010.06333","kind":"arxiv","version":3}},"canonical_sha256":"77f874db69df016418141be8b198c547ac783a8e46a0515f1160f10a5f8f5c54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77f874db69df016418141be8b198c547ac783a8e46a0515f1160f10a5f8f5c54","first_computed_at":"2026-07-05T02:31:19.886768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:31:19.886768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"thZETbcgMKozETMtU61Qcjt/CVF35kyMEPKXl+i6+51XIcHVzRAf/ysyQFXQwLrQosknEzamZ8MSXNh77cbaAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:31:19.887241Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.06333","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8af28ae704305c83a9c0e4055892f4fe4176861c3535d78a786eb23d895a9a2","sha256:9499a034a0cea84a9b14f4e12e7a1cd1788f126fec0ec32dbbeb9afb14cc81b0"],"state_sha256":"da537fc106990973d424ed8be9cd7ec963ded1e1d257617ca7372e4605697853"}