{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IIRS5V2AJTEFXKLI7I5SFIOLIF","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":"755186914fb394de61bf35f2dc2f244f7a1f515265d8b713765dfd8edc37fca5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-02T06:31:30Z","title_canon_sha256":"2f359879e759ca1166b7bc9e2eda03bae81f8ff847e4826cb479a79f6c85a2c1"},"schema_version":"1.0","source":{"id":"1410.0458","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0458","created_at":"2026-05-18T00:10:31Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0458v4","created_at":"2026-05-18T00:10:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0458","created_at":"2026-05-18T00:10:31Z"},{"alias_kind":"pith_short_12","alias_value":"IIRS5V2AJTEF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IIRS5V2AJTEFXKLI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IIRS5V2A","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:ca787626bdaed06731f0b2fa5f9afc53f41568f2bcc544547d7dc7ff9f858afa","target":"graph","created_at":"2026-05-18T00:10:31Z","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":"We connect this question to a problem of estimating the probability that the image of certain random matrices does not intersect with a subset of the unit sphere $\\mathbb{S}^{n-1}$. In this way, the case of a discretized Brownian motion is related to Gordon's escape theorem dealing with standard Gaussian matrices. The approach allows us to prove that with high probability, the $\\pi/2$-covering time of certain random walks on $\\mathbb{S}^{n-1}$ is of order $n$. For certain spherical simplices on $\\mathbb{S}^{n-1}$, we extend the \"escape\" phenomenon to a broad class of random matrices; as an app","authors_text":"Konstantin Tikhomirov, Pierre Youssef","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-02T06:31:30Z","title":"When does a discrete-time random walk in $\\mathbb{R}^n$ absorb the origin into its convex hull?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0458","kind":"arxiv","version":4},"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:a1329b872dbcba205e13a400b05d7ffe9e506e5f5bb0c532b604b98a983ad734","target":"record","created_at":"2026-05-18T00:10:31Z","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":"755186914fb394de61bf35f2dc2f244f7a1f515265d8b713765dfd8edc37fca5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-02T06:31:30Z","title_canon_sha256":"2f359879e759ca1166b7bc9e2eda03bae81f8ff847e4826cb479a79f6c85a2c1"},"schema_version":"1.0","source":{"id":"1410.0458","kind":"arxiv","version":4}},"canonical_sha256":"42232ed7404cc85ba968fa3b22a1cb416d6f61a2da025d42006a5dbaabf41f55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42232ed7404cc85ba968fa3b22a1cb416d6f61a2da025d42006a5dbaabf41f55","first_computed_at":"2026-05-18T00:10:31.027553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:31.027553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uWK6qJ23Y23UodsgfTGh68Zr/ba4Vg2xqINj41tdP2ed468VdCGVb/OlL1KdXQ5UKRP+WY6ZTTFikDsxERnJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:31.028180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0458","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1329b872dbcba205e13a400b05d7ffe9e506e5f5bb0c532b604b98a983ad734","sha256:ca787626bdaed06731f0b2fa5f9afc53f41568f2bcc544547d7dc7ff9f858afa"],"state_sha256":"30e4b9c175500ad8a865795295b3965bdb2cca011674959c6934fc3754f88824"}