{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CZESOWBRZ6VPYAVNRGLVNJV7E7","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":"931d5386c544df107cb9ed38eebdfd74123a71c577b23de1fe47367f51e7d5c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-26T12:21:38Z","title_canon_sha256":"b276504be6d0953786315f0d3a6cdb397aef2265fb0914194cb37e2712fdb930"},"schema_version":"1.0","source":{"id":"1204.5897","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5897","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5897v1","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5897","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"CZESOWBRZ6VP","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CZESOWBRZ6VPYAVN","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CZESOWBR","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:4cc951ea84beb3ac793d94f1238085204445e1b406181ea8a3eafc1b2466e617","target":"graph","created_at":"2026-05-18T02:43:09Z","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":"Let $X=\\{X(t)\\}_{t\\geq0}$ be an operator semistable L\\'evy process in $\\rd$ with exponent $E$, where $E$ is an invertible linear operator on $\\rd$ and $X$ is semi-selfsimilar with respect to $E$. By refining arguments given in Meerschaert and Xiao \\cite{MX} for the special case of an operator stable (selfsimilar) L\\'evy process, for an arbitrary Borel set $B\\subseteq\\rr_+$ we determine the Hausdorff dimension of the partial range $X(B)$ in terms of the real parts of the eigenvalues of $E$ and the Hausdorff dimension of $B$.","authors_text":"Lina Wedrich, Peter Kern","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-26T12:21:38Z","title":"Hausdorff dimension of operator semistable L\\'evy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5897","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":"sha256:6a39cfdf6c3bc5e555a793edf6d0e2852e5ba270f715060498eb2f7250ceed31","target":"record","created_at":"2026-05-18T02:43:09Z","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":"931d5386c544df107cb9ed38eebdfd74123a71c577b23de1fe47367f51e7d5c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-26T12:21:38Z","title_canon_sha256":"b276504be6d0953786315f0d3a6cdb397aef2265fb0914194cb37e2712fdb930"},"schema_version":"1.0","source":{"id":"1204.5897","kind":"arxiv","version":1}},"canonical_sha256":"1649275831cfaafc02ad899756a6bf27fbe6772f4c8ff6aa4f5c66f2fc334b62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1649275831cfaafc02ad899756a6bf27fbe6772f4c8ff6aa4f5c66f2fc334b62","first_computed_at":"2026-05-18T02:43:09.621035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:09.621035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/HIT4F2Nu1levGViQFBJw0GySb6YMbRAMuskvgVHhOli/JUjcM4pOWmjEwIs9YQaTu6WiUEv01c1nbL7ZloKCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:09.621443Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5897","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a39cfdf6c3bc5e555a793edf6d0e2852e5ba270f715060498eb2f7250ceed31","sha256:4cc951ea84beb3ac793d94f1238085204445e1b406181ea8a3eafc1b2466e617"],"state_sha256":"b652f86245670b9703559d539d79346c16ac5b8d70fd84ef9c535e26eab112df"}