{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OMI7O5GEI3KTTD7MLKH2ZMKRNQ","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":"7367d68bb6a8c7419f6910a02e0bfc77ffa82c117331573224150658c25cefda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-17T15:07:01Z","title_canon_sha256":"56ccf50973816459f7057996791bc053c8402659b0bf456a8a5ff3497ff64d5c"},"schema_version":"1.0","source":{"id":"1905.07312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07312","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07312v1","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07312","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"OMI7O5GEI3KT","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OMI7O5GEI3KTTD7M","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OMI7O5GE","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:3228b65e7c034dc52b7dca7426edca01fe2e90cb7936ee88d773915306423961","target":"graph","created_at":"2026-05-17T23:45:55Z","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":"The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and sufficient conditions are derived for a symmetric and continuous matrix function to be an isotropic covariance matrix function on all compact two-point homogeneous spaces. It is also shown that, for a symmetric and continuous matrix function with compact support, if it makes an isotropic covariance matrix function in the Euclidean space, then it makes an isot","authors_text":"Chunsheng Ma, Tianshi Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-17T15:07:01Z","title":"Isotropic covariance matrix functions on compact two-point homogeneous spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07312","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":"sha256:27e6df5a822bce17e4ee8322e9da60b7de29cc9b3475e142f44f065fcdc286eb","target":"record","created_at":"2026-05-17T23:45:55Z","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":"7367d68bb6a8c7419f6910a02e0bfc77ffa82c117331573224150658c25cefda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-17T15:07:01Z","title_canon_sha256":"56ccf50973816459f7057996791bc053c8402659b0bf456a8a5ff3497ff64d5c"},"schema_version":"1.0","source":{"id":"1905.07312","kind":"arxiv","version":1}},"canonical_sha256":"7311f774c446d5398fec5a8facb1516c2263ef60a37754a7185b45d2ec97e19e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7311f774c446d5398fec5a8facb1516c2263ef60a37754a7185b45d2ec97e19e","first_computed_at":"2026-05-17T23:45:55.895347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:55.895347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cWX5CnruQyelRsrMDsmJg2rhaoMxBlBlc20GTQv0NtQZuhQqiIRk7ruB+k2XLAC4CPEU3RbVwjeemQIm3TP7BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:55.896000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27e6df5a822bce17e4ee8322e9da60b7de29cc9b3475e142f44f065fcdc286eb","sha256:3228b65e7c034dc52b7dca7426edca01fe2e90cb7936ee88d773915306423961"],"state_sha256":"83c220c5b89082306568366395f0dc12a584724c870f7c1635b9e37f81ea1c0f"}