{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CX274KA6HV7OIFGPTS5SUDK2AM","short_pith_number":"pith:CX274KA6","canonical_record":{"source":{"id":"1607.05929","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-20T12:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"95f31332f11c6c193a3735738e91c76a65d483db2e5849030e4ea126de05d7b3","abstract_canon_sha256":"58b776168eed0acffcca45e5e5a962a522de0a35789be59a5abce2694c83c15d"},"schema_version":"1.0"},"canonical_sha256":"15f5fe281e3d7ee414cf9cbb2a0d5a03159831390c7b5d1707671d36e495f440","source":{"kind":"arxiv","id":"1607.05929","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05929","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05929v2","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05929","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"CX274KA6HV7O","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CX274KA6HV7OIFGP","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CX274KA6","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CX274KA6HV7OIFGPTS5SUDK2AM","target":"record","payload":{"canonical_record":{"source":{"id":"1607.05929","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-20T12:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"95f31332f11c6c193a3735738e91c76a65d483db2e5849030e4ea126de05d7b3","abstract_canon_sha256":"58b776168eed0acffcca45e5e5a962a522de0a35789be59a5abce2694c83c15d"},"schema_version":"1.0"},"canonical_sha256":"15f5fe281e3d7ee414cf9cbb2a0d5a03159831390c7b5d1707671d36e495f440","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:11.566447Z","signature_b64":"X7Igc4aUjqSvbU3WzyYiIJ6iTSxA0TaBCbck9sKJGt1edDZNha7Wx0T/Bjjy0tEbBNXS9v0Ea15sSgftN63tCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15f5fe281e3d7ee414cf9cbb2a0d5a03159831390c7b5d1707671d36e495f440","last_reissued_at":"2026-05-18T00:12:11.565876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:11.565876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.05929","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pSPXuW0BrLoT5uv66CLMux6LWRQX5EnwwAeN5zBany/yp1YLA9psKr/ONz6R0UQzkW7KoZO46EAOFOaa3FDVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:17:47.929144Z"},"content_sha256":"68dbbd2521a8081d3373eddfc782540e1a082818eab0dd7ffc7d6fcdf1e55cff","schema_version":"1.0","event_id":"sha256:68dbbd2521a8081d3373eddfc782540e1a082818eab0dd7ffc7d6fcdf1e55cff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CX274KA6HV7OIFGPTS5SUDK2AM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High order algorithm for the time-tempered fractional Feynman-Kac equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Minghua Chen, Weihua Deng","submitted_at":"2016-07-20T12:06:47Z","abstract_excerpt":"We provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in [Wu, Deng, and Barkai, Phys. Rev. E., 84 (2016), 032151], being called the time-tempered fractional Feynman-Kac equation. The key step of designing the algorithms is to discretize the time tempered fractional substantial derivative, being defined as $${^S\\!}D_t^{\\gamma,\\widetilde{\\lambda}} G(x,p,t)\\!=\\!D_t^{\\gamma,\\widetilde{\\lambda}} G(x,p,t)\\!-\\!\\lambda^\\gamma G(x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05929","kind":"arxiv","version":2},"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":"2026-05-18T00:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CixQmz7aP2alaeNiRWiz7hZ7xsyzLsgiiCeCHKsQNxpaQmlr8Jep2lQ0A7EKtYtMeDEGHl+pngQ9Gp4u+aF5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:17:47.929804Z"},"content_sha256":"5fbcb6b3c9f034626ada7584df3bf6bbbe47c010aab70b2b23e635715980ca82","schema_version":"1.0","event_id":"sha256:5fbcb6b3c9f034626ada7584df3bf6bbbe47c010aab70b2b23e635715980ca82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CX274KA6HV7OIFGPTS5SUDK2AM/bundle.json","state_url":"https://pith.science/pith/CX274KA6HV7OIFGPTS5SUDK2AM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CX274KA6HV7OIFGPTS5SUDK2AM/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":"2026-05-26T00:17:47Z","links":{"resolver":"https://pith.science/pith/CX274KA6HV7OIFGPTS5SUDK2AM","bundle":"https://pith.science/pith/CX274KA6HV7OIFGPTS5SUDK2AM/bundle.json","state":"https://pith.science/pith/CX274KA6HV7OIFGPTS5SUDK2AM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CX274KA6HV7OIFGPTS5SUDK2AM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CX274KA6HV7OIFGPTS5SUDK2AM","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":"58b776168eed0acffcca45e5e5a962a522de0a35789be59a5abce2694c83c15d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-20T12:06:47Z","title_canon_sha256":"95f31332f11c6c193a3735738e91c76a65d483db2e5849030e4ea126de05d7b3"},"schema_version":"1.0","source":{"id":"1607.05929","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05929","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05929v2","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05929","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"CX274KA6HV7O","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CX274KA6HV7OIFGP","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CX274KA6","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:5fbcb6b3c9f034626ada7584df3bf6bbbe47c010aab70b2b23e635715980ca82","target":"graph","created_at":"2026-05-18T00:12:11Z","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 provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in [Wu, Deng, and Barkai, Phys. Rev. E., 84 (2016), 032151], being called the time-tempered fractional Feynman-Kac equation. The key step of designing the algorithms is to discretize the time tempered fractional substantial derivative, being defined as $${^S\\!}D_t^{\\gamma,\\widetilde{\\lambda}} G(x,p,t)\\!=\\!D_t^{\\gamma,\\widetilde{\\lambda}} G(x,p,t)\\!-\\!\\lambda^\\gamma G(x","authors_text":"Minghua Chen, Weihua Deng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-20T12:06:47Z","title":"High order algorithm for the time-tempered fractional Feynman-Kac equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05929","kind":"arxiv","version":2},"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":"sha256:68dbbd2521a8081d3373eddfc782540e1a082818eab0dd7ffc7d6fcdf1e55cff","target":"record","created_at":"2026-05-18T00:12:11Z","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":"58b776168eed0acffcca45e5e5a962a522de0a35789be59a5abce2694c83c15d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-20T12:06:47Z","title_canon_sha256":"95f31332f11c6c193a3735738e91c76a65d483db2e5849030e4ea126de05d7b3"},"schema_version":"1.0","source":{"id":"1607.05929","kind":"arxiv","version":2}},"canonical_sha256":"15f5fe281e3d7ee414cf9cbb2a0d5a03159831390c7b5d1707671d36e495f440","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15f5fe281e3d7ee414cf9cbb2a0d5a03159831390c7b5d1707671d36e495f440","first_computed_at":"2026-05-18T00:12:11.565876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:11.565876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X7Igc4aUjqSvbU3WzyYiIJ6iTSxA0TaBCbck9sKJGt1edDZNha7Wx0T/Bjjy0tEbBNXS9v0Ea15sSgftN63tCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:11.566447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.05929","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68dbbd2521a8081d3373eddfc782540e1a082818eab0dd7ffc7d6fcdf1e55cff","sha256:5fbcb6b3c9f034626ada7584df3bf6bbbe47c010aab70b2b23e635715980ca82"],"state_sha256":"063b71fbeeef982fa3d399a96a859d8836733c3c8a42a0a4eba68757286ffbfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fof5z8/5aA/oqyhn6gn0jX8RNmsps8hKbNSmji68bZv8edB6R+T122VyCzRZGjd0nRa1LCouwY4XAfcySi0SDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:17:47.933556Z","bundle_sha256":"2738fc0466d883c59af89514adba6426db378f60a51810d9f07e16b8f43f349e"}}