{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7IA6TWMZN3FPJQYNFX6YEOTCX6","short_pith_number":"pith:7IA6TWMZ","canonical_record":{"source":{"id":"2606.23980","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-22T22:13:55Z","cross_cats_sorted":["cs.NA","physics.bio-ph","physics.comp-ph","q-fin.CP","q-fin.PR"],"title_canon_sha256":"f73caa9b45687e2a784e2e6673daee3a801a28bc24443092a86ba8a2cf947f4b","abstract_canon_sha256":"f94fc3389b7fc3ec58346a0dd866ba70bbff10c1ff015a72bae6986146721587"},"schema_version":"1.0"},"canonical_sha256":"fa01e9d9996ecaf4c30d2dfd823a62bfa95c693e889da968348e8f4c921e6838","source":{"kind":"arxiv","id":"2606.23980","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23980","created_at":"2026-06-24T00:14:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23980v1","created_at":"2026-06-24T00:14:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23980","created_at":"2026-06-24T00:14:32Z"},{"alias_kind":"pith_short_12","alias_value":"7IA6TWMZN3FP","created_at":"2026-06-24T00:14:32Z"},{"alias_kind":"pith_short_16","alias_value":"7IA6TWMZN3FPJQYN","created_at":"2026-06-24T00:14:32Z"},{"alias_kind":"pith_short_8","alias_value":"7IA6TWMZ","created_at":"2026-06-24T00:14:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7IA6TWMZN3FPJQYNFX6YEOTCX6","target":"record","payload":{"canonical_record":{"source":{"id":"2606.23980","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-22T22:13:55Z","cross_cats_sorted":["cs.NA","physics.bio-ph","physics.comp-ph","q-fin.CP","q-fin.PR"],"title_canon_sha256":"f73caa9b45687e2a784e2e6673daee3a801a28bc24443092a86ba8a2cf947f4b","abstract_canon_sha256":"f94fc3389b7fc3ec58346a0dd866ba70bbff10c1ff015a72bae6986146721587"},"schema_version":"1.0"},"canonical_sha256":"fa01e9d9996ecaf4c30d2dfd823a62bfa95c693e889da968348e8f4c921e6838","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T00:14:32.194493Z","signature_b64":"xouhbfBpiS0sS1s6LgBg5O3gNZt4W1bp2XbIiQ2uRhRVKXrgY0HYvXFAR4Sq+UskiqAJ7GId1eZiRXmmjJ7vCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa01e9d9996ecaf4c30d2dfd823a62bfa95c693e889da968348e8f4c921e6838","last_reissued_at":"2026-06-24T00:14:32.194087Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T00:14:32.194087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.23980","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":"2026-06-24T00:14:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oigu4y7HZyba/txS0MSnr6CuN82SWtkJm0LqGoRyZMqkgnLO2BK3XDQn3N4j4wk6K9W103UriCXgfmtDSpSlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:50:38.564229Z"},"content_sha256":"39a078b525336fa2d24e87702ed3abfc50cd72159c4df1ec2dcf70ff81cba465","schema_version":"1.0","event_id":"sha256:39a078b525336fa2d24e87702ed3abfc50cd72159c4df1ec2dcf70ff81cba465"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7IA6TWMZN3FPJQYNFX6YEOTCX6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.bio-ph","physics.comp-ph","q-fin.CP","q-fin.PR"],"primary_cat":"math.NA","authors_text":"Andrey Itkin","submitted_at":"2026-06-22T22:13:55Z","abstract_excerpt":"The Fokker-Planck equation is fundamental to statistical mechanics, yet in settings with multiple state variables, anisotropic (cross-) diffusion, and jumps, conventional discretizations frequently produce non-physical negative probability densities. Building on the operator approach of \"A. Itkin, Pricing derivatives under Levy models. Modern finite difference and pseudo-differential operators approach, Springer, 2017, ISBN 978-1-4939-6792-6\", we introduce a family of \"Diagonal Frog\" discretizations whose spatial operators are eventually M-matrices (EM-matrices). Although these operators lack "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23980","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23980/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-24T00:14:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B8XdGKYN2EB6PSCerANmeae+CtD2hAngOjpZ8L/gPc4nx7uAJ7Rl4KUnpTHtID34eyeGp2onrhZYPlXNXNo4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:50:38.564765Z"},"content_sha256":"7301994a6fc6310f2f2100af42c9c3d49e5f37eea653947c1c85ec4ecf10174c","schema_version":"1.0","event_id":"sha256:7301994a6fc6310f2f2100af42c9c3d49e5f37eea653947c1c85ec4ecf10174c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IA6TWMZN3FPJQYNFX6YEOTCX6/bundle.json","state_url":"https://pith.science/pith/7IA6TWMZN3FPJQYNFX6YEOTCX6