{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RJ7M36VHZFG2UWWPJB6CPRFOPQ","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":"026fe5e4336b8f01f47dfcc4ee09f7fd2ab708f10064ae0477b454cc146b128d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CA","submitted_at":"2017-04-05T01:31:29Z","title_canon_sha256":"f32f3a29df9bce90de9f1d0d63004875b27402d830fb6e8cdb6b5a31ace77817"},"schema_version":"1.0","source":{"id":"1704.01237","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01237","created_at":"2026-05-17T23:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01237v2","created_at":"2026-05-17T23:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01237","created_at":"2026-05-17T23:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"RJ7M36VHZFG2","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RJ7M36VHZFG2UWWP","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RJ7M36VH","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:bea15787ba8162a5d233d656333807a40800b0d3a2cdec5f3f01c37928123eb9","target":"graph","created_at":"2026-05-17T23:50:50Z","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 provide walks through dimensions for isotropic positive definite functions defined over complex spheres. We show that the analogues of Mont\\'ee and Descente operators as proposed by Beatson and zu Castell [J. Approx. Theory 221 (2017), 22-37] on the basis of the original Matheron operator [Les variables r\\'egionalis\\'ees et leur estimation, Masson, Paris, 1965], allow for similar walks through dimensions. We show that the Mont\\'ee operators also preserve, up to a constant, strict positive definiteness. For the Descente operators, we show that strict positive definiteness is preserved under ","authors_text":"Ana Paula Peron, Emilio Porcu, Eugenio Massa","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CA","submitted_at":"2017-04-05T01:31:29Z","title":"Positive Definite Functions on Complex Spheres and their Walks through Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01237","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:ab81fe48f62b4356864f801f42bdc79eb2c756c9fd61380cdf7a42a97e51f18c","target":"record","created_at":"2026-05-17T23:50:50Z","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":"026fe5e4336b8f01f47dfcc4ee09f7fd2ab708f10064ae0477b454cc146b128d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.CA","submitted_at":"2017-04-05T01:31:29Z","title_canon_sha256":"f32f3a29df9bce90de9f1d0d63004875b27402d830fb6e8cdb6b5a31ace77817"},"schema_version":"1.0","source":{"id":"1704.01237","kind":"arxiv","version":2}},"canonical_sha256":"8a7ecdfaa7c94daa5acf487c27c4ae7c1e0ebdd06429160c441d3e5e857cbcc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a7ecdfaa7c94daa5acf487c27c4ae7c1e0ebdd06429160c441d3e5e857cbcc1","first_computed_at":"2026-05-17T23:50:50.704447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:50.704447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0kY2MNxX7cZkKAEY2awwhT7OKLUnQEyCL6chZHEEjdcchfdTTVXr20t/P4aUP5x9pyvu27akpU3SivcUHNk4Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:50.705194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.01237","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab81fe48f62b4356864f801f42bdc79eb2c756c9fd61380cdf7a42a97e51f18c","sha256:bea15787ba8162a5d233d656333807a40800b0d3a2cdec5f3f01c37928123eb9"],"state_sha256":"13fac905a1751bf715727fd672fe8b19449c12195cfdfb0c51327c217cd94fb1"}