{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QD2TNDO6GEA4KBONO44GULI7JP","short_pith_number":"pith:QD2TNDO6","schema_version":"1.0","canonical_sha256":"80f5368dde3101c505cd77386a2d1f4bf94275ff937136667bf55f767dbe1827","source":{"kind":"arxiv","id":"1805.01404","version":2},"attestation_state":"computed","paper":{"title":"Projections of scaled Bessel processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Constantinos Kardaras, Johannes Ruf","submitted_at":"2018-05-03T16:20:57Z","abstract_excerpt":"Let $X$ and $Y$ denote two independent squared Bessel processes of dimension $m$ and $n-m$, respectively, with $n\\geq 2$ and $m \\in [0, n)$, making $X+Y$ a squared Bessel process of dimension $n$. For appropriately chosen function $s$, the process $s (X+Y)$ is a local martingale. We study the representation and the dynamics of $s(X+Y)$, projected on the filtration generated by $X$. This projection is a strict supermartingale if, and only if, $m<2$. The finite-variation term in its Doob-Meyer decomposition only charges the support of the Markov local time of $X$ at zero."},"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":"1805.01404","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-03T16:20:57Z","cross_cats_sorted":[],"title_canon_sha256":"b7d8256cf5c47a31afd9ac6571fe64ae7046e3bb77c219fd6bc13134b947d739","abstract_canon_sha256":"8975a3cec4c745cf7873d694fdd09d2f51271c52e1ba0fbeb75cb9a2d6741c58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:04.213592Z","signature_b64":"aagV7nHOb8TXj/Q47nys8UhmiMNDPs4qiCmEoWn4KP3hCJTuXsumpyBOPSTsQGPBf2XAO1wdMPCmQXPcp+ShCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80f5368dde3101c505cd77386a2d1f4bf94275ff937136667bf55f767dbe1827","last_reissued_at":"2026-05-17T23:46:04.212908Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:04.212908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Projections of scaled Bessel processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Constantinos Kardaras, Johannes Ruf","submitted_at":"2018-05-03T16:20:57Z","abstract_excerpt":"Let $X$ and $Y$ denote two independent squared Bessel processes of dimension $m$ and $n-m$, respectively, with $n\\geq 2$ and $m \\in [0, n)$, making $X+Y$ a squared Bessel process of dimension $n$. For appropriately chosen function $s$, the process $s (X+Y)$ is a local martingale. We study the representation and the dynamics of $s(X+Y)$, projected on the filtration generated by $X$. This projection is a strict supermartingale if, and only if, $m<2$. The finite-variation term in its Doob-Meyer decomposition only charges the support of the Markov local time of $X$ at zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01404","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":"1805.01404","created_at":"2026-05-17T23:46:04.213019+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.01404v2","created_at":"2026-05-17T23:46:04.213019+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01404","created_at":"2026-05-17T23:46:04.213019+00:00"},{"alias_kind":"pith_short_12","alias_value":"QD2TNDO6GEA4","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QD2TNDO6GEA4KBON","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QD2TNDO6","created_at":"2026-05-18T12:32:46.962924+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/QD2TNDO6GEA4KBONO44GULI7JP","json":"https://pith.science/pith/QD2TNDO6GEA4KBONO44GULI7JP.json","graph_json":"https://pith.science/api/pith-number/QD2TNDO6GEA4KBONO44GULI7JP/graph.json","events_json":"https://pith.science/api/pith-number/QD2TNDO6GEA4KBONO44GULI7JP/events.json","paper":"https://pith.science/paper/QD2TNDO6"},"agent_actions":{"view_html":"https://pith.science/pith/QD2TNDO6GEA4KBONO44GULI7JP","download_json":"https://pith.science/pith/QD2TNDO6GEA4KBONO44GULI7JP.json","view_paper":"https://pith.science/paper/QD2TNDO6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.01404&json=true","fetch_graph":"https://pith.science/api/pith-number/QD2TNDO6GEA4KBONO44GULI7JP/graph.json","fetch_events":"https://pith.science/api/pith-number/QD2TNDO6GEA4KBONO44GULI7JP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QD2TNDO6GEA4KBONO44GULI7JP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QD2TNDO6GEA4KBONO44GULI7JP/action/storage_attestation","attest_author":"https://pith.science/pith/QD2TNDO6GEA4KBONO44GULI7JP/action/author_attestation","sign_citation":"https://pith.science/pith/QD2TNDO6GEA4KBONO44GULI7JP/action/citation_signature","submit_replication":"https://pith.science/pith/QD2TNDO6GEA4KBONO44GULI7JP/action/replication_record"}},"created_at":"2026-05-17T23:46:04.213019+00:00","updated_at":"2026-05-17T23:46:04.213019+00:00"}