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IA6TWMZN3FPJQYNFX6YEOTCX6/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":"2026-08-04T17:50:38Z","links":{"resolver":"https://pith.science/pith/7IA6TWMZN3FPJQYNFX6YEOTCX6","bundle":"https://pith.science/pith/7IA6TWMZN3FPJQYNFX6YEOTCX6/bundle.json","state":"https://pith.science/pith/7IA6TWMZN3FPJQYNFX6YEOTCX6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IA6TWMZN3FPJQYNFX6YEOTCX6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7IA6TWMZN3FPJQYNFX6YEOTCX6","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":"f94fc3389b7fc3ec58346a0dd866ba70bbff10c1ff015a72bae6986146721587","cross_cats_sorted":["cs.NA","physics.bio-ph","physics.comp-ph","q-fin.CP","q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-22T22:13:55Z","title_canon_sha256":"f73caa9b45687e2a784e2e6673daee3a801a28bc24443092a86ba8a2cf947f4b"},"schema_version":"1.0","source":{"id":"2606.23980","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23980","created_at":"2026-06-24T00:14:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23980v1","created_at":"2026-06-24T00:14:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23980","created_at":"2026-06-24T00:14:32Z"},{"alias_kind":"pith_short_12","alias_value":"7IA6TWMZN3FP","created_at":"2026-06-24T00:14:32Z"},{"alias_kind":"pith_short_16","alias_value":"7IA6TWMZN3FPJQYN","created_at":"2026-06-24T00:14:32Z"},{"alias_kind":"pith_short_8","alias_value":"7IA6TWMZ","created_at":"2026-06-24T00:14:32Z"}],"graph_snapshots":[{"event_id":"sha256:7301994a6fc6310f2f2100af42c9c3d49e5f37eea653947c1c85ec4ecf10174c","target":"graph","created_at":"2026-06-24T00:14:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.23980/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Fokker-Planck equation is fundamental to statistical mechanics, yet in settings with multiple state variables, anisotropic (cross-) diffusion, and jumps, conventional discretizations frequently produce non-physical negative probability densities. Building on the operator approach of \"A. Itkin, Pricing derivatives under Levy models. Modern finite difference and pseudo-differential operators approach, Springer, 2017, ISBN 978-1-4939-6792-6\", we introduce a family of \"Diagonal Frog\" discretizations whose spatial operators are eventually M-matrices (EM-matrices). Although these operators lack ","authors_text":"Andrey Itkin","cross_cats":["cs.NA","physics.bio-ph","physics.comp-ph","q-fin.CP","q-fin.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-22T22:13:55Z","title":"Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23980","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":"sha256:39a078b525336fa2d24e87702ed3abfc50cd72159c4df1ec2dcf70ff81cba465","target":"record","created_at":"2026-06-24T00:14:32Z","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":"f94fc3389b7fc3ec58346a0dd866ba70bbff10c1ff015a72bae6986146721587","cross_cats_sorted":["cs.NA","physics.bio-ph","physics.comp-ph","q-fin.CP","q-fin.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-22T22:13:55Z","title_canon_sha256":"f73caa9b45687e2a784e2e6673daee3a801a28bc24443092a86ba8a2cf947f4b"},"schema_version":"1.0","source":{"id":"2606.23980","kind":"arxiv","version":1}},"canonical_sha256":"fa01e9d9996ecaf4c30d2dfd823a62bfa95c693e889da968348e8f4c921e6838","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa01e9d9996ecaf4c30d2dfd823a62bfa95c693e889da968348e8f4c921e6838","first_computed_at":"2026-06-24T00:14:32.194087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T00:14:32.194087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xouhbfBpiS0sS1s6LgBg5O3gNZt4W1bp2XbIiQ2uRhRVKXrgY0HYvXFAR4Sq+UskiqAJ7GId1eZiRXmmjJ7vCQ==","signature_status":"signed_v1","signed_at":"2026-06-24T00:14:32.194493Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23980","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39a078b525336fa2d24e87702ed3abfc50cd72159c4df1ec2dcf70ff81cba465","sha256:7301994a6fc6310f2f2100af42c9c3d49e5f37eea653947c1c85ec4ecf10174c"],"state_sha256":"ce8375026aff6e81d960f81c5825a3614f2adda80234939478bc563b40cc9c64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XKA6gW5lqKMBB3KtrDqg9yMjqICetNeKn+uaUs97xjqNGJeWzfgPRhvehR6r1E7VEVqWO4g1xY1xenqAovb3AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T17:50:38.600594Z","bundle_sha256":"efb45eaf1235ed23a458e9275aac66be7a9f85754df5b85b5c6385a741925855"}}