{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WR34DMQKXDZMQV64OKL5YCCGPM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0ecffd393b22a85692ff6a0919fb006c524a32fc3d0038fa5d8e322a0374365d","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T13:18:13Z","title_canon_sha256":"a4f257e13bd022d75a64fbe58caadfbb1de60a114d5aff92ac0b2bdfdf05ccc6"},"schema_version":"1.0","source":{"id":"1404.6113","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6113","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6113v2","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6113","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"WR34DMQKXDZM","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WR34DMQKXDZMQV64","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WR34DMQK","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:5abee56885862cd712e34b2d746a7bd32e78d749c9910373a38ef0a4e2e69700","target":"graph","created_at":"2026-05-18T02:52:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Dmitry Zaporozhets, Zakhar Kabluchko","cross_cats":["math.FA","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T13:18:13Z","title":"Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6113","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:45ae671aff16b883a4e72a9aff87bce0d428fa2a52084673faa3541cda758bf1","target":"record","created_at":"2026-05-18T02:52:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0ecffd393b22a85692ff6a0919fb006c524a32fc3d0038fa5d8e322a0374365d","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T13:18:13Z","title_canon_sha256":"a4f257e13bd022d75a64fbe58caadfbb1de60a114d5aff92ac0b2bdfdf05ccc6"},"schema_version":"1.0","source":{"id":"1404.6113","kind":"arxiv","version":2}},"canonical_sha256":"b477c1b20ab8f2c857dc7297dc08467b36bde7caf1bf4009e5bc48777fefdc40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b477c1b20ab8f2c857dc7297dc08467b36bde7caf1bf4009e5bc48777fefdc40","first_computed_at":"2026-05-18T02:52:05.829329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:05.829329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U0iciOXUeS+VkgJ4fclTIYTiwtpFyIJC4+ozyf3hu/FV/YCDKqQEgjzr6CgAhMJzNA5uKWEUL2cabguId7MbCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:05.829855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6113","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45ae671aff16b883a4e72a9aff87bce0d428fa2a52084673faa3541cda758bf1","sha256:5abee56885862cd712e34b2d746a7bd32e78d749c9910373a38ef0a4e2e69700"],"state_sha256":"9d52f4df305b56ce9f0e45e5c8f08a0cdc1b8a3503ab56a38df038c9e7dceb31"}