{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:E6KEQHUBZSX7ZPOAVPRQ7LRL5F","short_pith_number":"pith:E6KEQHUB","schema_version":"1.0","canonical_sha256":"2794481e81ccaffcbdc0abe30fae2be949cdb1d8ca8e4d8515331f467e3295d8","source":{"kind":"arxiv","id":"1202.1342","version":5},"attestation_state":"computed","paper":{"title":"A limit process for partial match queries in random quadtrees and $2$-d trees","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":"2012-02-07T03:36:00Z","abstract_excerpt":"We consider the problem of recovering items matching a partially specified pattern in multidimensional trees (quadtrees 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 a random query $\\xi$, independent and uniformly distributed on $[0,1]$, satisfies $\\mathbf {E}[{C_n(\\xi )}]\\sim\\kappa n^{\\beta}$, where $\\kappa$ and $\\beta$ are explicit constants. We develop an approach based o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1202.1342","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-07T03:36:00Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"27efce210e51243104e5eb7bf6456ef73a154a0a9501fcc6ec9ef12a533cc0bf","abstract_canon_sha256":"663fb61c916beab6d7da72e5579b9e53955796f64f949b3ad32a36e2c07e5365"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:28.575735Z","signature_b64":"fhPOdOh8CbcvG8dC5b3tDxHeC+pzUSfXcmWA07caQDDUbx8BfpnIU+DngJoLAOcOtfX+fzrg5rstK5NGiS/ADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2794481e81ccaffcbdc0abe30fae2be949cdb1d8ca8e4d8515331f467e3295d8","last_reissued_at":"2026-05-18T03:05:28.574912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:28.574912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A limit process for partial match queries in random quadtrees and $2$-d trees","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":"2012-02-07T03:36:00Z","abstract_excerpt":"We consider the problem of recovering items matching a partially specified pattern in multidimensional trees (quadtrees 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 a random query $\\xi$, independent and uniformly distributed on $[0,1]$, satisfies $\\mathbf {E}[{C_n(\\xi )}]\\sim\\kappa n^{\\beta}$, where $\\kappa$ and $\\beta$ are explicit constants. We develop an approach based o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1342","kind":"arxiv","version":5},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1202.1342","created_at":"2026-05-18T03:05:28.575042+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.1342v5","created_at":"2026-05-18T03:05:28.575042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1342","created_at":"2026-05-18T03:05:28.575042+00:00"},{"alias_kind":"pith_short_12","alias_value":"E6KEQHUBZSX7","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"E6KEQHUBZSX7ZPOA","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"E6KEQHUB","created_at":"2026-05-18T12:27:04.183437+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E6KEQHUBZSX7ZPOAVPRQ7LRL5F","json":"https://pith.science/pith/E6KEQHUBZSX7ZPOAVPRQ7LRL5F.json","graph_json":"https://pith.science/api/pith-number/E6KEQHUBZSX7ZPOAVPRQ7LRL5F/graph.json","events_json":"https://pith.science/api/pith-number/E6KEQHUBZSX7ZPOAVPRQ7LRL5F/events.json","paper":"https://pith.science/paper/E6KEQHUB"},"agent_actions":{"view_html":"https://pith.science/pith/E6KEQHUBZSX7ZPOAVPRQ7LRL5F","download_json":"https://pith.science/pith/E6KEQHUBZSX7ZPOAVPRQ7LRL5F.json","view_paper":"https://pith.science/paper/E6KEQHUB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.1342&json=true","fetch_graph":"https://pith.science/api/pith-number/E6KEQHUBZSX7ZPOAVPRQ7LRL5F/graph.json","fetch_events":"https://pith.science/api/pith-number/E6KEQHUBZSX7ZPOAVPRQ7LRL5F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E6KEQHUBZSX7ZPOAVPRQ7LRL5F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E6KEQHUBZSX7ZPOAVPRQ7LRL5F/action/storage_attestation","attest_author":"https://pith.science/pith/E6KEQHUBZSX7ZPOAVPRQ7LRL5F/action/author_attestation","sign_citation":"https://pith.science/pith/E6KEQHUBZSX7ZPOAVPRQ7LRL5F/action/citation_signature","submit_replication":"https://pith.science/pith/E6KEQHUBZSX7ZPOAVPRQ7LRL5F/action/replication_record"}},"created_at":"2026-05-18T03:05:28.575042+00:00","updated_at":"2026-05-18T03:05:28.575042+00:00"}