{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3R2VYIWUNNMU3BZY4GERFKUS3U","short_pith_number":"pith:3R2VYIWU","schema_version":"1.0","canonical_sha256":"dc755c22d46b594d8738e18912aa92dd1172f4d07ccb203725d18456633f31b7","source":{"kind":"arxiv","id":"1310.4054","version":11},"attestation_state":"computed","paper":{"title":"Discretely sampled signals and the rough Hoff process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ben Hambly, Guy Flint, Terry Lyons","submitted_at":"2013-10-15T13:54:31Z","abstract_excerpt":"We introduce a canonical method for transforming a discrete sequential data set into an associated rough path made up of lead-lag increments. In particular, by sampling a $d$-dimensional continuous semimartingale $X:[0,1] \\rightarrow \\mathbb{R}^d$ at a set of times $D=(t_i)$, we construct a piecewise linear, axis-directed process $X^D: [0,1] \\rightarrow\\mathbb{R}^{2d}$ comprised of a past and future component. We call such an object the Hoff process associated with the discrete data $\\{X_{t}\\}_{t_i\\in D}$. The Hoff process can be lifted to its natural rough path enhancement and we consider the"},"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":"1310.4054","kind":"arxiv","version":11},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-15T13:54:31Z","cross_cats_sorted":[],"title_canon_sha256":"e7df1e0c98432c473ad5afecf09a9c1194ea1e7085d241f602a706ec4bdc74a9","abstract_canon_sha256":"5faa90b2183ded29a65d20aacc85777fbf59910f5e90baa1fa9374b63c36653b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:58.659617Z","signature_b64":"EbBK4zoSiE8aoQ5vacBmukWwDEUdHznGYa5y73PczUuNdN2vQx7aAZi1x11w/9f67pgGTVwJ5UpOaEkd2VOpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc755c22d46b594d8738e18912aa92dd1172f4d07ccb203725d18456633f31b7","last_reissued_at":"2026-05-18T01:07:58.658998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:58.658998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discretely sampled signals and the rough Hoff process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ben Hambly, Guy Flint, Terry Lyons","submitted_at":"2013-10-15T13:54:31Z","abstract_excerpt":"We introduce a canonical method for transforming a discrete sequential data set into an associated rough path made up of lead-lag increments. In particular, by sampling a $d$-dimensional continuous semimartingale $X:[0,1] \\rightarrow \\mathbb{R}^d$ at a set of times $D=(t_i)$, we construct a piecewise linear, axis-directed process $X^D: [0,1] \\rightarrow\\mathbb{R}^{2d}$ comprised of a past and future component. We call such an object the Hoff process associated with the discrete data $\\{X_{t}\\}_{t_i\\in D}$. The Hoff process can be lifted to its natural rough path enhancement and we consider the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4054","kind":"arxiv","version":11},"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":"1310.4054","created_at":"2026-05-18T01:07:58.659083+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4054v11","created_at":"2026-05-18T01:07:58.659083+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4054","created_at":"2026-05-18T01:07:58.659083+00:00"},{"alias_kind":"pith_short_12","alias_value":"3R2VYIWUNNMU","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3R2VYIWUNNMU3BZY","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3R2VYIWU","created_at":"2026-05-18T12:27:32.513160+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/3R2VYIWUNNMU3BZY4GERFKUS3U","json":"https://pith.science/pith/3R2VYIWUNNMU3BZY4GERFKUS3U.json","graph_json":"https://pith.science/api/pith-number/3R2VYIWUNNMU3BZY4GERFKUS3U/graph.json","events_json":"https://pith.science/api/pith-number/3R2VYIWUNNMU3BZY4GERFKUS3U/events.json","paper":"https://pith.science/paper/3R2VYIWU"},"agent_actions":{"view_html":"https://pith.science/pith/3R2VYIWUNNMU3BZY4GERFKUS3U","download_json":"https://pith.science/pith/3R2VYIWUNNMU3BZY4GERFKUS3U.json","view_paper":"https://pith.science/paper/3R2VYIWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4054&json=true","fetch_graph":"https://pith.science/api/pith-number/3R2VYIWUNNMU3BZY4GERFKUS3U/graph.json","fetch_events":"https://pith.science/api/pith-number/3R2VYIWUNNMU3BZY4GERFKUS3U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3R2VYIWUNNMU3BZY4GERFKUS3U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3R2VYIWUNNMU3BZY4GERFKUS3U/action/storage_attestation","attest_author":"https://pith.science/pith/3R2VYIWUNNMU3BZY4GERFKUS3U/action/author_attestation","sign_citation":"https://pith.science/pith/3R2VYIWUNNMU3BZY4GERFKUS3U/action/citation_signature","submit_replication":"https://pith.science/pith/3R2VYIWUNNMU3BZY4GERFKUS3U/action/replication_record"}},"created_at":"2026-05-18T01:07:58.659083+00:00","updated_at":"2026-05-18T01:07:58.659083+00:00"}