{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CQSHQRGIJ545FZEMKJHEDPZYIF","short_pith_number":"pith:CQSHQRGI","schema_version":"1.0","canonical_sha256":"14247844c84f79d2e48c524e41bf384147d97f69095301cd1b86afe6ea427fa7","source":{"kind":"arxiv","id":"2606.25854","version":1},"attestation_state":"computed","paper":{"title":"Sharp approximate Carath\\'eodory theorem and application to iterated Delaunay refinement","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"cs.CG","authors_text":"Rapha\\\"el Tinarrage","submitted_at":"2026-06-24T14:02:42Z","abstract_excerpt":"We analyze the decrease of simplex diameters under iterated refinement of spherical Delaunay complexes. Unlike in ordinary subdivision, the refined Delaunay complex need not be a subdivision of the previous one, so mesh contraction is not automatic. We derive explicit contraction bounds for several families of Steiner points, including Delaunay analogues of barycentric and edgewise subdivision. The proof reduces the problem to sharp covering estimates for Euclidean simplices. These estimates are obtained through a strengthening of Maurey's empirical method via pivotal sampling and a dimension-"},"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":"2606.25854","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2026-06-24T14:02:42Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"42495d30c034384a2285b741976a846414c8f90513a8e39a379951cd801fdb7a","abstract_canon_sha256":"ab46c1847f21b7b43245838d849918b604c214152be5e15fa971ecf9bc7d9e6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:41.142590Z","signature_b64":"xje+Y8fEFlQ1C3gVQWDdc5eXidT/l5Gkf35nJRyDw4o9LzIOSZ/PDNdpi6HUy5H4iskjSxz1eusO4xzQaBSaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14247844c84f79d2e48c524e41bf384147d97f69095301cd1b86afe6ea427fa7","last_reissued_at":"2026-06-25T01:18:41.142114Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:41.142114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp approximate Carath\\'eodory theorem and application to iterated Delaunay refinement","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"cs.CG","authors_text":"Rapha\\\"el Tinarrage","submitted_at":"2026-06-24T14:02:42Z","abstract_excerpt":"We analyze the decrease of simplex diameters under iterated refinement of spherical Delaunay complexes. Unlike in ordinary subdivision, the refined Delaunay complex need not be a subdivision of the previous one, so mesh contraction is not automatic. We derive explicit contraction bounds for several families of Steiner points, including Delaunay analogues of barycentric and edgewise subdivision. The proof reduces the problem to sharp covering estimates for Euclidean simplices. These estimates are obtained through a strengthening of Maurey's empirical method via pivotal sampling and a dimension-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25854","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.25854/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.25854","created_at":"2026-06-25T01:18:41.142217+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.25854v1","created_at":"2026-06-25T01:18:41.142217+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25854","created_at":"2026-06-25T01:18:41.142217+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQSHQRGIJ545","created_at":"2026-06-25T01:18:41.142217+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQSHQRGIJ545FZEM","created_at":"2026-06-25T01:18:41.142217+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQSHQRGI","created_at":"2026-06-25T01:18:41.142217+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/CQSHQRGIJ545FZEMKJHEDPZYIF","json":"https://pith.science/pith/CQSHQRGIJ545FZEMKJHEDPZYIF.json","graph_json":"https://pith.science/api/pith-number/CQSHQRGIJ545FZEMKJHEDPZYIF/graph.json","events_json":"https://pith.science/api/pith-number/CQSHQRGIJ545FZEMKJHEDPZYIF/events.json","paper":"https://pith.science/paper/CQSHQRGI"},"agent_actions":{"view_html":"https://pith.science/pith/CQSHQRGIJ545FZEMKJHEDPZYIF","download_json":"https://pith.science/pith/CQSHQRGIJ545FZEMKJHEDPZYIF.json","view_paper":"https://pith.science/paper/CQSHQRGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.25854&json=true","fetch_graph":"https://pith.science/api/pith-number/CQSHQRGIJ545FZEMKJHEDPZYIF/graph.json","fetch_events":"https://pith.science/api/pith-number/CQSHQRGIJ545FZEMKJHEDPZYIF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQSHQRGIJ545FZEMKJHEDPZYIF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQSHQRGIJ545FZEMKJHEDPZYIF/action/storage_attestation","attest_author":"https://pith.science/pith/CQSHQRGIJ545FZEMKJHEDPZYIF/action/author_attestation","sign_citation":"https://pith.science/pith/CQSHQRGIJ545FZEMKJHEDPZYIF/action/citation_signature","submit_replication":"https://pith.science/pith/CQSHQRGIJ545FZEMKJHEDPZYIF/action/replication_record"}},"created_at":"2026-06-25T01:18:41.142217+00:00","updated_at":"2026-06-25T01:18:41.142217+00:00"}