{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OKWMIVPVWLYXWYOSR73XJQUYO5","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":"8e5c7121b10525f234552bc7afe22ef067a703d702f12248fd349bbf839c63bd","cross_cats_sorted":["math.NA","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2015-09-23T08:59:39Z","title_canon_sha256":"e7173d9268629cb6b70e549df2b00918356f8cee6af96316bad8b26f995f5671"},"schema_version":"1.0","source":{"id":"1509.06890","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06890","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06890v1","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06890","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"OKWMIVPVWLYX","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OKWMIVPVWLYXWYOS","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OKWMIVPV","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:e9600d329b0fc70b91a1d70547936e2c2cd801f62d40879ddd8444f84da802d9","target":"graph","created_at":"2026-05-18T01:32:17Z","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 derive the numerical schemes for the strong order integration of the set of the stochastic differential equations (SDEs) corresponding to the non-stationary Parker transport equation (PTE). PTE is 5-dimensional (3 spatial coordinates, particles energy and time) Fokker- Planck type equation describing the non-stationary the galactic cosmic ray (GCR) particles transport in the heliosphere. We present the formulas for the numerical solution of the obtained set of SDEs driven by a Wiener process in the case of the full three-dimensional diffusion tensor. We introduce the solution applying the s","authors_text":"A. Wawrzynczak, M. Kluczek, R. Modzelewska","cross_cats":["math.NA","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2015-09-23T08:59:39Z","title":"Numerical methods for solution of the stochastic differential equations equivalent to the non-stationary Parker's transport equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06890","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:a189fa5711f676611c9e4e7413821512624135afd2f1c988ab319b20e9ea9398","target":"record","created_at":"2026-05-18T01:32:17Z","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":"8e5c7121b10525f234552bc7afe22ef067a703d702f12248fd349bbf839c63bd","cross_cats_sorted":["math.NA","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2015-09-23T08:59:39Z","title_canon_sha256":"e7173d9268629cb6b70e549df2b00918356f8cee6af96316bad8b26f995f5671"},"schema_version":"1.0","source":{"id":"1509.06890","kind":"arxiv","version":1}},"canonical_sha256":"72acc455f5b2f17b61d28ff774c2987761989a85d7c845565c2320f493df244c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72acc455f5b2f17b61d28ff774c2987761989a85d7c845565c2320f493df244c","first_computed_at":"2026-05-18T01:32:17.629553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:17.629553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GY5VfUEm5CXzIjg8R93DT5NqTUcMJyz/W5cN5SQ2U8II0+CrVRfA5fKa2wb2PXPNwbYI/hTEhe9gZGux2TISCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:17.630216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06890","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a189fa5711f676611c9e4e7413821512624135afd2f1c988ab319b20e9ea9398","sha256:e9600d329b0fc70b91a1d70547936e2c2cd801f62d40879ddd8444f84da802d9"],"state_sha256":"5caad24681c02f15b624731a7ce2f0476efd6fc594c3f27280166be5840740c0"}