{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:DDOOXHSSY2R4FFGFFJ2I2MSNRC","short_pith_number":"pith:DDOOXHSS","canonical_record":{"source":{"id":"0910.1784","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-09T16:46:17Z","cross_cats_sorted":[],"title_canon_sha256":"2256ad33cdf011717aed92a08d7fe532e92eb3185f3e9c05117809bd38e7c66f","abstract_canon_sha256":"d3bfce137ae416952f415f962b57099d20ac1510c826ffa2c5987c85740fe6cb"},"schema_version":"1.0"},"canonical_sha256":"18dceb9e52c6a3c294c52a748d324d88990ac77866f600d84fe5b89564d57fe0","source":{"kind":"arxiv","id":"0910.1784","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1784","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1784v5","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1784","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"DDOOXHSSY2R4","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DDOOXHSSY2R4FFGF","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DDOOXHSS","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:DDOOXHSSY2R4FFGFFJ2I2MSNRC","target":"record","payload":{"canonical_record":{"source":{"id":"0910.1784","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-09T16:46:17Z","cross_cats_sorted":[],"title_canon_sha256":"2256ad33cdf011717aed92a08d7fe532e92eb3185f3e9c05117809bd38e7c66f","abstract_canon_sha256":"d3bfce137ae416952f415f962b57099d20ac1510c826ffa2c5987c85740fe6cb"},"schema_version":"1.0"},"canonical_sha256":"18dceb9e52c6a3c294c52a748d324d88990ac77866f600d84fe5b89564d57fe0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:37.403723Z","signature_b64":"OMKbx1WEUUOKu61B3dCpNhD+g1dC7NL6+Af6fDxJnvaj5M5+0UXwYHfYW9FAjzraSgGatFvgqi844mJBJNR1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18dceb9e52c6a3c294c52a748d324d88990ac77866f600d84fe5b89564d57fe0","last_reissued_at":"2026-05-18T03:36:37.403142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:37.403142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.1784","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Si0mGjSxOB4eGJhzY9nunYQbv2EgqvZeqgQW1bFjcQW8rJ/HEFN9IdLB4SOFQmzOWP1VbJ1DoQkBbKG3jDSHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:36:42.014124Z"},"content_sha256":"006595e60350d99e9e0c4ac33f76dfe1dd5f765d9b41ac308ccf140f8122b9fb","schema_version":"1.0","event_id":"sha256:006595e60350d99e9e0c4ac33f76dfe1dd5f765d9b41ac308ccf140f8122b9fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:DDOOXHSSY2R4FFGFFJ2I2MSNRC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On strong solutions for positive definite jump-diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eberhard Mayerhofer, Oliver Pfaffel, Robert Stelzer","submitted_at":"2009-10-09T16:46:17Z","abstract_excerpt":"We show the existence of unique global strong solutions of a class of stochastic differential equations on the cone of symmetric positive definite matrices. Our result includes affine diffusion processes and therefore extends considerably the known statements concerning Wishart processes, which have recently been extensively employed in financial mathematics. Moreover, we consider stochastic differential equations where the diffusion coefficient is given by the alpha-th positive semidefinite power of the process itself with 0.5<alpha<1 and obtain existence conditions for them. In the case of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1784","kind":"arxiv","version":5},"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":"2026-05-18T03:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tMsnlV6wkZjMDuauc24MkeJeYoGugt9XdhuS1H9WpHpR3ZoAa4rEIEH7T98+U3V8EE7OOT9Zcx6v5kf5zJnbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:36:42.014477Z"},"content_sha256":"adac2672e375f4d63083eca9ef6398d2c5a70519e0ea4eb9325409a81a22a4b5","schema_version":"1.0","event_id":"sha256:adac2672e375f4d63083eca9ef6398d2c5a70519e0ea4eb9325409a81a22a4b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DDOOXHSSY2R4FFGFFJ2I2MSNRC/bundle.json","state_url":"https://pith.science/pith/DDOOXHSSY2R4FFGFFJ2I2MSNRC