{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NH5DON3A6RRPORL2YA4U5WKVNZ","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":"ea8e3fa9b0fb8971069479eaa3d95e3193e6ef2c60450e1b4a07a6accb9384a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-16T16:28:08Z","title_canon_sha256":"bffcd4e8d9fcded800716a80d5b498717252c278ea5b202b1816c5c5879cc530"},"schema_version":"1.0","source":{"id":"1612.05541","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05541","created_at":"2026-05-18T00:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05541v2","created_at":"2026-05-18T00:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05541","created_at":"2026-05-18T00:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"NH5DON3A6RRP","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NH5DON3A6RRPORL2","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NH5DON3A","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:dfd32a50c324e9f75f28595f1ff2f528a4b423cf9af86d8892baca9ca49426c3","target":"graph","created_at":"2026-05-18T00:28:07Z","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":"In this paper approximation methods for infinite-dimensional Levy processes, also called (time-dependent) Levy fields, are introduced. For square integrable fields beyond the Gaussian case, it is no longer given that the one-dimensional distributions in the spectral representation with respect to the covariance operator are independent. When simulated via a Karhunen-Loeve expansion a set of dependent but uncorrelated one-dimensional Levy processes has to be generated. The dependence structure among the one-dimensional processes ensures that the resulting field exhibits the correct point-wise m","authors_text":"Andrea Barth, Andreas Stein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-16T16:28:08Z","title":"Approximation and simulation of infinite-dimensional Levy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05541","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:bfd8c582d1ca7a634684608c70717c469e11bc58fa7e1ca70340022600877920","target":"record","created_at":"2026-05-18T00:28:07Z","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":"ea8e3fa9b0fb8971069479eaa3d95e3193e6ef2c60450e1b4a07a6accb9384a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-16T16:28:08Z","title_canon_sha256":"bffcd4e8d9fcded800716a80d5b498717252c278ea5b202b1816c5c5879cc530"},"schema_version":"1.0","source":{"id":"1612.05541","kind":"arxiv","version":2}},"canonical_sha256":"69fa373760f462f7457ac0394ed9556e56117d2b59d2c78b17dfa948f61667a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69fa373760f462f7457ac0394ed9556e56117d2b59d2c78b17dfa948f61667a6","first_computed_at":"2026-05-18T00:28:07.156936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:07.156936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BNcd4dw+4QrpBNRLDsb9hANAtFGD544DGwvoCki4PrkzXvFx52aURBIyHmXh0nPOrhF8+UsiDnKYpTQNuqXJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:07.157795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05541","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfd8c582d1ca7a634684608c70717c469e11bc58fa7e1ca70340022600877920","sha256:dfd32a50c324e9f75f28595f1ff2f528a4b423cf9af86d8892baca9ca49426c3"],"state_sha256":"1122d7947d787310ffd9e1124c021c490f04bc07a9cd019f99c3443bd9d1295d"}