{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UT4L3TEQPOXU27B3KMIUCS3N4O","short_pith_number":"pith:UT4L3TEQ","canonical_record":{"source":{"id":"1801.07399","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-01-23T05:35:00Z","cross_cats_sorted":["cs.DC","cs.DS"],"title_canon_sha256":"e6535fe6738a3963356f4f5496416c1688a1af963650bb1b6fdbd4a7a13a39ea","abstract_canon_sha256":"2d46fabdeec797e8e3e8feaad21927e008df517100a5cd4045109c1eac3a5e69"},"schema_version":"1.0"},"canonical_sha256":"a4f8bdcc907baf4d7c3b5311414b6de38749a176b586765ea4e675bd36e29e90","source":{"kind":"arxiv","id":"1801.07399","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07399","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07399v2","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07399","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"UT4L3TEQPOXU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UT4L3TEQPOXU27B3","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UT4L3TEQ","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UT4L3TEQPOXU27B3KMIUCS3N4O","target":"record","payload":{"canonical_record":{"source":{"id":"1801.07399","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-01-23T05:35:00Z","cross_cats_sorted":["cs.DC","cs.DS"],"title_canon_sha256":"e6535fe6738a3963356f4f5496416c1688a1af963650bb1b6fdbd4a7a13a39ea","abstract_canon_sha256":"2d46fabdeec797e8e3e8feaad21927e008df517100a5cd4045109c1eac3a5e69"},"schema_version":"1.0"},"canonical_sha256":"a4f8bdcc907baf4d7c3b5311414b6de38749a176b586765ea4e675bd36e29e90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:21.913301Z","signature_b64":"avsSpsuFL1Uk3xyLuDhqwbjZKpZm2XFqY7s9r3TIVl2tTvS2d6sVwBY1x+pOPYQlSULneaq8tnX5eNJqz0XDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4f8bdcc907baf4d7c3b5311414b6de38749a176b586765ea4e675bd36e29e90","last_reissued_at":"2026-05-18T00:14:21.912460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:21.912460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.07399","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uk/CpTZ8YmoCddTSctJl2nmsMrFJiPWp5+HeahVoVbqjlKMUnEi/T4Kz9JSdNaVsdCPSZe6JVCV9YQ3qWVmnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T19:07:26.064794Z"},"content_sha256":"4a0c231f9bce7a3df64865a22109786f54ae502a566a161d23aad86d35703d26","schema_version":"1.0","event_id":"sha256:4a0c231f9bce7a3df64865a22109786f54ae502a566a161d23aad86d35703d26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UT4L3TEQPOXU27B3KMIUCS3N4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Onion Curve: A Space Filling Curve with Near-Optimal Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.DS"],"primary_cat":"cs.CG","authors_text":"Cuong Nguyen, Pan Xu, Srikanta Tirthapura","submitted_at":"2018-01-23T05:35:00Z","abstract_excerpt":"Space filling curves (SFCs) are widely used in the design of indexes for spatial and temporal data. Clustering is a key metric for an SFC, that measures how well the curve preserves locality in moving from higher dimensions to a single dimension. We present the {\\em onion curve}, an SFC whose clustering performance is provably close to optimal for the cube and near-cube shaped query sets, irrespective of the side length of the query. We show that in contrast, the clustering performance of the widely used Hilbert curve can be far from optimal, even for cube-shaped queries. Since the clustering "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07399","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ui9pcF+ugNPaGcURvG2JMbV/NXNTJYJsDx0rJTZ4iIj9o5dqwgoF2znE+Wosjb2gcoJAEBK0zdAPVOEeVFztBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T19:07:26.065140Z"},"content_sha256":"dc7ac4b32c42964488ff309f8f9c0b9fa0342e2df20f88d809b6469109b6e525","schema_version":"1.0","event_id":"sha256:dc7ac4b32c42964488ff309f8f9c0b9fa0342e2df20f88d809b6469109b6e525"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UT4L3TEQPOXU27B3KMIUCS3N4O/bundle.json","state_url":"https://pith.science/pith/UT4L3TEQPOXU27B3KMIUCS3N4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UT4L3TEQPOXU27B3KMIUCS3N4O/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":"2026-05-20T19:07:26Z","links":{"resolver":"https://pith.science/pith/UT4L3TEQPOXU27B3KMIUCS3N4O","bundle":"https://pith.science/pith/UT4L3TEQPOXU27B3KMIUCS3N4O/bundle.json","state":"https://pith.science/pith/UT4L3TEQPOXU27B3KMIUCS3N4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UT4L3TEQPOXU27B3KMIUCS3N4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UT4L3TEQPOXU27B3KMIUCS3N4O","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":"2d46fabdeec797e8e3e8feaad21927e008df517100a5cd4045109c1eac3a5e69","cross_cats_sorted":["cs.DC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-01-23T05:35:00Z","title_canon_sha256":"e6535fe6738a3963356f4f5496416c1688a1af963650bb1b6fdbd4a7a13a39ea"},"schema_version":"1.0","source":{"id":"1801.07399","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07399","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07399v2","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07399","created_at":"2026-05-18T00:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"UT4L3TEQPOXU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UT4L3TEQPOXU27B3","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UT4L3TEQ","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:dc7ac4b32c42964488ff309f8f9c0b9fa0342e2df20f88d809b6469109b6e525","target":"graph","created_at":"2026-05-18T00:14:21Z","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":"Space filling curves (SFCs) are widely used in the design of indexes for spatial and temporal data. Clustering is a key metric for an SFC, that measures how well the curve preserves locality in moving from higher dimensions to a single dimension. We present the {\\em onion curve}, an SFC whose clustering performance is provably close to optimal for the cube and near-cube shaped query sets, irrespective of the side length of the query. We show that in contrast, the clustering performance of the widely used Hilbert curve can be far from optimal, even for cube-shaped queries. Since the clustering ","authors_text":"Cuong Nguyen, Pan Xu, Srikanta Tirthapura","cross_cats":["cs.DC","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-01-23T05:35:00Z","title":"Onion Curve: A Space Filling Curve with Near-Optimal Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07399","kind":"arxiv","version":2},"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":"sha256:4a0c231f9bce7a3df64865a22109786f54ae502a566a161d23aad86d35703d26","target":"record","created_at":"2026-05-18T00:14:21Z","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":"2d46fabdeec797e8e3e8feaad21927e008df517100a5cd4045109c1eac3a5e69","cross_cats_sorted":["cs.DC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-01-23T05:35:00Z","title_canon_sha256":"e6535fe6738a3963356f4f5496416c1688a1af963650bb1b6fdbd4a7a13a39ea"},"schema_version":"1.0","source":{"id":"1801.07399","kind":"arxiv","version":2}},"canonical_sha256":"a4f8bdcc907baf4d7c3b5311414b6de38749a176b586765ea4e675bd36e29e90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4f8bdcc907baf4d7c3b5311414b6de38749a176b586765ea4e675bd36e29e90","first_computed_at":"2026-05-18T00:14:21.912460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:21.912460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"avsSpsuFL1Uk3xyLuDhqwbjZKpZm2XFqY7s9r3TIVl2tTvS2d6sVwBY1x+pOPYQlSULneaq8tnX5eNJqz0XDBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:21.913301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.07399","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a0c231f9bce7a3df64865a22109786f54ae502a566a161d23aad86d35703d26","sha256:dc7ac4b32c42964488ff309f8f9c0b9fa0342e2df20f88d809b6469109b6e525"],"state_sha256":"bcc809d42c85bc93d418a6c861c135701960b67df03b04920e77a71847880a60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z8XJUeUXdT/fgS8TllrX6U0XlIJqEs1Lfk4M/OaanD1HYhNGwdVhvXBlMfjqfsgqgN+JJrFM8H4JfnvnqmhWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T19:07:26.067257Z","bundle_sha256":"7cedbf78709a8ea90bf76f9ad3173a9b53b1f1a620cfe3224d23bc9cc84e3c6f"}}