{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:II6IP64P3I7SMNCM4JPLLXA6FL","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":"d1347d4f7fae9f8aa57d1080a9fba033dfb0449df59d24076a6ad32fcbc3023a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-01T01:29:12Z","title_canon_sha256":"f3f8582e5954aa9596c183f8a36a044bf0537a77fc78f57ef69405cb47a29b7e"},"schema_version":"1.0","source":{"id":"1104.0059","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0059","created_at":"2026-05-18T04:16:11Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0059v1","created_at":"2026-05-18T04:16:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0059","created_at":"2026-05-18T04:16:11Z"},{"alias_kind":"pith_short_12","alias_value":"II6IP64P3I7S","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"II6IP64P3I7SMNCM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"II6IP64P","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:b544b62898ba748d94ac31424a51dda55a5f9f46b7ba60c0afb8ea54e034cde5","target":"graph","created_at":"2026-05-18T04:16:11Z","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":"Multivariate random fields whose distributions are invariant under operator-scalings in both time-domain and state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are characterized. Two classes of operator-self-similar stable random fields $X=\\{X(t), t \\in \\R^d\\}$ with values in $\\R^m$ are constructed by utilizing homogeneous functions and stochastic integral representations.","authors_text":"Yimin Xiao, Yuqiang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-01T01:29:12Z","title":"Multivariate Operator-Self-Similar Random Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0059","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":"sha256:35a1520842e174651e4c8fa2fb7d37f60222161dfed0903017499ac765d57341","target":"record","created_at":"2026-05-18T04:16:11Z","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":"d1347d4f7fae9f8aa57d1080a9fba033dfb0449df59d24076a6ad32fcbc3023a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-04-01T01:29:12Z","title_canon_sha256":"f3f8582e5954aa9596c183f8a36a044bf0537a77fc78f57ef69405cb47a29b7e"},"schema_version":"1.0","source":{"id":"1104.0059","kind":"arxiv","version":1}},"canonical_sha256":"423c87fb8fda3f26344ce25eb5dc1e2ac4d41075cc1ce5fa3c6200f68996347b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"423c87fb8fda3f26344ce25eb5dc1e2ac4d41075cc1ce5fa3c6200f68996347b","first_computed_at":"2026-05-18T04:16:11.869590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:11.869590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4q/4ohGnEjd0dBJOYOJJgieiJ36tH05mSGLFB8TV3gb+HmfVNowD4cI0cGbY92z/0FZMz8Nk1o9yMn2pv8JBBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:11.869931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0059","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35a1520842e174651e4c8fa2fb7d37f60222161dfed0903017499ac765d57341","sha256:b544b62898ba748d94ac31424a51dda55a5f9f46b7ba60c0afb8ea54e034cde5"],"state_sha256":"7a35afbd3b203d97ebb69537df206e880be844115417fb2192562835977e7522"}