{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U5OZBSZRVTHIV7PLCBLIYAN4JG","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":"2d287d0f93b4a78e5644c0c672c1d71b382991fab9955dff55a0eceb7ed01370","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-27T15:34:56Z","title_canon_sha256":"07763799ec084f09b76c45c6d1eb85b4b2368e8f3773cd4f572efde162697ba8"},"schema_version":"1.0","source":{"id":"1806.10535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10535","created_at":"2026-05-18T00:12:12Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10535v1","created_at":"2026-05-18T00:12:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10535","created_at":"2026-05-18T00:12:12Z"},{"alias_kind":"pith_short_12","alias_value":"U5OZBSZRVTHI","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U5OZBSZRVTHIV7PL","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U5OZBSZR","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:cab0fda0ff60eaf5379f79abd4c05afd6cb096802e15755ff7ff45170ed7576e","target":"graph","created_at":"2026-05-18T00:12:12Z","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":"In a recent article, Alishahi and Zamani discuss the spherical ensemble, a rotationally invariant determinantal point process on the 2-sphere. In this paper we extend this process in a natural way to the 2d-dimensional sphere. We prove that the expected value of the Riesz s-energy associated to this determinantal point process has a reasonably low value compared to the known asymptotic expansion of the minimal Riesz s-energy.","authors_text":"Carlos Beltr\\'an, Uju\\'e Etayo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-27T15:34:56Z","title":"A generalization of the spherical ensemble to even-dimensional spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10535","kind":"arxiv","version":1},"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:a23efd423e54f4ed76f4c5ad191c95dbf8f031c0730fdbd8c34f22f75ae72d03","target":"record","created_at":"2026-05-18T00:12:12Z","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":"2d287d0f93b4a78e5644c0c672c1d71b382991fab9955dff55a0eceb7ed01370","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-27T15:34:56Z","title_canon_sha256":"07763799ec084f09b76c45c6d1eb85b4b2368e8f3773cd4f572efde162697ba8"},"schema_version":"1.0","source":{"id":"1806.10535","kind":"arxiv","version":1}},"canonical_sha256":"a75d90cb31acce8afdeb10568c01bc4993da1eb59a3f7af0a0403cb2e5c5f7d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a75d90cb31acce8afdeb10568c01bc4993da1eb59a3f7af0a0403cb2e5c5f7d4","first_computed_at":"2026-05-18T00:12:12.099711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:12.099711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+RhtyDM/D+ZpxE92qNgZf4o/v0ZN4uPSdUv0fZ2B27si1cVVY7jxIUKdTyO+p5eeZcHyPNJzKsm2VY4s5VHMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:12.100455Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a23efd423e54f4ed76f4c5ad191c95dbf8f031c0730fdbd8c34f22f75ae72d03","sha256:cab0fda0ff60eaf5379f79abd4c05afd6cb096802e15755ff7ff45170ed7576e"],"state_sha256":"f009d0374cc07de6893b9dd1fba340bd64fcff893b5d6e3142f2b4c70299ad6e"}