{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3UNFAIOSL6E33DA7NQYZSJAJAB","short_pith_number":"pith:3UNFAIOS","canonical_record":{"source":{"id":"1107.2231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-12T10:08:58Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"962052cfeca9245d68db4e1fe933a16a04fbc7283df5f2a7ea3b58adbd977251","abstract_canon_sha256":"f1b2b039bebf1c86eb5b437ea7bc9c73081f7f0f705656b21374289eca54cf2e"},"schema_version":"1.0"},"canonical_sha256":"dd1a5021d25f89bd8c1f6c31992409007b7c216939bdafabe8f42e0fa08cb608","source":{"kind":"arxiv","id":"1107.2231","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2231","created_at":"2026-05-18T04:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2231v1","created_at":"2026-05-18T04:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2231","created_at":"2026-05-18T04:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"3UNFAIOSL6E3","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3UNFAIOSL6E33DA7","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3UNFAIOS","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3UNFAIOSL6E33DA7NQYZSJAJAB","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-12T10:08:58Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"962052cfeca9245d68db4e1fe933a16a04fbc7283df5f2a7ea3b58adbd977251","abstract_canon_sha256":"f1b2b039bebf1c86eb5b437ea7bc9c73081f7f0f705656b21374289eca54cf2e"},"schema_version":"1.0"},"canonical_sha256":"dd1a5021d25f89bd8c1f6c31992409007b7c216939bdafabe8f42e0fa08cb608","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:25.008953Z","signature_b64":"3UWkqd7eMWTDMg9CrYFBLcQazAhkOIR8wUz1GpLHYwEPi6OtK+11Nn9ERbGjcpiwCwKJ2zypcFbiYnTPaUvpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd1a5021d25f89bd8c1f6c31992409007b7c216939bdafabe8f42e0fa08cb608","last_reissued_at":"2026-05-18T04:18:25.008365Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:25.008365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2231","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":"2026-05-18T04:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tz58l7r/+rBVGj3/2bQTuXqeO3cUsTswezQmReTb9qNmhDiDzevDfqN6nwGDydG2TB/RU+vn5ovSaovL7FtYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T02:01:28.034740Z"},"content_sha256":"d478dba0b19a4a910599a309c4aeca0c085e2b9ebc084872dd9c88d6252c5807","schema_version":"1.0","event_id":"sha256:d478dba0b19a4a910599a309c4aeca0c085e2b9ebc084872dd9c88d6252c5807"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3UNFAIOSL6E33DA7NQYZSJAJAB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial match queries in random quadtrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"math.PR","authors_text":"Henning Sulzbach, Nicolas Broutin, Ralph Neininger","submitted_at":"2011-07-12T10:08:58Z","abstract_excerpt":"We consider the problem of recovering items matching a partially specified pattern in multidimensional trees (quad trees and k-d trees). We assume the traditional model where the data consist of independent and uniform points in the unit square. For this model, in a structure on $n$ points, it is known that the number of nodes $C_n(\\xi)$ to visit in order to report the items matching an independent and uniformly on $[0,1]$ random query $\\xi$ satisfies $\\Ec{C_n(\\xi)}\\sim \\kappa n^{\\beta}$, where $\\kappa$ and $\\beta$ are explicit constants. We develop an approach based on the analysis of the cos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2231","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":""},"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":"2026-05-18T04:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ImVbOLfhvD4mVwDK3YTZw41USRivqls+yKKUSVteeDQUe06q3PGw9iGqgTrv1T7Wo81j0FRBUIr1/MuRy0xnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T02:01:28.035090Z"},"content_sha256":"67e19fe11c923e6df7494e56f6abf0e107da0ca41fbc7a8f55fafc2210f834d9","schema_version":"1.0","event_id":"sha256:67e19fe11c923e6df7494e56f6abf0e107da0ca41fbc7a8f55fafc2210f834d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3UNFAIOSL6E33DA7NQYZSJAJAB/bundle.json","state_url":"https://pith.science/pith/3UNFAIOSL6E33DA7NQYZSJAJAB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3UNFAIOSL6E33DA7NQYZSJAJAB/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":"2026-05-23T02:01:28Z","links":{"resolver":"https://pith.science/pith/3UNFAIOSL6E33DA7NQYZSJAJAB","bundle":"https://pith.science/pith/3UNFAIOSL6E33DA7NQYZSJAJAB/bundle.json","state":"https://pith.science/pith/3UNFAIOSL6E33DA7NQYZSJAJAB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3UNFAIOSL6E33DA7NQYZSJAJAB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3UNFAIOSL6E33DA7NQYZSJAJAB","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":"f1b2b039bebf1c86eb5b437ea7bc9c73081f7f0f705656b21374289eca54cf2e","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-12T10:08:58Z","title_canon_sha256":"962052cfeca9245d68db4e1fe933a16a04fbc7283df5f2a7ea3b58adbd977251"},"schema_version":"1.0","source":{"id":"1107.2231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2231","created_at":"2026-05-18T04:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2231v1","created_at":"2026-05-18T04:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2231","created_at":"2026-05-18T04:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"3UNFAIOSL6E3","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3UNFAIOSL6E33DA7","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3UNFAIOS","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:67e19fe11c923e6df7494e56f6abf0e107da0ca41fbc7a8f55fafc2210f834d9","target":"graph","created_at":"2026-05-18T04:18:25Z","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 recovering items matching a partially specified pattern in multidimensional trees (quad trees and k-d trees). We assume the traditional model where the data consist of independent and uniform points in the unit square. For this model, in a structure on $n$ points, it is known that the number of nodes $C_n(\\xi)$ to visit in order to report the items matching an independent and uniformly on $[0,1]$ random query $\\xi$ satisfies $\\Ec{C_n(\\xi)}\\sim \\kappa n^{\\beta}$, where $\\kappa$ and $\\beta$ are explicit constants. We develop an approach based on the analysis of the cos","authors_text":"Henning Sulzbach, Nicolas Broutin, Ralph Neininger","cross_cats":["cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-12T10:08:58Z","title":"Partial match queries in random quadtrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2231","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:d478dba0b19a4a910599a309c4aeca0c085e2b9ebc084872dd9c88d6252c5807","target":"record","created_at":"2026-05-18T04:18:25Z","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":"f1b2b039bebf1c86eb5b437ea7bc9c73081f7f0f705656b21374289eca54cf2e","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-12T10:08:58Z","title_canon_sha256":"962052cfeca9245d68db4e1fe933a16a04fbc7283df5f2a7ea3b58adbd977251"},"schema_version":"1.0","source":{"id":"1107.2231","kind":"arxiv","version":1}},"canonical_sha256":"dd1a5021d25f89bd8c1f6c31992409007b7c216939bdafabe8f42e0fa08cb608","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd1a5021d25f89bd8c1f6c31992409007b7c216939bdafabe8f42e0fa08cb608","first_computed_at":"2026-05-18T04:18:25.008365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:25.008365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3UWkqd7eMWTDMg9CrYFBLcQazAhkOIR8wUz1GpLHYwEPi6OtK+11Nn9ERbGjcpiwCwKJ2zypcFbiYnTPaUvpAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:25.008953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d478dba0b19a4a910599a309c4aeca0c085e2b9ebc084872dd9c88d6252c5807","sha256:67e19fe11c923e6df7494e56f6abf0e107da0ca41fbc7a8f55fafc2210f834d9"],"state_sha256":"0c3ce01245719c1ad84191041323e0cc9b413d850cfba9100ce63d7d7dcd2c31"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjycX3SdD/XKYCEX7eCSKtiLloaapTxKtpvAy25Qo7qTzO9Bu5ki8NzUN0/QQMMBnDmz1+v1QxBJrr/KPcY9Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T02:01:28.037783Z","bundle_sha256":"a23130bd4235af2c0829c1cbe6b8d5a51714ca471d66260e828f9c5306a51bf3"}}