{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EORWBOSRILFSUAZAP5JNUMTCJJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aed354b64d00449950e6e467d3fb834d0dec4842141c999bd8aa8df6a9b57dd5","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-16T16:41:14Z","title_canon_sha256":"5f09d6f970d193435947ee5976160155e45aa5643cbcb6ac748b873a151581b8"},"schema_version":"1.0","source":{"id":"1602.05084","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05084","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05084v3","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05084","created_at":"2026-05-17T23:55:30Z"},{"alias_kind":"pith_short_12","alias_value":"EORWBOSRILFS","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EORWBOSRILFSUAZA","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EORWBOSR","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:9498d51d4fad189d47ab78448d6be5c8e04bcdf66f43e758317735bc894d6b2f","target":"graph","created_at":"2026-05-17T23:55:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We derive a Karhunen-Lo\\`eve expansion of the Gauss process $B_t - g(t)\\int_0^1 g'(u)\\,d B_u$, $t\\in[0,1]$, where $(B_t)_{t\\in[0,1]}$ is a standard Wiener process and $g:[0,1]\\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\\int_0^1 (g'(u))^2\\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\\frac{\\sqrt{2}}{\\pi}\\sin(\\pi t)$, $t\\in[0,1]$, and $g(t)=t$, $t\\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.","authors_text":"Matyas Barczy, Rezs\\H{o} L. Lovas","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-16T16:41:14Z","title":"Karhunen-Lo\\`eve expansion for a generalization of Wiener bridge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05084","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b398841a69f7bc570c1ea33b26d91e6eea8dabe53104ea4ff5f9e2da6944091e","target":"record","created_at":"2026-05-17T23:55:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aed354b64d00449950e6e467d3fb834d0dec4842141c999bd8aa8df6a9b57dd5","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-16T16:41:14Z","title_canon_sha256":"5f09d6f970d193435947ee5976160155e45aa5643cbcb6ac748b873a151581b8"},"schema_version":"1.0","source":{"id":"1602.05084","kind":"arxiv","version":3}},"canonical_sha256":"23a360ba5142cb2a03207f52da32624a6f1e05fd16a8bb11fbeea6466cb1f7ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23a360ba5142cb2a03207f52da32624a6f1e05fd16a8bb11fbeea6466cb1f7ac","first_computed_at":"2026-05-17T23:55:30.166384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:30.166384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FcFCgFloXaoXNsLmPcu21pUVbyXUxxEZnr+OsQP313UjkL0cZvCzQjnaEZ7bJ2GV4ww6cOhLfIDM2yvw5o2vCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:30.166874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05084","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b398841a69f7bc570c1ea33b26d91e6eea8dabe53104ea4ff5f9e2da6944091e","sha256:9498d51d4fad189d47ab78448d6be5c8e04bcdf66f43e758317735bc894d6b2f"],"state_sha256":"1473ddbbf43784a542883ba64c7c3d551a6f91f12a23d4b01c859b679d235282"}