{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:EK5DMOCK2AETKRYL6M2X7QMEFS","short_pith_number":"pith:EK5DMOCK","schema_version":"1.0","canonical_sha256":"22ba36384ad00935470bf3357fc1842c80d642f3c69a0e746ec01e2caf8767ba","source":{"kind":"arxiv","id":"1008.3944","version":1},"attestation_state":"computed","paper":{"title":"On the monotonicity of the expected volume of a random simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.PR","authors_text":"Luis Rademacher","submitted_at":"2010-08-24T00:34:38Z","abstract_excerpt":"Let a random simplex in a d-dimensional convex body be the convex hull of d+1 random points from the body. We study the following question: As a function of the convex body, is the expected volume of a random simplex monotone non-decreasing under inclusion? We show that this holds if d is 1 or 2, and does not hold if d >= 4. We also prove similar results for higher moments of the volume of a random simplex, in particular for the second moment, which corresponds to the determinant of the covariance matrix of the convex body. These questions are motivated by the slicing conjecture."},"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":"1008.3944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-08-24T00:34:38Z","cross_cats_sorted":["math.FA","math.MG"],"title_canon_sha256":"4a67da1de7d51162e70688264a88feb0a7969a370c999b3b87123344855fcf65","abstract_canon_sha256":"642e40969d84421ee121b741a85f5ab78dd594427856ad5480b0c9e828ce6203"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:44.364650Z","signature_b64":"DCSj48UN4YMeK2YiJtreL69gRKXmh7seEF+Cakd0HrT0YUuD5GGhCSXtAHjBkrXbkgbUFlVVIuOywy3iHYWhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22ba36384ad00935470bf3357fc1842c80d642f3c69a0e746ec01e2caf8767ba","last_reissued_at":"2026-05-18T03:02:44.364041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:44.364041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the monotonicity of the expected volume of a random simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.PR","authors_text":"Luis Rademacher","submitted_at":"2010-08-24T00:34:38Z","abstract_excerpt":"Let a random simplex in a d-dimensional convex body be the convex hull of d+1 random points from the body. We study the following question: As a function of the convex body, is the expected volume of a random simplex monotone non-decreasing under inclusion? We show that this holds if d is 1 or 2, and does not hold if d >= 4. We also prove similar results for higher moments of the volume of a random simplex, in particular for the second moment, which corresponds to the determinant of the covariance matrix of the convex body. These questions are motivated by the slicing conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3944","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":"1008.3944","created_at":"2026-05-18T03:02:44.364127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.3944v1","created_at":"2026-05-18T03:02:44.364127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3944","created_at":"2026-05-18T03:02:44.364127+00:00"},{"alias_kind":"pith_short_12","alias_value":"EK5DMOCK2AET","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"EK5DMOCK2AETKRYL","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"EK5DMOCK","created_at":"2026-05-18T12:26:06.534383+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/EK5DMOCK2AETKRYL6M2X7QMEFS","json":"https://pith.science/pith/EK5DMOCK2AETKRYL6M2X7QMEFS.json","graph_json":"https://pith.science/api/pith-number/EK5DMOCK2AETKRYL6M2X7QMEFS/graph.json","events_json":"https://pith.science/api/pith-number/EK5DMOCK2AETKRYL6M2X7QMEFS/events.json","paper":"https://pith.science/paper/EK5DMOCK"},"agent_actions":{"view_html":"https://pith.science/pith/EK5DMOCK2AETKRYL6M2X7QMEFS","download_json":"https://pith.science/pith/EK5DMOCK2AETKRYL6M2X7QMEFS.json","view_paper":"https://pith.science/paper/EK5DMOCK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.3944&json=true","fetch_graph":"https://pith.science/api/pith-number/EK5DMOCK2AETKRYL6M2X7QMEFS/graph.json","fetch_events":"https://pith.science/api/pith-number/EK5DMOCK2AETKRYL6M2X7QMEFS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EK5DMOCK2AETKRYL6M2X7QMEFS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EK5DMOCK2AETKRYL6M2X7QMEFS/action/storage_attestation","attest_author":"https://pith.science/pith/EK5DMOCK2AETKRYL6M2X7QMEFS/action/author_attestation","sign_citation":"https://pith.science/pith/EK5DMOCK2AETKRYL6M2X7QMEFS/action/citation_signature","submit_replication":"https://pith.science/pith/EK5DMOCK2AETKRYL6M2X7QMEFS/action/replication_record"}},"created_at":"2026-05-18T03:02:44.364127+00:00","updated_at":"2026-05-18T03:02:44.364127+00:00"}