{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RRWQW62DQ7DVHWI76YYXRRKFTG","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":"441b72995240ab5acf71ae65aeace1ff2af63983f9b4cc13e97a1358fa3590c0","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-09T08:44:22Z","title_canon_sha256":"c739ca159ff494bb40f22d82ccdea224185b6df85255e62d550e0b61401c34a0"},"schema_version":"1.0","source":{"id":"1611.02851","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02851","created_at":"2026-05-18T00:25:11Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02851v2","created_at":"2026-05-18T00:25:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02851","created_at":"2026-05-18T00:25:11Z"},{"alias_kind":"pith_short_12","alias_value":"RRWQW62DQ7DV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RRWQW62DQ7DVHWI7","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RRWQW62D","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:f23182c77a72153d38a3dc23ad3daf7c2fdb0ca2d9ebbac23ab544527b5caec8","target":"graph","created_at":"2026-05-18T00:25:11Z","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 study the regularity properties of Gaussian fields defined over spheres cross time. In particular, we consider two alternative spectral decompositions for a Gaussian field on $\\mathbb{S}^d \\times \\mathbb{R}$. For each decomposition, we establish regularity properties through Sobolev and interpolation spaces. We then propose a simulation method and study its level of accuracy in the $L^2$ sense. The method turns to be both fast and efficient.","authors_text":"Alfredo Alegr\\'ia, Emilio Porcu, Jorge Clarke de La Cerda (CEREMADE), Jorge De La Cerda","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-09T08:44:22Z","title":"Regularity properties and simulations of Gaussian random fields on the Sphere cross Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02851","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":"sha256:05c5fd5529a2d9c69ef54a4fa7a254a3e6bb8e138c27bbc383a4b911d13c6f3f","target":"record","created_at":"2026-05-18T00:25:11Z","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":"441b72995240ab5acf71ae65aeace1ff2af63983f9b4cc13e97a1358fa3590c0","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-09T08:44:22Z","title_canon_sha256":"c739ca159ff494bb40f22d82ccdea224185b6df85255e62d550e0b61401c34a0"},"schema_version":"1.0","source":{"id":"1611.02851","kind":"arxiv","version":2}},"canonical_sha256":"8c6d0b7b4387c753d91ff63178c54599ba745ff0018b8f420faee7404fb3cb52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c6d0b7b4387c753d91ff63178c54599ba745ff0018b8f420faee7404fb3cb52","first_computed_at":"2026-05-18T00:25:11.883581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:11.883581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QsCwjPJgrx2xkgUwz2qV9qqkXEQ80Mq2bGw//TzvKKkzznODWyf3TNJ0QC0FMBTAyQJyCEgnzaKkNCrIpsyWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:11.884094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02851","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05c5fd5529a2d9c69ef54a4fa7a254a3e6bb8e138c27bbc383a4b911d13c6f3f","sha256:f23182c77a72153d38a3dc23ad3daf7c2fdb0ca2d9ebbac23ab544527b5caec8"],"state_sha256":"811c466c464a8f0c755dbef340d36f4081ae5ee9613fd489512dd0d886491e0f"}