{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7VRYK7P22GNURMQQFJPZPRCR77","short_pith_number":"pith:7VRYK7P2","canonical_record":{"source":{"id":"1311.2883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-12T19:03:13Z","cross_cats_sorted":["math-ph","math.AP","math.MP","math.PR"],"title_canon_sha256":"84ef6944d2ed8c95262d4e7981e4eb209a5bec5c1e2112991cffb6372a420884","abstract_canon_sha256":"f25ef17add368c4ef720271f63e869c92a469c5fbe05b31a4ecb89d7dd699609"},"schema_version":"1.0"},"canonical_sha256":"fd63857dfad19b48b2102a5f97c451fff724e7b7ba3c12a37645b7e5276c3f37","source":{"kind":"arxiv","id":"1311.2883","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2883","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2883v1","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2883","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"7VRYK7P22GNU","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7VRYK7P22GNURMQQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7VRYK7P2","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7VRYK7P22GNURMQQFJPZPRCR77","target":"record","payload":{"canonical_record":{"source":{"id":"1311.2883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-12T19:03:13Z","cross_cats_sorted":["math-ph","math.AP","math.MP","math.PR"],"title_canon_sha256":"84ef6944d2ed8c95262d4e7981e4eb209a5bec5c1e2112991cffb6372a420884","abstract_canon_sha256":"f25ef17add368c4ef720271f63e869c92a469c5fbe05b31a4ecb89d7dd699609"},"schema_version":"1.0"},"canonical_sha256":"fd63857dfad19b48b2102a5f97c451fff724e7b7ba3c12a37645b7e5276c3f37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:13.387097Z","signature_b64":"cAl71E5n/sv1PaA6LVqZdVc94w97CC/Gu9F9R9ebukcrOv/BIn5Kv/yfl2qY+3XtLr8KjJTThiu+oPoknyk/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd63857dfad19b48b2102a5f97c451fff724e7b7ba3c12a37645b7e5276c3f37","last_reissued_at":"2026-05-18T00:41:13.386409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:13.386409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.2883","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":"2026-05-18T00:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6DkorIXDU4MhrXG1PCo1+52t7REj0qeuohl0Zgsttj8YNAs6N5CAyv/WPLodvl90Vso7X0DxPekykPLO7fXgCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:31:31.693602Z"},"content_sha256":"f33b37b77b25a52a53b374d443b4cc1ece547a03d6781f2365f802441b1e6a82","schema_version":"1.0","event_id":"sha256:f33b37b77b25a52a53b374d443b4cc1ece547a03d6781f2365f802441b1e6a82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7VRYK7P22GNURMQQFJPZPRCR77","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Feynman formulae and phase space Feynman path integrals for tau-quantization of some L\\'evy-Khintchine type Hamilton functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","math.PR"],"primary_cat":"math.FA","authors_text":"Martin Grothaus, Oleg Smolyanov, Yana Butko","submitted_at":"2013-11-12T19:03:13Z","abstract_excerpt":"This note is devoted to representation of some evolution semigroups. The semigroups are generated by pseudo-differential operators, which are obtained by different (parametrized by a number $\\tau$) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains functions which are second order polynomials with respect to the momentum variable and also some other functions. The considered semigroups are represented as limits of $n$-fold iterated integrals when $n$ tends to infinity (such representations are called Feynman formulae). Some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2883","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":"2026-05-18T00:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yV20U7Ee2c8HE7XYXIN4lULzHpV3jnkqdeKWSf2VzuMcxRbhBnouVSAefSuPdBTl60AxnOlhOQVbEEOrmo3cBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:31:31.693945Z"},"content_sha256":"6925487316a4eb6385094f57c5bcbc9a1d6e49c5cb1a1317e08c8fba28bacfc1","schema_version":"1.0","event_id":"sha256:6925487316a4eb6385094f57c5bcbc9a1d6e49c5cb1a1317e08c8fba28bacfc1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7VRYK7P22GNURMQQFJPZPRCR77/bundle.json","state_url