{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5C57XPJXKJPTR2HZBXF2SFACNL","short_pith_number":"pith:5C57XPJX","canonical_record":{"source":{"id":"2505.18321","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-23T19:27:31Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"bacaba21f7460cb58353c22a2a267df20b00c375f93d0faa4bfb71054f7700bc","abstract_canon_sha256":"aa959b304ac3f4e82b741b29f09fbe2b7a5b8a8f6b062f93192f7883c33974fa"},"schema_version":"1.0"},"canonical_sha256":"e8bbfbbd37525f38e8f90dcba914026ac6b3a9cedfd0e2ac60c4c1fa80e32efe","source":{"kind":"arxiv","id":"2505.18321","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.18321","created_at":"2026-07-05T11:08:44Z"},{"alias_kind":"arxiv_version","alias_value":"2505.18321v1","created_at":"2026-07-05T11:08:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.18321","created_at":"2026-07-05T11:08:44Z"},{"alias_kind":"pith_short_12","alias_value":"5C57XPJXKJPT","created_at":"2026-07-05T11:08:44Z"},{"alias_kind":"pith_short_16","alias_value":"5C57XPJXKJPTR2HZ","created_at":"2026-07-05T11:08:44Z"},{"alias_kind":"pith_short_8","alias_value":"5C57XPJX","created_at":"2026-07-05T11:08:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5C57XPJXKJPTR2HZBXF2SFACNL","target":"record","payload":{"canonical_record":{"source":{"id":"2505.18321","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-23T19:27:31Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"bacaba21f7460cb58353c22a2a267df20b00c375f93d0faa4bfb71054f7700bc","abstract_canon_sha256":"aa959b304ac3f4e82b741b29f09fbe2b7a5b8a8f6b062f93192f7883c33974fa"},"schema_version":"1.0"},"canonical_sha256":"e8bbfbbd37525f38e8f90dcba914026ac6b3a9cedfd0e2ac60c4c1fa80e32efe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:08:44.694387Z","signature_b64":"nrS7u1qvAU2RXq8Lh3T/aRpBe1JdGWT942q+P1h/Y3vRHDDQkK20vnSLJTYdquKFN4vKFfc2Puo9WLn+Yz19Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8bbfbbd37525f38e8f90dcba914026ac6b3a9cedfd0e2ac60c4c1fa80e32efe","last_reissued_at":"2026-07-05T11:08:44.693929Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:08:44.693929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.18321","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":"2026-07-05T11:08:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+A2Ni6QCXXoeFnFTaLaFEUmqUsp9tBF5NoKM9XuYFv2vBAAJUR790GtQML0SE9kBIVtsbxh4zXWqtpmJsrDkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:48:49.044160Z"},"content_sha256":"187ed33343429cf4782e9a0288faf55d22cc8bef1726ba069bb0e61b7dd22091","schema_version":"1.0","event_id":"sha256:187ed33343429cf4782e9a0288faf55d22cc8bef1726ba069bb0e61b7dd22091"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5C57XPJXKJPTR2HZBXF2SFACNL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A structure-preserving local discontinuous Galerkin method for the Fokker-Planck-Landau equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Andr\\'es Galindo-Olarte, Irene M. Gamba, Kun Huang, Rodrigo Gonz\\'alez-Hern\\'andez","submitted_at":"2025-05-23T19:27:31Z","abstract_excerpt":"In this work, we introduce a structure-preserving local discontinuous Galerkin (LDG) method \\cite{cockburn1998local} for solving the non-local non-linear Fokker-Planck-Landau (FPL) equations. We rephrase the structure-preserving strategy of Shiroto and Sentoku\\cite{shiroto2019structure} in the language of numerical analysis, and extend it to the LDG framework. We propose a method that is not only conservative, but also stabilized through upwind flux. The apparent contradiction between conservation laws and numerical stabilization is elegantly resolved by leveraging the properties of the jump t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.18321","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/2505.18321/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":"2026-07-05T11:08:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"spNImmONy/ntKRcHcPdzXhp+WKv0hrJqqpCCCcFC4lJt1i+/PIn3nfpOnizpQW1fiXUO7leT56qhoaY8th5PDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:48:49.044731Z"},"content_sha256":"1f9b8962d6a70a3a76ae39197b9bfe986732cfc1498b8b614ae3a1a14194849d","schema_version":"1.0","event_id":"sha256:1f9b8962d6a70a3a76ae39197b9bfe986732cfc1498b8b614ae3a1a14194849d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5C57XPJXKJPTR2HZBXF2SFACNL/bundle.json","state_url":"https