{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KL3JBOOMPOKZY5TDVUEL7TBKBK","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":"ab983c10005247d0a13126c8b0543fb90c99d7ee50f554c63d317dd48e79ffc5","cross_cats_sorted":["cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-13T10:52:03Z","title_canon_sha256":"692214ab2d3883938511f12393d01e5398d849e669d51b658d5c3b7de32ffb4d"},"schema_version":"1.0","source":{"id":"1612.04094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04094","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04094v1","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04094","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"pith_short_12","alias_value":"KL3JBOOMPOKZ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KL3JBOOMPOKZY5TD","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KL3JBOOM","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:c5683fb7151a025f224b83082970bce3973eb17320865749772100c41b21b87f","target":"graph","created_at":"2026-05-18T00:55:05Z","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":"We consider the problem of representing multidimensional data where the domain of each dimension is organized hierarchically, and the queries require summary information at a different node in the hierarchy of each dimension. This is the typical case of OLAP databases. A basic approach is to represent each hierarchy as a one-dimensional line and recast the queries as multidimensional range queries. This approach can be implemented compactly by generalizing to more dimensions the $k^2$-treap, a compact representation of two-dimensional points that allows for efficient summarization queries alon","authors_text":"Ana Cerdeira-Pena, Fernando Silva-Coira, Gonzalo Navarro, Miguel R. Penabad, Narciso L\\'opez-L\\'opez, Nieves R. Brisaboa","cross_cats":["cs.DB"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-13T10:52:03Z","title":"Efficient Representation of Multidimensional Data over Hierarchical Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04094","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":"sha256:53e9228608788b15cd569b92f2e260217fb0ec1b77f8cce9fe1a828114474e7a","target":"record","created_at":"2026-05-18T00:55:05Z","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":"ab983c10005247d0a13126c8b0543fb90c99d7ee50f554c63d317dd48e79ffc5","cross_cats_sorted":["cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-13T10:52:03Z","title_canon_sha256":"692214ab2d3883938511f12393d01e5398d849e669d51b658d5c3b7de32ffb4d"},"schema_version":"1.0","source":{"id":"1612.04094","kind":"arxiv","version":1}},"canonical_sha256":"52f690b9cc7b959c7663ad08bfcc2a0aa123bf40356942ef5c7d2bb4cb37cb5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52f690b9cc7b959c7663ad08bfcc2a0aa123bf40356942ef5c7d2bb4cb37cb5c","first_computed_at":"2026-05-18T00:55:05.564207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:05.564207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v+Nj4ASYEJ0w4hc27ibVWVHbnL22TeeRiWiU8j03VqEBUH5nMdF/nTVkZxbo3Vq7OqavzG+cqH/2w+T14i2qCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:05.564907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53e9228608788b15cd569b92f2e260217fb0ec1b77f8cce9fe1a828114474e7a","sha256:c5683fb7151a025f224b83082970bce3973eb17320865749772100c41b21b87f"],"state_sha256":"5fc5d29ed364491b8630c6dc8ac856b24381e1461949f85576da14bec0b1cbb8"}