{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VDTYQPUKYPIBIFY743XDNS7SM5","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":"6d991a8a60c1b60544631080e8e65550b7f1c80186a5fe2e7850370b38057b22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-11T18:44:24Z","title_canon_sha256":"7919f191650c32c02c295624bbbdce367f8d29ab912a6b3ce4fb88bc49991cf4"},"schema_version":"1.0","source":{"id":"1806.04181","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04181","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04181v1","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04181","created_at":"2026-05-18T00:13:36Z"},{"alias_kind":"pith_short_12","alias_value":"VDTYQPUKYPIB","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VDTYQPUKYPIBIFY7","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VDTYQPUK","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:29a1636e31ba14a14a27dbc2f33fdc283d9697cc596b12f8f2f06ca95c3e38ec","target":"graph","created_at":"2026-05-18T00:13:36Z","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":"This paper studies the problem of equivalence of Gaussian measures induced by Gaussian random fields (GRFs) with stationary increments and proves a sufficient condition for the equivalence in terms of the behavior of the spectral measures at infinity. The main results extend those of Stein (2004), Van Zanten (2007, 2008) and are applicable to a rich family of nonstationary space-time models with possible anisotropy behavior.","authors_text":"Abolfazl Safikhani, Yimin Xiao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-11T18:44:24Z","title":"Spectral Conditions for Equivalence of Gaussian Random Fields with Stationary Increments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04181","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":"sha256:785b65e8d8c9d7fec6acef81d6537dcb1328b344198bf4e7a48f0395b471a97d","target":"record","created_at":"2026-05-18T00:13:36Z","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":"6d991a8a60c1b60544631080e8e65550b7f1c80186a5fe2e7850370b38057b22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-11T18:44:24Z","title_canon_sha256":"7919f191650c32c02c295624bbbdce367f8d29ab912a6b3ce4fb88bc49991cf4"},"schema_version":"1.0","source":{"id":"1806.04181","kind":"arxiv","version":1}},"canonical_sha256":"a8e7883e8ac3d014171fe6ee36cbf2674ac0ae8a8010e31ad5a5fae5d62a6653","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8e7883e8ac3d014171fe6ee36cbf2674ac0ae8a8010e31ad5a5fae5d62a6653","first_computed_at":"2026-05-18T00:13:36.379842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:36.379842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ok7tqhLhmWttwmW392oX/yrMGTpTOqq5Fm1lfKYMMT6M6JCen59LXtf7zycWQ6Yo8AKgc28z1l5cOIQxFO+WAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:36.380569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.04181","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:785b65e8d8c9d7fec6acef81d6537dcb1328b344198bf4e7a48f0395b471a97d","sha256:29a1636e31ba14a14a27dbc2f33fdc283d9697cc596b12f8f2f06ca95c3e38ec"],"state_sha256":"64ab348f07dab0782ddbdd25ef0cb1e4f1fc14cdf9924fc281e2da824732182d"}