{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1993:NAAAFAA6KDQYODD4GRSEVO7VMS","short_pith_number":"pith:NAAAFAA6","schema_version":"1.0","canonical_sha256":"680002801e50e1870c7c34644abbf564a7d75c67c964eb49b040ae173cc0f97d","source":{"kind":"arxiv","id":"comp-gas/9302001","version":1},"attestation_state":"computed","paper":{"title":"Some comments on the correlation dimension of $1/f^\\alpha$ noise","license":"","headline":"","cross_cats":["nlin.CG"],"primary_cat":"comp-gas","authors_text":"James Theiler","submitted_at":"1993-02-10T00:00:00Z","abstract_excerpt":"It has recently been observed that a stochastic (infinite degree of freedom) time series with a $1/f^\\alpha$ power spectrum can exhibit a finite correlation dimension, even for arbitrarily large data sets. [A.R. Osborne and A.~Provenzale, {\\sl Physica D} {\\bf 35}, 357 (1989).] I will discuss the relevance of this observation to the practical estimation of dimension from a time series, and in particular I will argue that a good dimension algorithm need not be trapped by this anomalous fractal scaling. Further, I will analytically treat the case of gaussian \\onefas noise, with explicit high and "},"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":"comp-gas/9302001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"comp-gas","submitted_at":"1993-02-10T00:00:00Z","cross_cats_sorted":["nlin.CG"],"title_canon_sha256":"43f95f709558ec71cb5cd2f6b50a52def3b96c55c3edb1a91b8594019d9ba9c7","abstract_canon_sha256":"a419e201296ebce7d111efc62f731b353798f18350db4d12f4289980e36dc491"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:08:32.376348Z","signature_b64":"IZdBY4AqUVsVNNll3nJM/B4knkSpEmjb6rvkLO8Qr+oSlEXPPg6OvEmngLH/MOQDTI3IHzMdNl1jN5XTQrj1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"680002801e50e1870c7c34644abbf564a7d75c67c964eb49b040ae173cc0f97d","last_reissued_at":"2026-07-04T15:08:32.375965Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:08:32.375965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some comments on the correlation dimension of $1/f^\\alpha$ noise","license":"","headline":"","cross_cats":["nlin.CG"],"primary_cat":"comp-gas","authors_text":"James Theiler","submitted_at":"1993-02-10T00:00:00Z","abstract_excerpt":"It has recently been observed that a stochastic (infinite degree of freedom) time series with a $1/f^\\alpha$ power spectrum can exhibit a finite correlation dimension, even for arbitrarily large data sets. [A.R. Osborne and A.~Provenzale, {\\sl Physica D} {\\bf 35}, 357 (1989).] I will discuss the relevance of this observation to the practical estimation of dimension from a time series, and in particular I will argue that a good dimension algorithm need not be trapped by this anomalous fractal scaling. Further, I will analytically treat the case of gaussian \\onefas noise, with explicit high and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"comp-gas/9302001","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/comp-gas/9302001/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"comp-gas/9302001","created_at":"2026-07-04T15:08:32.376029+00:00"},{"alias_kind":"arxiv_version","alias_value":"comp-gas/9302001v1","created_at":"2026-07-04T15:08:32.376029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.comp-gas/9302001","created_at":"2026-07-04T15:08:32.376029+00:00"},{"alias_kind":"pith_short_12","alias_value":"NAAAFAA6KDQY","created_at":"2026-07-04T15:08:32.376029+00:00"},{"alias_kind":"pith_short_16","alias_value":"NAAAFAA6KDQYODD4","created_at":"2026-07-04T15:08:32.376029+00:00"},{"alias_kind":"pith_short_8","alias_value":"NAAAFAA6","created_at":"2026-07-04T15:08:32.376029+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/NAAAFAA6KDQYODD4GRSEVO7VMS","json":"https://pith.science/pith/NAAAFAA6KDQYODD4GRSEVO7VMS.json","graph_json":"https://pith.science/api/pith-number/NAAAFAA6KDQYODD4GRSEVO7VMS/graph.json","events_json":"https://pith.science/api/pith-number/NAAAFAA6KDQYODD4GRSEVO7VMS/events.json","paper":"https://pith.science/paper/NAAAFAA6"},"agent_actions":{"view_html":"https://pith.science/pith/NAAAFAA6KDQYODD4GRSEVO7VMS","download_json":"https://pith.science/pith/NAAAFAA6KDQYODD4GRSEVO7VMS.json","view_paper":"https://pith.science/paper/NAAAFAA6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=comp-gas/9302001&json=true","fetch_graph":"https://pith.science/api/pith-number/NAAAFAA6KDQYODD4GRSEVO7VMS/graph.json","fetch_events":"https://pith.science/api/pith-number/NAAAFAA6KDQYODD4GRSEVO7VMS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NAAAFAA6KDQYODD4GRSEVO7VMS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NAAAFAA6KDQYODD4GRSEVO7VMS/action/storage_attestation","attest_author":"https://pith.science/pith/NAAAFAA6KDQYODD4GRSEVO7VMS/action/author_attestation","sign_citation":"https://pith.science/pith/NAAAFAA6KDQYODD4GRSEVO7VMS/action/citation_signature","submit_replication":"https://pith.science/pith/NAAAFAA6KDQYODD4GRSEVO7VMS/action/replication_record"}},"created_at":"2026-07-04T15:08:32.376029+00:00","updated_at":"2026-07-04T15:08:32.376029+00:00"}