{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:24TOKPMSS4XKPGB3WN6QVBYEF7","short_pith_number":"pith:24TOKPMS","schema_version":"1.0","canonical_sha256":"d726e53d92972ea7983bb37d0a87042fe671fde2616b9bc88fd0a834a205a38c","source":{"kind":"arxiv","id":"1508.06641","version":1},"attestation_state":"computed","paper":{"title":"Decomposition and limit theorems for a class of self-similar Gaussian processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Harnett, David Nualart","submitted_at":"2015-08-26T20:10:12Z","abstract_excerpt":"We introduce a new class of self-similar Gaussian stochastic processes, where the covariance is defined in terms of a fractional Brownian motion and another Gaussian process. A special case is the solution in time to the fractional-colored stochastic heat equation described in Tudor (2013). We prove that the process can be decomposed into a fractional Brownian motion (with a different parameter than the one that defines the covariance), and a Gaussian process first described in Lei and Nualart (2008). The component processes can be expressed as stochastic integrals with respect to the Brownian"},"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":"1508.06641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-26T20:10:12Z","cross_cats_sorted":[],"title_canon_sha256":"310b5b33242f6c8d45774aeab5086baf02d6115037b8ec65ded82dbc77e734a8","abstract_canon_sha256":"5020d31eea8703920b6643bb9b3db8d1419aa50d6ea8aaafb4ecb7d2ec76ffe3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:41.432280Z","signature_b64":"w1vscLW1CR6rWByLAVPTc77cNfciLn0bEHGkuYwzt0d99kLcLSJ0atGo8kn38dBkZf8xeKKrWHJwu0HgxLG6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d726e53d92972ea7983bb37d0a87042fe671fde2616b9bc88fd0a834a205a38c","last_reissued_at":"2026-05-18T01:34:41.431653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:41.431653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decomposition and limit theorems for a class of self-similar Gaussian processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Harnett, David Nualart","submitted_at":"2015-08-26T20:10:12Z","abstract_excerpt":"We introduce a new class of self-similar Gaussian stochastic processes, where the covariance is defined in terms of a fractional Brownian motion and another Gaussian process. A special case is the solution in time to the fractional-colored stochastic heat equation described in Tudor (2013). We prove that the process can be decomposed into a fractional Brownian motion (with a different parameter than the one that defines the covariance), and a Gaussian process first described in Lei and Nualart (2008). The component processes can be expressed as stochastic integrals with respect to the Brownian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06641","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":"1508.06641","created_at":"2026-05-18T01:34:41.431754+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.06641v1","created_at":"2026-05-18T01:34:41.431754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06641","created_at":"2026-05-18T01:34:41.431754+00:00"},{"alias_kind":"pith_short_12","alias_value":"24TOKPMSS4XK","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"24TOKPMSS4XKPGB3","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"24TOKPMS","created_at":"2026-05-18T12:28:59.999130+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/24TOKPMSS4XKPGB3WN6QVBYEF7","json":"https://pith.science/pith/24TOKPMSS4XKPGB3WN6QVBYEF7.json","graph_json":"https://pith.science/api/pith-number/24TOKPMSS4XKPGB3WN6QVBYEF7/graph.json","events_json":"https://pith.science/api/pith-number/24TOKPMSS4XKPGB3WN6QVBYEF7/events.json","paper":"https://pith.science/paper/24TOKPMS"},"agent_actions":{"view_html":"https://pith.science/pith/24TOKPMSS4XKPGB3WN6QVBYEF7","download_json":"https://pith.science/pith/24TOKPMSS4XKPGB3WN6QVBYEF7.json","view_paper":"https://pith.science/paper/24TOKPMS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.06641&json=true","fetch_graph":"https://pith.science/api/pith-number/24TOKPMSS4XKPGB3WN6QVBYEF7/graph.json","fetch_events":"https://pith.science/api/pith-number/24TOKPMSS4XKPGB3WN6QVBYEF7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/24TOKPMSS4XKPGB3WN6QVBYEF7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/24TOKPMSS4XKPGB3WN6QVBYEF7/action/storage_attestation","attest_author":"https://pith.science/pith/24TOKPMSS4XKPGB3WN6QVBYEF7/action/author_attestation","sign_citation":"https://pith.science/pith/24TOKPMSS4XKPGB3WN6QVBYEF7/action/citation_signature","submit_replication":"https://pith.science/pith/24TOKPMSS4XKPGB3WN6QVBYEF7/action/replication_record"}},"created_at":"2026-05-18T01:34:41.431754+00:00","updated_at":"2026-05-18T01:34:41.431754+00:00"}