{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AQHH24VFAIDXZMXS3FSGSKFQ2D","short_pith_number":"pith:AQHH24VF","canonical_record":{"source":{"id":"1310.4333","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T11:25:42Z","cross_cats_sorted":[],"title_canon_sha256":"981e65a8b193e74e76ec50277240a6a5120ed63bc06de7467b6f85d6f387f14d","abstract_canon_sha256":"aa36232e2a2e62cb76d0db37668390eb28c0890ff82893379bd79e5fd86f19f4"},"schema_version":"1.0"},"canonical_sha256":"040e7d72a502077cb2f2d9646928b0d0d3fc5198018694f77a56e7f614803ce4","source":{"kind":"arxiv","id":"1310.4333","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4333","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4333v3","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4333","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"AQHH24VFAIDX","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AQHH24VFAIDXZMXS","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AQHH24VF","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AQHH24VFAIDXZMXS3FSGSKFQ2D","target":"record","payload":{"canonical_record":{"source":{"id":"1310.4333","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T11:25:42Z","cross_cats_sorted":[],"title_canon_sha256":"981e65a8b193e74e76ec50277240a6a5120ed63bc06de7467b6f85d6f387f14d","abstract_canon_sha256":"aa36232e2a2e62cb76d0db37668390eb28c0890ff82893379bd79e5fd86f19f4"},"schema_version":"1.0"},"canonical_sha256":"040e7d72a502077cb2f2d9646928b0d0d3fc5198018694f77a56e7f614803ce4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:15.762104Z","signature_b64":"2xabgr94ABlVoqJFb7n57YYFUGa2EnQCXrXE4xj9nVX4BAH/iPHxLWs93vIamAtqnqRRKLyCcSLYQ1/pfBxHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"040e7d72a502077cb2f2d9646928b0d0d3fc5198018694f77a56e7f614803ce4","last_reissued_at":"2026-05-18T01:36:15.761502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:15.761502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.4333","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"91uQ81kDREXNVeKRRPYDXbLk5crubEs/S8Ijx1CfSJmiic87+N9NVLtYh4hxX+6xRGcOmiVBd9YiYDtaJi8wAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:10:46.277453Z"},"content_sha256":"b52b3326d90e948f69f593cbfbaa4dd71364947b6d2ccdb821159665278ef8eb","schema_version":"1.0","event_id":"sha256:b52b3326d90e948f69f593cbfbaa4dd71364947b6d2ccdb821159665278ef8eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AQHH24VFAIDXZMXS3FSGSKFQ2D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A criterion for invariant measures of It\\^{o} processes based on the symbol","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Schnurr, Anita Behme","submitted_at":"2013-10-16T11:25:42Z","abstract_excerpt":"An integral criterion for the existence of an invariant measure of an It\\^{o} process is developed. This new criterion is based on the probabilistic symbol of the It\\^{o} process. In contrast to the standard integral criterion for invariant measures of Markov processes based on the generator, no test functions and hence no information on the domain of the generator is needed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4333","kind":"arxiv","version":3},"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":"2026-05-18T01:36:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"92XZ/1YyDQ51BtMYnUV9VtdHWi73EVZA9Ve5EMmWI/Xd2inIfKS29KgVMymFGCBRpaVq63m4ns79cLS0gUTHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:10:46.277793Z"},"content_sha256":"43dce5e238325ba5a059217f6f3f10d7061d9c0021175ccc7d60e9850c82b27c","schema_version":"1.0","event_id":"sha256:43dce5e238325ba5a059217f6f3f10d7061d9c0021175ccc7d60e9850c82b27c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQHH24VFAIDXZMXS3FSGSKFQ2D/bundle.json","state_url":"https://pith.science/pith/AQHH24VFAIDXZMXS3FSGSKFQ2D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQHH24VFAIDXZMXS3FSGSKFQ2D/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":"2026-05-28T13:10:46Z","links":{"resolver":"https://pith.science/pith/AQHH24VFAIDXZMXS3FSGSKFQ2D","bundle":"https://pith.science/pith/AQHH24VFAIDXZMXS3FSGSKFQ2D/bundle.json","state":"https://pith.science/pith/AQHH24VFAIDXZMXS3FSGSKFQ2D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQHH24VFAIDXZMXS3FSGSKFQ2D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AQHH24VFAIDXZMXS3FSGSKFQ2D","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":"aa36232e2a2e62cb76d0db37668390eb28c0890ff82893379bd79e5fd86f19f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T11:25:42Z","title_canon_sha256":"981e65a8b193e74e76ec50277240a6a5120ed63bc06de7467b6f85d6f387f14d"},"schema_version":"1.0","source":{"id":"1310.4333","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4333","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4333v3","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4333","created_at":"2026-05-18T01:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"AQHH24VFAIDX","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AQHH24VFAIDXZMXS","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AQHH24VF","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:43dce5e238325ba5a059217f6f3f10d7061d9c0021175ccc7d60e9850c82b27c","target":"graph","created_at":"2026-05-18T01:36:15Z","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":"An integral criterion for the existence of an invariant measure of an It\\^{o} process is developed. This new criterion is based on the probabilistic symbol of the It\\^{o} process. In contrast to the standard integral criterion for invariant measures of Markov processes based on the generator, no test functions and hence no information on the domain of the generator is needed.","authors_text":"Alexander Schnurr, Anita Behme","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T11:25:42Z","title":"A criterion for invariant measures of It\\^{o} processes based on the symbol"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4333","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:b52b3326d90e948f69f593cbfbaa4dd71364947b6d2ccdb821159665278ef8eb","target":"record","created_at":"2026-05-18T01:36:15Z","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":"aa36232e2a2e62cb76d0db37668390eb28c0890ff82893379bd79e5fd86f19f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-16T11:25:42Z","title_canon_sha256":"981e65a8b193e74e76ec50277240a6a5120ed63bc06de7467b6f85d6f387f14d"},"schema_version":"1.0","source":{"id":"1310.4333","kind":"arxiv","version":3}},"canonical_sha256":"040e7d72a502077cb2f2d9646928b0d0d3fc5198018694f77a56e7f614803ce4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"040e7d72a502077cb2f2d9646928b0d0d3fc5198018694f77a56e7f614803ce4","first_computed_at":"2026-05-18T01:36:15.761502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:15.761502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2xabgr94ABlVoqJFb7n57YYFUGa2EnQCXrXE4xj9nVX4BAH/iPHxLWs93vIamAtqnqRRKLyCcSLYQ1/pfBxHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:15.762104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4333","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b52b3326d90e948f69f593cbfbaa4dd71364947b6d2ccdb821159665278ef8eb","sha256:43dce5e238325ba5a059217f6f3f10d7061d9c0021175ccc7d60e9850c82b27c"],"state_sha256":"7972ffe95f3a259130efa3031c7e86c7267b755c62cb7d8d9e491ffbc666cdaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ydet4PJ6VUDvpWzUjT5Lf2EJXMgTy+33nC8Mg1BaURys9pAr5ZSiIaiSGUNR+XQH1fGit5BAuA3dYZ4PNVwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:10:46.279645Z","bundle_sha256":"42de1e0a2513940ba1dce0bea949bb81404da2305d6b5edd6a3580d94685eea9"}}