{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:Q6D6GRD4N4CTNFVHI7IUDJPF52","short_pith_number":"pith:Q6D6GRD4","schema_version":"1.0","canonical_sha256":"8787e3447c6f053696a747d141a5e5eeb36d088bf0318d2e75c932161b94915e","source":{"kind":"arxiv","id":"1204.0824","version":1},"attestation_state":"computed","paper":{"title":"Self-improving Algorithms for Coordinate-wise Maxima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"C. Seshadhri, Kenneth L. Clarkson, Wolfgang Mulzer","submitted_at":"2012-04-03T22:42:57Z","abstract_excerpt":"Computing the coordinate-wise maxima of a planar point set is a classic and well-studied problem in computational geometry. We give an algorithm for this problem in the \\emph{self-improving setting}. We have $n$ (unknown) independent distributions $\\cD_1, \\cD_2, ..., \\cD_n$ of planar points. An input pointset $(p_1, p_2, ..., p_n)$ is generated by taking an independent sample $p_i$ from each $\\cD_i$, so the input distribution $\\cD$ is the product $\\prod_i \\cD_i$. A self-improving algorithm repeatedly gets input sets from the distribution $\\cD$ (which is \\emph{a priori} unknown) and tries to op"},"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":"1204.0824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-04-03T22:42:57Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"9e47a4e8a8f3dd35b804a8c31e75b91c6052cfa6b5bd56e78f7a07dfed08be06","abstract_canon_sha256":"94f214f4c1947901b4e6c57d093d1df80e72e2ba11d40dcced89a1a37ad30fcd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:15.636745Z","signature_b64":"zwHIV23u3lahvAtWTUqe/HYYWKvDvo6R5de5ihRBjch8bvgjY4Y2HKnW3KVj089XFkB/t6A00CQvmpkjQH9dCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8787e3447c6f053696a747d141a5e5eeb36d088bf0318d2e75c932161b94915e","last_reissued_at":"2026-05-18T02:53:15.636107Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:15.636107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-improving Algorithms for Coordinate-wise Maxima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"C. Seshadhri, Kenneth L. Clarkson, Wolfgang Mulzer","submitted_at":"2012-04-03T22:42:57Z","abstract_excerpt":"Computing the coordinate-wise maxima of a planar point set is a classic and well-studied problem in computational geometry. We give an algorithm for this problem in the \\emph{self-improving setting}. We have $n$ (unknown) independent distributions $\\cD_1, \\cD_2, ..., \\cD_n$ of planar points. An input pointset $(p_1, p_2, ..., p_n)$ is generated by taking an independent sample $p_i$ from each $\\cD_i$, so the input distribution $\\cD$ is the product $\\prod_i \\cD_i$. A self-improving algorithm repeatedly gets input sets from the distribution $\\cD$ (which is \\emph{a priori} unknown) and tries to op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0824","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1204.0824","created_at":"2026-05-18T02:53:15.636213+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.0824v1","created_at":"2026-05-18T02:53:15.636213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0824","created_at":"2026-05-18T02:53:15.636213+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q6D6GRD4N4CT","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q6D6GRD4N4CTNFVH","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q6D6GRD4","created_at":"2026-05-18T12:27:18.751474+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/Q6D6GRD4N4CTNFVHI7IUDJPF52","json":"https://pith.science/pith/Q6D6GRD4N4CTNFVHI7IUDJPF52.json","graph_json":"https://pith.science/api/pith-number/Q6D6GRD4N4CTNFVHI7IUDJPF52/graph.json","events_json":"https://pith.science/api/pith-number/Q6D6GRD4N4CTNFVHI7IUDJPF52/events.json","paper":"https://pith.science/paper/Q6D6GRD4"},"agent_actions":{"view_html":"https://pith.science/pith/Q6D6GRD4N4CTNFVHI7IUDJPF52","download_json":"https://pith.science/pith/Q6D6GRD4N4CTNFVHI7IUDJPF52.json","view_paper":"https://pith.science/paper/Q6D6GRD4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.0824&json=true","fetch_graph":"https://pith.science/api/pith-number/Q6D6GRD4N4CTNFVHI7IUDJPF52/graph.json","fetch_events":"https://pith.science/api/pith-number/Q6D6GRD4N4CTNFVHI7IUDJPF52/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q6D6GRD4N4CTNFVHI7IUDJPF52/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q6D6GRD4N4CTNFVHI7IUDJPF52/action/storage_attestation","attest_author":"https://pith.science/pith/Q6D6GRD4N4CTNFVHI7IUDJPF52/action/author_attestation","sign_citation":"https://pith.science/pith/Q6D6GRD4N4CTNFVHI7IUDJPF52/action/citation_signature","submit_replication":"https://pith.science/pith/Q6D6GRD4N4CTNFVHI7IUDJPF52/action/replication_record"}},"created_at":"2026-05-18T02:53:15.636213+00:00","updated_at":"2026-05-18T02:53:15.636213+00:00"}