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DDOOXHSSY2R4FFGFFJ2I2MSNRC/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":"2026-06-23T17:36:42Z","links":{"resolver":"https://pith.science/pith/DDOOXHSSY2R4FFGFFJ2I2MSNRC","bundle":"https://pith.science/pith/DDOOXHSSY2R4FFGFFJ2I2MSNRC/bundle.json","state":"https://pith.science/pith/DDOOXHSSY2R4FFGFFJ2I2MSNRC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DDOOXHSSY2R4FFGFFJ2I2MSNRC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:DDOOXHSSY2R4FFGFFJ2I2MSNRC","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":"d3bfce137ae416952f415f962b57099d20ac1510c826ffa2c5987c85740fe6cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-09T16:46:17Z","title_canon_sha256":"2256ad33cdf011717aed92a08d7fe532e92eb3185f3e9c05117809bd38e7c66f"},"schema_version":"1.0","source":{"id":"0910.1784","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1784","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1784v5","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1784","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"DDOOXHSSY2R4","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DDOOXHSSY2R4FFGF","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DDOOXHSS","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:adac2672e375f4d63083eca9ef6398d2c5a70519e0ea4eb9325409a81a22a4b5","target":"graph","created_at":"2026-05-18T03:36:37Z","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 show the existence of unique global strong solutions of a class of stochastic differential equations on the cone of symmetric positive definite matrices. Our result includes affine diffusion processes and therefore extends considerably the known statements concerning Wishart processes, which have recently been extensively employed in financial mathematics. Moreover, we consider stochastic differential equations where the diffusion coefficient is given by the alpha-th positive semidefinite power of the process itself with 0.5<alpha<1 and obtain existence conditions for them. In the case of a","authors_text":"Eberhard Mayerhofer, Oliver Pfaffel, Robert Stelzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-09T16:46:17Z","title":"On strong solutions for positive definite jump-diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1784","kind":"arxiv","version":5},"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":"sha256:006595e60350d99e9e0c4ac33f76dfe1dd5f765d9b41ac308ccf140f8122b9fb","target":"record","created_at":"2026-05-18T03:36:37Z","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":"d3bfce137ae416952f415f962b57099d20ac1510c826ffa2c5987c85740fe6cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-09T16:46:17Z","title_canon_sha256":"2256ad33cdf011717aed92a08d7fe532e92eb3185f3e9c05117809bd38e7c66f"},"schema_version":"1.0","source":{"id":"0910.1784","kind":"arxiv","version":5}},"canonical_sha256":"18dceb9e52c6a3c294c52a748d324d88990ac77866f600d84fe5b89564d57fe0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18dceb9e52c6a3c294c52a748d324d88990ac77866f600d84fe5b89564d57fe0","first_computed_at":"2026-05-18T03:36:37.403142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:37.403142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OMKbx1WEUUOKu61B3dCpNhD+g1dC7NL6+Af6fDxJnvaj5M5+0UXwYHfYW9FAjzraSgGatFvgqi844mJBJNR1CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:37.403723Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.1784","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:006595e60350d99e9e0c4ac33f76dfe1dd5f765d9b41ac308ccf140f8122b9fb","sha256:adac2672e375f4d63083eca9ef6398d2c5a70519e0ea4eb9325409a81a22a4b5"],"state_sha256":"3aea49c95864913cf384717f0e330c0dd20f17f5547ae99b6db3a1326d1394e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3qD01mgIbTcoVF9JQEJFpM7sPbj+ZS5J48M2xYaDTeTCwm5HqHCHFPFKnnpLtolJ0YM0snVjb9KSzbSoRxNIAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:36:42.016543Z","bundle_sha256":"c265739368774ab46297dd107b44871addca4a9047973ca3a5a4fa3fa2ebe20d"}}