{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:D77S25IDREJBJHYGMV65NRAVEH","short_pith_number":"pith:D77S25ID","schema_version":"1.0","canonical_sha256":"1fff2d75038912149f06657dd6c41521e97e8fbe759c8dc3d3784bfd92c58199","source":{"kind":"arxiv","id":"1002.3680","version":2},"attestation_state":"computed","paper":{"title":"An extension of bifractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Khalifa Es-Sebaiy (SAMM), Xavier Bardina","submitted_at":"2010-02-19T08:23:35Z","abstract_excerpt":"In this paper we introduce and study a self-similar Gaussian process that is the bifractional Brownian motion $B^{H,K}$ with parameters $H\\in (0,1)$ and $K\\in(1,2)$ such that $HK\\in(0,1)$. A remarkable difference between the case $K\\in(0,1)$ and our situation is that this process is a semimartingale when $2HK=1$."},"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":"1002.3680","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-02-19T08:23:35Z","cross_cats_sorted":[],"title_canon_sha256":"2259c9b8c1aae6f661693c92f04c537a6ef41220d7e21a269a68db8f181a6ff7","abstract_canon_sha256":"f52c87c42bd72de8714111e0db14b768500d8e4c90df50297b814ef935944027"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:40.436881Z","signature_b64":"PR/AMP8iLChd45F84dvmZkAJrf8JngfMLOZx5eo3BJ2MxPvVWxkNBw4NN7w/I4FTa8hL2YWbPbNZ8AcEeJdDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fff2d75038912149f06657dd6c41521e97e8fbe759c8dc3d3784bfd92c58199","last_reissued_at":"2026-05-18T04:22:40.436487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:40.436487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An extension of bifractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Khalifa Es-Sebaiy (SAMM), Xavier Bardina","submitted_at":"2010-02-19T08:23:35Z","abstract_excerpt":"In this paper we introduce and study a self-similar Gaussian process that is the bifractional Brownian motion $B^{H,K}$ with parameters $H\\in (0,1)$ and $K\\in(1,2)$ such that $HK\\in(0,1)$. A remarkable difference between the case $K\\in(0,1)$ and our situation is that this process is a semimartingale when $2HK=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3680","kind":"arxiv","version":2},"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":"1002.3680","created_at":"2026-05-18T04:22:40.436539+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.3680v2","created_at":"2026-05-18T04:22:40.436539+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3680","created_at":"2026-05-18T04:22:40.436539+00:00"},{"alias_kind":"pith_short_12","alias_value":"D77S25IDREJB","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"D77S25IDREJBJHYG","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"D77S25ID","created_at":"2026-05-18T12:26:06.534383+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/D77S25IDREJBJHYGMV65NRAVEH","json":"https://pith.science/pith/D77S25IDREJBJHYGMV65NRAVEH.json","graph_json":"https://pith.science/api/pith-number/D77S25IDREJBJHYGMV65NRAVEH/graph.json","events_json":"https://pith.science/api/pith-number/D77S25IDREJBJHYGMV65NRAVEH/events.json","paper":"https://pith.science/paper/D77S25ID"},"agent_actions":{"view_html":"https://pith.science/pith/D77S25IDREJBJHYGMV65NRAVEH","download_json":"https://pith.science/pith/D77S25IDREJBJHYGMV65NRAVEH.json","view_paper":"https://pith.science/paper/D77S25ID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.3680&json=true","fetch_graph":"https://pith.science/api/pith-number/D77S25IDREJBJHYGMV65NRAVEH/graph.json","fetch_events":"https://pith.science/api/pith-number/D77S25IDREJBJHYGMV65NRAVEH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D77S25IDREJBJHYGMV65NRAVEH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D77S25IDREJBJHYGMV65NRAVEH/action/storage_attestation","attest_author":"https://pith.science/pith/D77S25IDREJBJHYGMV65NRAVEH/action/author_attestation","sign_citation":"https://pith.science/pith/D77S25IDREJBJHYGMV65NRAVEH/action/citation_signature","submit_replication":"https://pith.science/pith/D77S25IDREJBJHYGMV65NRAVEH/action/replication_record"}},"created_at":"2026-05-18T04:22:40.436539+00:00","updated_at":"2026-05-18T04:22:40.436539+00:00"}