{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SCIVNNX6XK3UTKC2FFSLVHVCOY","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":"600837901e6159c6cfbc5537707516778e00775320002bf3622cee44863d12e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-04T19:50:16Z","title_canon_sha256":"8fae2c7841920637381ad4b120f8f7e1eec39d56903beeec0b1362bfcaa6f7f9"},"schema_version":"1.0","source":{"id":"1302.0818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0818","created_at":"2026-05-18T03:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0818v1","created_at":"2026-05-18T03:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0818","created_at":"2026-05-18T03:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"SCIVNNX6XK3U","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SCIVNNX6XK3UTKC2","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SCIVNNX6","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:c1edc6e1c37bef2e3ae710adc858f788d6f8f3e59ff8d7ebf1a891c50895a175","target":"graph","created_at":"2026-05-18T03:34:36Z","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":"We study the sample paths properties of Operator scaling Gaussian random fields. Such fields are anisotropic generalizations of anisotropic self-similar random fields as anisotropic Fractional Brownian Motion. Some characteristic properties of the anisotropy are revealed by the regularity of the sample paths. The sharpest way of measuring smoothness is related to these anisotropies and thus to the geometry of these fields.","authors_text":"B. Vedel, M. Clausel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-04T19:50:16Z","title":"An optimality result about sample path properties of Operator Scaling Gaussian Random Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0818","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:b41882dcc4ac6c3363d9501dad1983e06cef6dfda2766f2d392b28264bf86e6f","target":"record","created_at":"2026-05-18T03:34:36Z","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":"600837901e6159c6cfbc5537707516778e00775320002bf3622cee44863d12e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-04T19:50:16Z","title_canon_sha256":"8fae2c7841920637381ad4b120f8f7e1eec39d56903beeec0b1362bfcaa6f7f9"},"schema_version":"1.0","source":{"id":"1302.0818","kind":"arxiv","version":1}},"canonical_sha256":"909156b6febab749a85a2964ba9ea27625b5f25c8ed16277a66edb28bf8b43ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"909156b6febab749a85a2964ba9ea27625b5f25c8ed16277a66edb28bf8b43ec","first_computed_at":"2026-05-18T03:34:36.207720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:36.207720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CAmZgN90kr0ryoJdsuwG8SwPxQPspPnz+UMYFMIIZL1LtiIsiKosH4ATHrnPPsgbmw1KAJD376/ftR5e9FxDAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:36.208268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b41882dcc4ac6c3363d9501dad1983e06cef6dfda2766f2d392b28264bf86e6f","sha256:c1edc6e1c37bef2e3ae710adc858f788d6f8f3e59ff8d7ebf1a891c50895a175"],"state_sha256":"4f5742d0146af311beda1198478579856ffcf1cfbd47e2a142b9e3a645caf619"}