{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2YW46UZI4CXD5TKYX2AU44LF6Y","short_pith_number":"pith:2YW46UZI","canonical_record":{"source":{"id":"1305.1868","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2013-05-08T16:10:06Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b89782955c38c3814633abfa036c744fb7dd906688666835264c4981d3e7839b","abstract_canon_sha256":"9bb85fda51822610c3603b70f5bdf276d48506cde80d71413aa51301ef7816ea"},"schema_version":"1.0"},"canonical_sha256":"d62dcf5328e0ae3ecd58be814e7165f62450d070ea44b908074a1f2cc3e324b2","source":{"kind":"arxiv","id":"1305.1868","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1868","created_at":"2026-05-18T03:26:10Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1868v1","created_at":"2026-05-18T03:26:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1868","created_at":"2026-05-18T03:26:10Z"},{"alias_kind":"pith_short_12","alias_value":"2YW46UZI4CXD","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2YW46UZI4CXD5TKY","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2YW46UZI","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2YW46UZI4CXD5TKYX2AU44LF6Y","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1868","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2013-05-08T16:10:06Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b89782955c38c3814633abfa036c744fb7dd906688666835264c4981d3e7839b","abstract_canon_sha256":"9bb85fda51822610c3603b70f5bdf276d48506cde80d71413aa51301ef7816ea"},"schema_version":"1.0"},"canonical_sha256":"d62dcf5328e0ae3ecd58be814e7165f62450d070ea44b908074a1f2cc3e324b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:10.994221Z","signature_b64":"+LwayhW1Z2s53kRoHDxqy4tsGfMkQrJ+Gdd38/dLB4YJkcHAS5PV3sXmdDMVlCPjG+i8GPodXf8xclPyZMXyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d62dcf5328e0ae3ecd58be814e7165f62450d070ea44b908074a1f2cc3e324b2","last_reissued_at":"2026-05-18T03:26:10.993561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:10.993561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1868","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hN9I4zIzr1V427MEeVQE52YH16rDBG/XgcKN4llPQeX8ha7bbt7DkWiF3h01QNSh/h09MbtTlBKoqwrlZgg7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:52:44.431204Z"},"content_sha256":"5dd149d2d4c16e8d347ed31cc813a59bc6556cce331619343a7c2ca0538994be","schema_version":"1.0","event_id":"sha256:5dd149d2d4c16e8d347ed31cc813a59bc6556cce331619343a7c2ca0538994be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2YW46UZI4CXD5TKYX2AU44LF6Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Galerkin approximation scheme for the mean correction in a mean-reversion stochastic differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.PR","authors_text":"Jiang-Lun Wu, Wei Yang","submitted_at":"2013-05-08T16:10:06Z","abstract_excerpt":"This paper is concerned with the following Markovian stochastic differential equation of mean-reversion type \\[ dR_t= (\\theta +\\sigma \\alpha(R_t, t))R_t dt +\\sigma R_t dB_t \\] with an initial value $R_0=r_0\\in\\mathbb{R}$, where $\\theta\\in\\mathbb{R}$ and $\\sigma>0$ are constants, and the mean correction function $\\alpha:\\mathbb{R}\\times[0,\\infty)\\to \\alpha(x,t)\\in\\mathbb{R}$ is twice continuously differentiable in $x$ and continuously differentiable in $t$. We first derive that under the assumption of path independence of the density process of Girsanov transformation for the above stochastic d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1868","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wf8GE7YqLGsAt/JG+9r6erz+VUsfbjurMvEhRC0BbtBv+pNo2kpqay1EjhhIeVpRj9UmVDMwkrFg6uVoti55DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:52:44.431568Z"},"content_sha256":"4f156a3489298dd42928254dfafdb0f75a228c72b7d89451d9585b0fb459a84e","schema_version":"1.0","event_id":"sha256:4f156a3489298dd42928254dfafdb0f75a228c72b7d89451d9585b0fb459a84e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2YW46UZI4CXD5TKYX2AU44LF6Y/bundle.json","state_url":"https://pith.science/pith/2YW46UZI4CXD5TKYX2AU44LF6Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2YW46UZI4CXD