{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RHNJKRNO76E434BZBQPVSYCFSH","short_pith_number":"pith:RHNJKRNO","schema_version":"1.0","canonical_sha256":"89da9545aeff89cdf0390c1f59604591c3f45113b3ef53292233b43f5d79454d","source":{"kind":"arxiv","id":"1812.08443","version":1},"attestation_state":"computed","paper":{"title":"Interaction of Poisson hyperplane processes and convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Rolf Schneider","submitted_at":"2018-12-20T09:44:19Z","abstract_excerpt":"Given a stationary and isotropic Poisson hyperplane process and a convex body $K$ in ${\\mathbb R}^d$, we consider the random polytope defined by the intersection of all closed halfspaces containing $K$ that are bounded by hyperplanes of the process not intersecting $K$. We investigate how well the expected mean width of this random polytope approximates the mean width of $K$ if the intensity of the hyperplane process tends to infinity."},"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":"1812.08443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-20T09:44:19Z","cross_cats_sorted":[],"title_canon_sha256":"c801c6387587a15efec9fb74908d0c1b23d1c79bd858345ee11b43f01cef1329","abstract_canon_sha256":"4978f0554054645ca7c8bf61b70b6cb27a6d43554469942f8b9e5bb476d357d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:42:14.248891Z","signature_b64":"5I/GrEaDaOZESyVyb6c3v9RsMjIuUQxXFjdRFC/dlZBmkKjxUQGwuY0GnypEnASVv1hEJgyBkvqaNEIwMQ3DAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89da9545aeff89cdf0390c1f59604591c3f45113b3ef53292233b43f5d79454d","last_reissued_at":"2026-07-05T00:42:14.248435Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:42:14.248435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interaction of Poisson hyperplane processes and convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Rolf Schneider","submitted_at":"2018-12-20T09:44:19Z","abstract_excerpt":"Given a stationary and isotropic Poisson hyperplane process and a convex body $K$ in ${\\mathbb R}^d$, we consider the random polytope defined by the intersection of all closed halfspaces containing $K$ that are bounded by hyperplanes of the process not intersecting $K$. We investigate how well the expected mean width of this random polytope approximates the mean width of $K$ if the intensity of the hyperplane process tends to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08443","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/1812.08443/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":"1812.08443","created_at":"2026-07-05T00:42:14.248482+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.08443v1","created_at":"2026-07-05T00:42:14.248482+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08443","created_at":"2026-07-05T00:42:14.248482+00:00"},{"alias_kind":"pith_short_12","alias_value":"RHNJKRNO76E4","created_at":"2026-07-05T00:42:14.248482+00:00"},{"alias_kind":"pith_short_16","alias_value":"RHNJKRNO76E434BZ","created_at":"2026-07-05T00:42:14.248482+00:00"},{"alias_kind":"pith_short_8","alias_value":"RHNJKRNO","created_at":"2026-07-05T00:42:14.248482+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.09498","citing_title":"Poisson hyperplane processes and approximation of convex bodies","ref_index":21,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RHNJKRNO76E434BZBQPVSYCFSH","json":"https://pith.science/pith/RHNJKRNO76E434BZBQPVSYCFSH.json","graph_json":"https://pith.science/api/pith-number/RHNJKRNO76E434BZBQPVSYCFSH/graph.json","events_json":"https://pith.science/api/pith-number/RHNJKRNO76E434BZBQPVSYCFSH/events.json","paper":"https://pith.science/paper/RHNJKRNO"},"agent_actions":{"view_html":"https://pith.science/pith/RHNJKRNO76E434BZBQPVSYCFSH","download_json":"https://pith.science/pith/RHNJKRNO76E434BZBQPVSYCFSH.json","view_paper":"https://pith.science/paper/RHNJKRNO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.08443&json=true","fetch_graph":"https://pith.science/api/pith-number/RHNJKRNO76E434BZBQPVSYCFSH/graph.json","fetch_events":"https://pith.science/api/pith-number/RHNJKRNO76E434BZBQPVSYCFSH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RHNJKRNO76E434BZBQPVSYCFSH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RHNJKRNO76E434BZBQPVSYCFSH/action/storage_attestation","attest_author":"https://pith.science/pith/RHNJKRNO76E434BZBQPVSYCFSH/action/author_attestation","sign_citation":"https://pith.science/pith/RHNJKRNO76E434BZBQPVSYCFSH/action/citation_signature","submit_replication":"https://pith.science/pith/RHNJKRNO76E434BZBQPVSYCFSH/action/replication_record"}},"created_at":"2026-07-05T00:42:14.248482+00:00","updated_at":"2026-07-05T00:42:14.248482+00:00"}