{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R6M2GA3RWJQGHITI4E2R2MMCAQ","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":"1628c7750af31c90033a11b0e429d969e26b073b2ab24624998acf0ef53bca09","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-23T09:29:47Z","title_canon_sha256":"ccfe4bc7049966cfdba01401a927de5bbfab307f6b659981065823a23aa1709c"},"schema_version":"1.0","source":{"id":"1811.09400","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09400","created_at":"2026-05-17T23:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09400v2","created_at":"2026-05-17T23:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09400","created_at":"2026-05-17T23:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"R6M2GA3RWJQG","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R6M2GA3RWJQGHITI","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R6M2GA3R","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:bdd92cd01f5511df50476a4d841154f6d32a8405af5ade244d1c4bd61310c205","target":"graph","created_at":"2026-05-17T23:52:04Z","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":"Consider a $d$-dimensional simplex whose vertices are random points chosen independently according to the standard Gaussian distribution on $\\mathbb R^d$. We prove that the expected angle sum of this random simplex equals the angle sum of the regular simplex of the same dimension $d$.","authors_text":"Dmitry Zaporozhets, Zakhar Kabluchko","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-23T09:29:47Z","title":"Angles of the Gaussian simplex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09400","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:a263a5f382d63759cd8f0bafae706d4c4e6fd9618aaad34ecfb2cde89e34dcdd","target":"record","created_at":"2026-05-17T23:52:04Z","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":"1628c7750af31c90033a11b0e429d969e26b073b2ab24624998acf0ef53bca09","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-23T09:29:47Z","title_canon_sha256":"ccfe4bc7049966cfdba01401a927de5bbfab307f6b659981065823a23aa1709c"},"schema_version":"1.0","source":{"id":"1811.09400","kind":"arxiv","version":2}},"canonical_sha256":"8f99a30371b26063a268e1351d3182040b8e3ae75237cfaa903c39439c0d536e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f99a30371b26063a268e1351d3182040b8e3ae75237cfaa903c39439c0d536e","first_computed_at":"2026-05-17T23:52:04.140654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:04.140654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AVWudFgfWGUzIbdHgdbL+Z8qbRvpN4mVaZIp2C21Npp3zSt6SnCSM5v01ILzjQXghFZCELeXfXQ6EE239VSaAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:04.141274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09400","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a263a5f382d63759cd8f0bafae706d4c4e6fd9618aaad34ecfb2cde89e34dcdd","sha256:bdd92cd01f5511df50476a4d841154f6d32a8405af5ade244d1c4bd61310c205"],"state_sha256":"a419a2d331736d1081751aed1eb9e903def3ea5af467b1b7001b90403f09f96c"}