{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JYSAFAVMQDCBFQIP7ML4ZHZJHE","short_pith_number":"pith:JYSAFAVM","schema_version":"1.0","canonical_sha256":"4e240282ac80c412c10ffb17cc9f29390e940eab260827b776e955c9c92d9ad8","source":{"kind":"arxiv","id":"1602.06148","version":2},"attestation_state":"computed","paper":{"title":"Gaussian polytopes: a cumulant-based approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Christoph Thaele, Julian Grote","submitted_at":"2016-02-19T13:35:28Z","abstract_excerpt":"The random convex hull of a Poisson point process in $\\mathbb{R}^d$ whose intensity measure is a multiple of the standard Gaussian measure on $\\mathbb{R}^d$ is investigated. The purpose of this paper is to invent a new viewpoint on these Gaussian polytopes that is based on cumulants and the general large deviation theory of Saulis and Statulevi\\v{c}ius. This leads to new and powerful concentration inequalities, moment bounds, Marcinkiewicz-Zygmund-type strong laws of large numbers, central limit theorems and moderate deviation principles for the volume and the face numbers. Corresponding resul"},"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":"1602.06148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-19T13:35:28Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"6acddc507805054eeb6b3bc1a9a2dc4ae72bc1455cb7c1d3f6ca42a9a04a5c7c","abstract_canon_sha256":"84c7abdf6713ab913b96c548a59a6498fb9464306df73f3bff84dc0e073214bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:04.626469Z","signature_b64":"FpzqmtmDeJhFfZ512YPsuOPADFiDV9Qvv0idR4Tn0y5nI0YQe1f0Um4dQiV1fmuQUxqRaL4AkcD45j5CsPsgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e240282ac80c412c10ffb17cc9f29390e940eab260827b776e955c9c92d9ad8","last_reissued_at":"2026-05-18T00:19:04.625719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:04.625719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gaussian polytopes: a cumulant-based approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Christoph Thaele, Julian Grote","submitted_at":"2016-02-19T13:35:28Z","abstract_excerpt":"The random convex hull of a Poisson point process in $\\mathbb{R}^d$ whose intensity measure is a multiple of the standard Gaussian measure on $\\mathbb{R}^d$ is investigated. The purpose of this paper is to invent a new viewpoint on these Gaussian polytopes that is based on cumulants and the general large deviation theory of Saulis and Statulevi\\v{c}ius. This leads to new and powerful concentration inequalities, moment bounds, Marcinkiewicz-Zygmund-type strong laws of large numbers, central limit theorems and moderate deviation principles for the volume and the face numbers. Corresponding resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06148","kind":"arxiv","version":2},"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":"1602.06148","created_at":"2026-05-18T00:19:04.625824+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.06148v2","created_at":"2026-05-18T00:19:04.625824+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06148","created_at":"2026-05-18T00:19:04.625824+00:00"},{"alias_kind":"pith_short_12","alias_value":"JYSAFAVMQDCB","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JYSAFAVMQDCBFQIP","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JYSAFAVM","created_at":"2026-05-18T12:30:25.849896+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/JYSAFAVMQDCBFQIP7ML4ZHZJHE","json":"https://pith.science/pith/JYSAFAVMQDCBFQIP7ML4ZHZJHE.json","graph_json":"https://pith.science/api/pith-number/JYSAFAVMQDCBFQIP7ML4ZHZJHE/graph.json","events_json":"https://pith.science/api/pith-number/JYSAFAVMQDCBFQIP7ML4ZHZJHE/events.json","paper":"https://pith.science/paper/JYSAFAVM"},"agent_actions":{"view_html":"https://pith.science/pith/JYSAFAVMQDCBFQIP7ML4ZHZJHE","download_json":"https://pith.science/pith/JYSAFAVMQDCBFQIP7ML4ZHZJHE.json","view_paper":"https://pith.science/paper/JYSAFAVM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.06148&json=true","fetch_graph":"https://pith.science/api/pith-number/JYSAFAVMQDCBFQIP7ML4ZHZJHE/graph.json","fetch_events":"https://pith.science/api/pith-number/JYSAFAVMQDCBFQIP7ML4ZHZJHE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JYSAFAVMQDCBFQIP7ML4ZHZJHE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JYSAFAVMQDCBFQIP7ML4ZHZJHE/action/storage_attestation","attest_author":"https://pith.science/pith/JYSAFAVMQDCBFQIP7ML4ZHZJHE/action/author_attestation","sign_citation":"https://pith.science/pith/JYSAFAVMQDCBFQIP7ML4ZHZJHE/action/citation_signature","submit_replication":"https://pith.science/pith/JYSAFAVMQDCBFQIP7ML4ZHZJHE/action/replication_record"}},"created_at":"2026-05-18T00:19:04.625824+00:00","updated_at":"2026-05-18T00:19:04.625824+00:00"}