{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WR34DMQKXDZMQV64OKL5YCCGPM","short_pith_number":"pith:WR34DMQK","schema_version":"1.0","canonical_sha256":"b477c1b20ab8f2c857dc7297dc08467b36bde7caf1bf4009e5bc48777fefdc40","source":{"kind":"arxiv","id":"1404.6113","version":2},"attestation_state":"computed","paper":{"title":"Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.PR","authors_text":"Dmitry Zaporozhets, Zakhar Kabluchko","submitted_at":"2014-04-24T13:18:13Z","abstract_excerpt":"A formula due to Sudakov relates the first intrinsic volume of a convex set in a Hilbert space to the maximum of the isonormal Gaussian process over this set. Using this formula we compute the first intrinsic volumes of infinite-dimensional convex compact sets including unit balls with respect to Sobolev-type seminorms and ellipsoids in the Hilbert space. We relate the distribution of the random one-dimensional projections of these sets to the distributions $S_1,S_2,C_1,C_2$ studied by Biane, Pitman, Yor [Bull.\\ AMS 38 (2001)]. We show that the $k$-th intrinsic volume of the set of all functio"},"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":"1404.6113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T13:18:13Z","cross_cats_sorted":["math.FA","math.MG"],"title_canon_sha256":"a4f257e13bd022d75a64fbe58caadfbb1de60a114d5aff92ac0b2bdfdf05ccc6","abstract_canon_sha256":"0ecffd393b22a85692ff6a0919fb006c524a32fc3d0038fa5d8e322a0374365d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:05.829855Z","signature_b64":"U0iciOXUeS+VkgJ4fclTIYTiwtpFyIJC4+ozyf3hu/FV/YCDKqQEgjzr6CgAhMJzNA5uKWEUL2cabguId7MbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b477c1b20ab8f2c857dc7297dc08467b36bde7caf1bf4009e5bc48777fefdc40","last_reissued_at":"2026-05-18T02:52:05.829329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:05.829329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.PR","authors_text":"Dmitry Zaporozhets, Zakhar Kabluchko","submitted_at":"2014-04-24T13:18:13Z","abstract_excerpt":"A formula due to Sudakov relates the first intrinsic volume of a convex set in a Hilbert space to the maximum of the isonormal Gaussian process over this set. Using this formula we compute the first intrinsic volumes of infinite-dimensional convex compact sets including unit balls with respect to Sobolev-type seminorms and ellipsoids in the Hilbert space. We relate the distribution of the random one-dimensional projections of these sets to the distributions $S_1,S_2,C_1,C_2$ studied by Biane, Pitman, Yor [Bull.\\ AMS 38 (2001)]. We show that the $k$-th intrinsic volume of the set of all functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6113","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":"1404.6113","created_at":"2026-05-18T02:52:05.829430+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.6113v2","created_at":"2026-05-18T02:52:05.829430+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6113","created_at":"2026-05-18T02:52:05.829430+00:00"},{"alias_kind":"pith_short_12","alias_value":"WR34DMQKXDZM","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WR34DMQKXDZMQV64","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WR34DMQK","created_at":"2026-05-18T12:28:54.890064+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/WR34DMQKXDZMQV64OKL5YCCGPM","json":"https://pith.science/pith/WR34DMQKXDZMQV64OKL5YCCGPM.json","graph_json":"https://pith.science/api/pith-number/WR34DMQKXDZMQV64OKL5YCCGPM/graph.json","events_json":"https://pith.science/api/pith-number/WR34DMQKXDZMQV64OKL5YCCGPM/events.json","paper":"https://pith.science/paper/WR34DMQK"},"agent_actions":{"view_html":"https://pith.science/pith/WR34DMQKXDZMQV64OKL5YCCGPM","download_json":"https://pith.science/pith/WR34DMQKXDZMQV64OKL5YCCGPM.json","view_paper":"https://pith.science/paper/WR34DMQK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.6113&json=true","fetch_graph":"https://pith.science/api/pith-number/WR34DMQKXDZMQV64OKL5YCCGPM/graph.json","fetch_events":"https://pith.science/api/pith-number/WR34DMQKXDZMQV64OKL5YCCGPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WR34DMQKXDZMQV64OKL5YCCGPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WR34DMQKXDZMQV64OKL5YCCGPM/action/storage_attestation","attest_author":"https://pith.science/pith/WR34DMQKXDZMQV64OKL5YCCGPM/action/author_attestation","sign_citation":"https://pith.science/pith/WR34DMQKXDZMQV64OKL5YCCGPM/action/citation_signature","submit_replication":"https://pith.science/pith/WR34DMQKXDZMQV64OKL5YCCGPM/action/replication_record"}},"created_at":"2026-05-18T02:52:05.829430+00:00","updated_at":"2026-05-18T02:52:05.829430+00:00"}