":"https://pith.science/pith/7VRYK7P22GNURMQQFJPZPRCR77/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7VRYK7P22GNURMQQFJPZPRCR77/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":"2026-06-01T15:31:31Z","links":{"resolver":"https://pith.science/pith/7VRYK7P22GNURMQQFJPZPRCR77","bundle":"https://pith.science/pith/7VRYK7P22GNURMQQFJPZPRCR77/bundle.json","state":"https://pith.science/pith/7VRYK7P22GNURMQQFJPZPRCR77/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7VRYK7P22GNURMQQFJPZPRCR77/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7VRYK7P22GNURMQQFJPZPRCR77","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":"f25ef17add368c4ef720271f63e869c92a469c5fbe05b31a4ecb89d7dd699609","cross_cats_sorted":["math-ph","math.AP","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-12T19:03:13Z","title_canon_sha256":"84ef6944d2ed8c95262d4e7981e4eb209a5bec5c1e2112991cffb6372a420884"},"schema_version":"1.0","source":{"id":"1311.2883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2883","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2883v1","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2883","created_at":"2026-05-18T00:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"7VRYK7P22GNU","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7VRYK7P22GNURMQQ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7VRYK7P2","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:6925487316a4eb6385094f57c5bcbc9a1d6e49c5cb1a1317e08c8fba28bacfc1","target":"graph","created_at":"2026-05-18T00:41:13Z","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 note is devoted to representation of some evolution semigroups. The semigroups are generated by pseudo-differential operators, which are obtained by different (parametrized by a number $\\tau$) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains functions which are second order polynomials with respect to the momentum variable and also some other functions. The considered semigroups are represented as limits of $n$-fold iterated integrals when $n$ tends to infinity (such representations are called Feynman formulae). Some","authors_text":"Martin Grothaus, Oleg Smolyanov, Yana Butko","cross_cats":["math-ph","math.AP","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-12T19:03:13Z","title":"Feynman formulae and phase space Feynman path integrals for tau-quantization of some L\\'evy-Khintchine type Hamilton functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2883","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:f33b37b77b25a52a53b374d443b4cc1ece547a03d6781f2365f802441b1e6a82","target":"record","created_at":"2026-05-18T00:41:13Z","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":"f25ef17add368c4ef720271f63e869c92a469c5fbe05b31a4ecb89d7dd699609","cross_cats_sorted":["math-ph","math.AP","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-12T19:03:13Z","title_canon_sha256":"84ef6944d2ed8c95262d4e7981e4eb209a5bec5c1e2112991cffb6372a420884"},"schema_version":"1.0","source":{"id":"1311.2883","kind":"arxiv","version":1}},"canonical_sha256":"fd63857dfad19b48b2102a5f97c451fff724e7b7ba3c12a37645b7e5276c3f37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd63857dfad19b48b2102a5f97c451fff724e7b7ba3c12a37645b7e5276c3f37","first_computed_at":"2026-05-18T00:41:13.386409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:13.386409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cAl71E5n/sv1PaA6LVqZdVc94w97CC/Gu9F9R9ebukcrOv/BIn5Kv/yfl2qY+3XtLr8KjJTThiu+oPoknyk/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:13.387097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f33b37b77b25a52a53b374d443b4cc1ece547a03d6781f2365f802441b1e6a82","sha256:6925487316a4eb6385094f57c5bcbc9a1d6e49c5cb1a1317e08c8fba28bacfc1"],"state_sha256":"e41a0ad4b56f4f03c69b45e6c8a486363c9ba01a926d949bd4a7a4bf14281b81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BS+C5DRSVg48iEiizjjR9pLDJUaMiCqEE2LNK1yRDFna3W5VcW09nYmT0ioMHCLAEfAk2Hpwj8UipWUlGBr3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:31:31.695863Z","bundle_sha256":"cfe30385442210fc21302f917ce07a5012ccf429e242a7d50044082ec7d557c3"}}