://pith.science/pith/5C57XPJXKJPTR2HZBXF2SFACNL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5C57XPJXKJPTR2HZBXF2SFACNL/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":"2026-08-08T22:48:49Z","links":{"resolver":"https://pith.science/pith/5C57XPJXKJPTR2HZBXF2SFACNL","bundle":"https://pith.science/pith/5C57XPJXKJPTR2HZBXF2SFACNL/bundle.json","state":"https://pith.science/pith/5C57XPJXKJPTR2HZBXF2SFACNL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5C57XPJXKJPTR2HZBXF2SFACNL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5C57XPJXKJPTR2HZBXF2SFACNL","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":"aa959b304ac3f4e82b741b29f09fbe2b7a5b8a8f6b062f93192f7883c33974fa","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-23T19:27:31Z","title_canon_sha256":"bacaba21f7460cb58353c22a2a267df20b00c375f93d0faa4bfb71054f7700bc"},"schema_version":"1.0","source":{"id":"2505.18321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.18321","created_at":"2026-07-05T11:08:44Z"},{"alias_kind":"arxiv_version","alias_value":"2505.18321v1","created_at":"2026-07-05T11:08:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.18321","created_at":"2026-07-05T11:08:44Z"},{"alias_kind":"pith_short_12","alias_value":"5C57XPJXKJPT","created_at":"2026-07-05T11:08:44Z"},{"alias_kind":"pith_short_16","alias_value":"5C57XPJXKJPTR2HZ","created_at":"2026-07-05T11:08:44Z"},{"alias_kind":"pith_short_8","alias_value":"5C57XPJX","created_at":"2026-07-05T11:08:44Z"}],"graph_snapshots":[{"event_id":"sha256:1f9b8962d6a70a3a76ae39197b9bfe986732cfc1498b8b614ae3a1a14194849d","target":"graph","created_at":"2026-07-05T11:08:44Z","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/2505.18321/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we introduce a structure-preserving local discontinuous Galerkin (LDG) method \\cite{cockburn1998local} for solving the non-local non-linear Fokker-Planck-Landau (FPL) equations. We rephrase the structure-preserving strategy of Shiroto and Sentoku\\cite{shiroto2019structure} in the language of numerical analysis, and extend it to the LDG framework. We propose a method that is not only conservative, but also stabilized through upwind flux. The apparent contradiction between conservation laws and numerical stabilization is elegantly resolved by leveraging the properties of the jump t","authors_text":"Andr\\'es Galindo-Olarte, Irene M. Gamba, Kun Huang, Rodrigo Gonz\\'alez-Hern\\'andez","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-23T19:27:31Z","title":"A structure-preserving local discontinuous Galerkin method for the Fokker-Planck-Landau equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.18321","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":"sha256:187ed33343429cf4782e9a0288faf55d22cc8bef1726ba069bb0e61b7dd22091","target":"record","created_at":"2026-07-05T11:08:44Z","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":"aa959b304ac3f4e82b741b29f09fbe2b7a5b8a8f6b062f93192f7883c33974fa","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-23T19:27:31Z","title_canon_sha256":"bacaba21f7460cb58353c22a2a267df20b00c375f93d0faa4bfb71054f7700bc"},"schema_version":"1.0","source":{"id":"2505.18321","kind":"arxiv","version":1}},"canonical_sha256":"e8bbfbbd37525f38e8f90dcba914026ac6b3a9cedfd0e2ac60c4c1fa80e32efe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8bbfbbd37525f38e8f90dcba914026ac6b3a9cedfd0e2ac60c4c1fa80e32efe","first_computed_at":"2026-07-05T11:08:44.693929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:08:44.693929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nrS7u1qvAU2RXq8Lh3T/aRpBe1JdGWT942q+P1h/Y3vRHDDQkK20vnSLJTYdquKFN4vKFfc2Puo9WLn+Yz19Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:08:44.694387Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.18321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:187ed33343429cf4782e9a0288faf55d22cc8bef1726ba069bb0e61b7dd22091","sha256:1f9b8962d6a70a3a76ae39197b9bfe986732cfc1498b8b614ae3a1a14194849d"],"state_sha256":"fa0c13e3a94f7fd15275a2008ae9605142f961149195b9a5d90fac6f1e500872"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6CIBDcZlKfIFzBA0Lx9H+HodaUNeiBaeC19FKAIzrdqsMa5iheY7CK7GRC86OFauDwknOR+y6YCDmB55RcbyBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T22:48:49.047889Z","bundle_sha256":"5ccec459f7fe3ffab3da60b847cd0fcc3b1a1b3d5ce11bec341dcbf0f19f2c42"}}