{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PYAH3LFWG5L4ER3USAWVBE65CC","short_pith_number":"pith:PYAH3LFW","canonical_record":{"source":{"id":"1204.5624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-25T11:25:52Z","cross_cats_sorted":[],"title_canon_sha256":"309ab15e9d86ea514dbf9902e3860080d2cb105094e355ad68add88f4d2466e6","abstract_canon_sha256":"f696501eccd448245a43d00b8bacc1ba4ac56e08e2916529966871d81eee6d26"},"schema_version":"1.0"},"canonical_sha256":"7e007dacb63757c24774902d5093dd109752527c87676bdc5ce7d5d4ad85ec9b","source":{"kind":"arxiv","id":"1204.5624","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5624","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5624v1","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5624","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"pith_short_12","alias_value":"PYAH3LFWG5L4","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PYAH3LFWG5L4ER3U","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PYAH3LFW","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PYAH3LFWG5L4ER3USAWVBE65CC","target":"record","payload":{"canonical_record":{"source":{"id":"1204.5624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-25T11:25:52Z","cross_cats_sorted":[],"title_canon_sha256":"309ab15e9d86ea514dbf9902e3860080d2cb105094e355ad68add88f4d2466e6","abstract_canon_sha256":"f696501eccd448245a43d00b8bacc1ba4ac56e08e2916529966871d81eee6d26"},"schema_version":"1.0"},"canonical_sha256":"7e007dacb63757c24774902d5093dd109752527c87676bdc5ce7d5d4ad85ec9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:01.854046Z","signature_b64":"8DLmprYglLnA4MjtbgKuGOd9Ku1rpmIHmfz1X4VTjykiaJ9bucvfJ4z2IsSXuwlHM3vW9Yoeyo6C2MABIQ9CBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e007dacb63757c24774902d5093dd109752527c87676bdc5ce7d5d4ad85ec9b","last_reissued_at":"2026-05-18T03:57:01.853149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:01.853149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.5624","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":"2026-05-18T03:57:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lwq3RjYGFcawIsQUih4MiIGFRlFsLR+xWyB+gjg/DGjx9n6FYyl5AvH88qY49VtlPAF/UMaZat0OVWF0D92RDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:35:08.299337Z"},"content_sha256":"3467dbc2f914daccdccc440dc635a7c951132d67d3e618b17706f9cdbf70d8c8","schema_version":"1.0","event_id":"sha256:3467dbc2f914daccdccc440dc635a7c951132d67d3e618b17706f9cdbf70d8c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PYAH3LFWG5L4ER3USAWVBE65CC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Pseudo-Differential Operator Construction of Markov Processes Using Feynman Path Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Potrykus","submitted_at":"2012-04-25T11:25:52Z","abstract_excerpt":"In this paper pseudo-differential operators with negative definite symbols are used to construct time- and space-inhomogeneous Markov processes. This is achieved by using the Markov evolution system associated with the fundamental solution of the corresponding pseudo-differential evolution equation. Negative definite symbols are non-standard and differ significantly from the class of H\\\"{o}rmander type symbols. The novelty of this work is the derivation and the representation of the fundamental solution as a Feynman path integral. This implies that the transition function of the constructed Ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5624","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":"2026-05-18T03:57:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RKAumlbNyK1Ob5ZllAp9PwWhPDXpzVw9MBvvxJD/ywYH272ERluRUDwARMdCk3q3fPmfrYOK8xiCf2jKFcFqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:35:08.299680Z"},"content_sha256":"e8a2e07cce845a2e23200bbefb638242e2f126059b5d21de415a74a3d85fa417","schema_version":"1.0","event_id":"sha256:e8a2e07cce845a2e23200bbefb638242e2f126059b5d21de415a74a3d85fa417"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PYAH3LFWG5L4ER3USAWVBE65CC/bundle.json","state_url":"https://pith.science/pith/PYAH3LFWG5L4ER3USAWVBE65CC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PYAH3LFWG5L4ER3USAWVBE65CC/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":"2026-06-02T02:35:08Z","links":{"resolver":"https://pith.science/pith/PYAH3LFWG5L4ER3USAWVBE65CC","bundle":"https://pith.science/pith/PYAH3LFWG5L4ER3USAWVBE65CC/bundle.json","state":"https://pith.science/pith/PYAH3LFWG5L4ER3USAWVBE65CC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PYAH3LFWG5L4ER3USAWVBE65CC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PYAH3LFWG5L4ER3USAWVBE65CC","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":"f696501eccd448245a43d00b8bacc1ba4ac56e08e2916529966871d81eee6d26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-25T11:25:52Z","title_canon_sha256":"309ab15e9d86ea514dbf9902e3860080d2cb105094e355ad68add88f4d2466e6"},"schema_version":"1.0","source":{"id":"1204.5624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5624","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5624v1","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5624","created_at":"2026-05-18T03:57:01Z"},{"alias_kind":"pith_short_12","alias_value":"PYAH3LFWG5L4","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PYAH3LFWG5L4ER3U","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PYAH3LFW","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:e8a2e07cce845a2e23200bbefb638242e2f126059b5d21de415a74a3d85fa417","target":"graph","created_at":"2026-05-18T03:57:01Z","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":"In this paper pseudo-differential operators with negative definite symbols are used to construct time- and space-inhomogeneous Markov processes. This is achieved by using the Markov evolution system associated with the fundamental solution of the corresponding pseudo-differential evolution equation. Negative definite symbols are non-standard and differ significantly from the class of H\\\"{o}rmander type symbols. The novelty of this work is the derivation and the representation of the fundamental solution as a Feynman path integral. This implies that the transition function of the constructed Ma","authors_text":"Alexander Potrykus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-25T11:25:52Z","title":"A Pseudo-Differential Operator Construction of Markov Processes Using Feynman Path Integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5624","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":"sha256:3467dbc2f914daccdccc440dc635a7c951132d67d3e618b17706f9cdbf70d8c8","target":"record","created_at":"2026-05-18T03:57:01Z","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":"f696501eccd448245a43d00b8bacc1ba4ac56e08e2916529966871d81eee6d26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-25T11:25:52Z","title_canon_sha256":"309ab15e9d86ea514dbf9902e3860080d2cb105094e355ad68add88f4d2466e6"},"schema_version":"1.0","source":{"id":"1204.5624","kind":"arxiv","version":1}},"canonical_sha256":"7e007dacb63757c24774902d5093dd109752527c87676bdc5ce7d5d4ad85ec9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e007dacb63757c24774902d5093dd109752527c87676bdc5ce7d5d4ad85ec9b","first_computed_at":"2026-05-18T03:57:01.853149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:01.853149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8DLmprYglLnA4MjtbgKuGOd9Ku1rpmIHmfz1X4VTjykiaJ9bucvfJ4z2IsSXuwlHM3vW9Yoeyo6C2MABIQ9CBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:01.854046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3467dbc2f914daccdccc440dc635a7c951132d67d3e618b17706f9cdbf70d8c8","sha256:e8a2e07cce845a2e23200bbefb638242e2f126059b5d21de415a74a3d85fa417"],"state_sha256":"18103eb001c1ba59881dad9bb97533fd6f1fa5eb765f6e279aa9ae3a641940b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mroFB4YShU5/hhHxlzbneUW1lmhpUuqzb9YTAVF3bkpUe222PVZFR0MxS1IejEs6j/TTWeYmHcd6h2iwYUpqBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:35:08.301551Z","bundle_sha256":"475ac161397e1d054ea6eacd1bac7b172201a3c721722279f0b5994ba917a2b8"}}