{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:ZQYJI4KGVAFF5IF4XQNULTPBLP","short_pith_number":"pith:ZQYJI4KG","schema_version":"1.0","canonical_sha256":"cc30947146a80a5ea0bcbc1b45cde15bd5dc7f346940f50667a99951e5bfb727","source":{"kind":"arxiv","id":"math/0602664","version":1},"attestation_state":"computed","paper":{"title":"Operator Scaling Stable Random Fields","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hans-Peter Scheffler, Hermine Bierm\\'e (MAP5), Mark M. Meerschaert","submitted_at":"2006-02-28T13:50:55Z","abstract_excerpt":"A scalar valued random field is called operator-scaling if it satisfies a self-similarity property for some matrix E with positive real parts of the eigenvalues. We present a moving average and a harmonizable representation of stable operator scaling random fields by utilizing so called E-homogeneous functions. These fields also have stationary increments and are stochastically continuous. In the Gaussian case critical H\\\"{o}lder-exponents and the Hausdorff-dimension of the sample paths are also obtained."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0602664","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-02-28T13:50:55Z","cross_cats_sorted":[],"title_canon_sha256":"e528b8edc7609889e9ea1142bea687eef4804adc0bc9aa11ff13c9e79445405b","abstract_canon_sha256":"cd27fa15457609e5d76c49cf68127a417992d93b71d7757ce20e642cbe4a16cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:50.489535Z","signature_b64":"2kkpOqIZXf9Pt70H7l8U18cTypqpcWnqLYteSj/7j016BvkzC6aD0hRHnBvimhzTRyrHdLxmJ9PJgW3CeDlUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc30947146a80a5ea0bcbc1b45cde15bd5dc7f346940f50667a99951e5bfb727","last_reissued_at":"2026-05-18T01:08:50.488898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:50.488898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operator Scaling Stable Random Fields","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hans-Peter Scheffler, Hermine Bierm\\'e (MAP5), Mark M. Meerschaert","submitted_at":"2006-02-28T13:50:55Z","abstract_excerpt":"A scalar valued random field is called operator-scaling if it satisfies a self-similarity property for some matrix E with positive real parts of the eigenvalues. We present a moving average and a harmonizable representation of stable operator scaling random fields by utilizing so called E-homogeneous functions. These fields also have stationary increments and are stochastically continuous. In the Gaussian case critical H\\\"{o}lder-exponents and the Hausdorff-dimension of the sample paths are also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602664","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0602664","created_at":"2026-05-18T01:08:50.488994+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0602664v1","created_at":"2026-05-18T01:08:50.488994+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0602664","created_at":"2026-05-18T01:08:50.488994+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZQYJI4KGVAFF","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZQYJI4KGVAFF5IF4","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZQYJI4KG","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZQYJI4KGVAFF5IF4XQNULTPBLP","json":"https://pith.science/pith/ZQYJI4KGVAFF5IF4XQNULTPBLP.json","graph_json":"https://pith.science/api/pith-number/ZQYJI4KGVAFF5IF4XQNULTPBLP/graph.json","events_json":"https://pith.science/api/pith-number/ZQYJI4KGVAFF5IF4XQNULTPBLP/events.json","paper":"https://pith.science/paper/ZQYJI4KG"},"agent_actions":{"view_html":"https://pith.science/pith/ZQYJI4KGVAFF5IF4XQNULTPBLP","download_json":"https://pith.science/pith/ZQYJI4KGVAFF5IF4XQNULTPBLP.json","view_paper":"https://pith.science/paper/ZQYJI4KG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0602664&json=true","fetch_graph":"https://pith.science/api/pith-number/ZQYJI4KGVAFF5IF4XQNULTPBLP/graph.json","fetch_events":"https://pith.science/api/pith-number/ZQYJI4KGVAFF5IF4XQNULTPBLP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZQYJI4KGVAFF5IF4XQNULTPBLP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZQYJI4KGVAFF5IF4XQNULTPBLP/action/storage_attestation","attest_author":"https://pith.science/pith/ZQYJI4KGVAFF5IF4XQNULTPBLP/action/author_attestation","sign_citation":"https://pith.science/pith/ZQYJI4KGVAFF5IF4XQNULTPBLP/action/citation_signature","submit_replication":"https://pith.science/pith/ZQYJI4KGVAFF5IF4XQNULTPBLP/action/replication_record"}},"created_at":"2026-05-18T01:08:50.488994+00:00","updated_at":"2026-05-18T01:08:50.488994+00:00"}