5TKYX2AU44LF6Y/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T16:52:44Z","links":{"resolver":"https://pith.science/pith/2YW46UZI4CXD5TKYX2AU44LF6Y","bundle":"https://pith.science/pith/2YW46UZI4CXD5TKYX2AU44LF6Y/bundle.json","state":"https://pith.science/pith/2YW46UZI4CXD5TKYX2AU44LF6Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2YW46UZI4CXD5TKYX2AU44LF6Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2YW46UZI4CXD5TKYX2AU44LF6Y","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":"9bb85fda51822610c3603b70f5bdf276d48506cde80d71413aa51301ef7816ea","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2013-05-08T16:10:06Z","title_canon_sha256":"b89782955c38c3814633abfa036c744fb7dd906688666835264c4981d3e7839b"},"schema_version":"1.0","source":{"id":"1305.1868","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1868","created_at":"2026-05-18T03:26:10Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1868v1","created_at":"2026-05-18T03:26:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1868","created_at":"2026-05-18T03:26:10Z"},{"alias_kind":"pith_short_12","alias_value":"2YW46UZI4CXD","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2YW46UZI4CXD5TKY","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2YW46UZI","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:4f156a3489298dd42928254dfafdb0f75a228c72b7d89451d9585b0fb459a84e","target":"graph","created_at":"2026-05-18T03:26:10Z","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":"This paper is concerned with the following Markovian stochastic differential equation of mean-reversion type \\[ dR_t= (\\theta +\\sigma \\alpha(R_t, t))R_t dt +\\sigma R_t dB_t \\] with an initial value $R_0=r_0\\in\\mathbb{R}$, where $\\theta\\in\\mathbb{R}$ and $\\sigma>0$ are constants, and the mean correction function $\\alpha:\\mathbb{R}\\times[0,\\infty)\\to \\alpha(x,t)\\in\\mathbb{R}$ is twice continuously differentiable in $x$ and continuously differentiable in $t$. We first derive that under the assumption of path independence of the density process of Girsanov transformation for the above stochastic d","authors_text":"Jiang-Lun Wu, Wei Yang","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2013-05-08T16:10:06Z","title":"A Galerkin approximation scheme for the mean correction in a mean-reversion stochastic differential equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1868","kind":"arxiv","version":1},"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":"sha256:5dd149d2d4c16e8d347ed31cc813a59bc6556cce331619343a7c2ca0538994be","target":"record","created_at":"2026-05-18T03:26:10Z","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":"9bb85fda51822610c3603b70f5bdf276d48506cde80d71413aa51301ef7816ea","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.PR","submitted_at":"2013-05-08T16:10:06Z","title_canon_sha256":"b89782955c38c3814633abfa036c744fb7dd906688666835264c4981d3e7839b"},"schema_version":"1.0","source":{"id":"1305.1868","kind":"arxiv","version":1}},"canonical_sha256":"d62dcf5328e0ae3ecd58be814e7165f62450d070ea44b908074a1f2cc3e324b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d62dcf5328e0ae3ecd58be814e7165f62450d070ea44b908074a1f2cc3e324b2","first_computed_at":"2026-05-18T03:26:10.993561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:10.993561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+LwayhW1Z2s53kRoHDxqy4tsGfMkQrJ+Gdd38/dLB4YJkcHAS5PV3sXmdDMVlCPjG+i8GPodXf8xclPyZMXyCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:10.994221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1868","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dd149d2d4c16e8d347ed31cc813a59bc6556cce331619343a7c2ca0538994be","sha256:4f156a3489298dd42928254dfafdb0f75a228c72b7d89451d9585b0fb459a84e"],"state_sha256":"ce74565ea4047fd85af1f5706c2fda2e851a4bae9500c9c411c3a49d4b97806f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v+C7BRr022oMWMwqh/0/NxrCr9Z347YHoByp+8Zj+n9XpdKbv+apf9BQCgQVT3fV5pGU8VAaQvnzkpcyDrQKDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:52:44.433728Z","bundle_sha256":"f9624519c6cd33061af7d2cac2b956e4538bc6eb8d8387bfd67056ac676d860e"}}