{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7XRU3RQ2XL7B6LZYP3ON4FPEG2","short_pith_number":"pith:7XRU3RQ2","canonical_record":{"source":{"id":"2505.19222","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-25T16:36:09Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b024e42b5a2f68f51826957c9d9e57305659f4f564f4242eb97442d5e4048131","abstract_canon_sha256":"7166741885934dee9e1890f4417c62e497b401fda56293015f3ef2c780ab312a"},"schema_version":"1.0"},"canonical_sha256":"fde34dc61abafe1f2f387edcde15e436a1a146a4c9d457bfe0ea46f50c69b9a4","source":{"kind":"arxiv","id":"2505.19222","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.19222","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"arxiv_version","alias_value":"2505.19222v3","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.19222","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_12","alias_value":"7XRU3RQ2XL7B","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_16","alias_value":"7XRU3RQ2XL7B6LZY","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_8","alias_value":"7XRU3RQ2","created_at":"2026-06-19T16:10:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7XRU3RQ2XL7B6LZYP3ON4FPEG2","target":"record","payload":{"canonical_record":{"source":{"id":"2505.19222","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-25T16:36:09Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b024e42b5a2f68f51826957c9d9e57305659f4f564f4242eb97442d5e4048131","abstract_canon_sha256":"7166741885934dee9e1890f4417c62e497b401fda56293015f3ef2c780ab312a"},"schema_version":"1.0"},"canonical_sha256":"fde34dc61abafe1f2f387edcde15e436a1a146a4c9d457bfe0ea46f50c69b9a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:29.868015Z","signature_b64":"QgpnWDZRleGAkerLFSdH+sBxOrUYIn78bO3uxzscognoOg2wuioxZl6K6IitjXW8nVhCeVggUctBk9bkE2YKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fde34dc61abafe1f2f387edcde15e436a1a146a4c9d457bfe0ea46f50c69b9a4","last_reissued_at":"2026-06-19T16:10:29.867617Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:29.867617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.19222","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:10:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FAIc9B06nqF5TkJxJAUyzjHGfBQ0DNeKDLwvVAlglukhkqbFDDQtU38z5wshqFm1f2eCd2EJzt7xBMOgc+M9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:15:51.760917Z"},"content_sha256":"b5b554bd5becd5483054291740d3bd8edaa044f80338ee0d8f52baed5be79f56","schema_version":"1.0","event_id":"sha256:b5b554bd5becd5483054291740d3bd8edaa044f80338ee0d8f52baed5be79f56"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7XRU3RQ2XL7B6LZYP3ON4FPEG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic numerical hypocoercivity of the space-time discontinuous Galerkin method for the Kolmogorov equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Emmanuil H. Georgoulis, Philip J. Herbert, Zhaonan Dong","submitted_at":"2025-05-25T16:36:09Z","abstract_excerpt":"We are concerned with discretisations of the classical Kolmogorov equation by a standard space-time discontinuous Galerkin method. {The} Kolmogorov equation serves as simple, yet rich enough in the present context, model problem for a wide range of kinetic-type equations: although it involves diffusion in one of the two spatial dimensions only, the combined nature of the first order transport/drift term and the degenerate diffusion are sufficient to `propagate dissipation' across the spatial domain in its entirety. This is a manifestation of the celebrated concept of hypocoercivity, a term coi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19222","kind":"arxiv","version":3},"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/2505.19222/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":"2026-06-19T16:10:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+UIO6AFOq7ks26jAQ69va9/KW4gufNCNNRUI44cPOkWtxhXYnO/At70VOvunaHy6Gm+u4eylj6MXM1V/vX8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T21:15:51.761293Z"},"content_sha256":"6423f72ed87c93b4d5bc02efef3b9f3f51c1d183e6635d1945e057c6b9866a0d","schema_version":"1.0","event_id":"sha256:6423f72ed87c93b4d5bc02efef3b9f3f51c1d183e6635d1945e057c6b9866a0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7XRU3RQ2XL7B6LZYP3ON4FPEG2/bundle.json","state_url":"https://pith.science/pith/7XRU3RQ2XL7B6LZYP3ON4FPEG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7XRU3RQ2XL7B6LZYP3ON4FPEG2/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":"2026-06-21T21:15:51Z","links":{"resolver":"https://pith.science/pith/7XRU3RQ2XL7B6LZYP3ON4FPEG2","bundle":"https://pith.science/pith/7XRU3RQ2XL7B6LZYP3ON4FPEG2/bundle.json","state":"https://pith.science/pith/7XRU3RQ2XL7B6LZYP3ON4FPEG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7XRU3RQ2XL7B6LZYP3ON4FPEG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7XRU3RQ2XL7B6LZYP3ON4FPEG2","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":"7166741885934dee9e1890f4417c62e497b401fda56293015f3ef2c780ab312a","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-25T16:36:09Z","title_canon_sha256":"b024e42b5a2f68f51826957c9d9e57305659f4f564f4242eb97442d5e4048131"},"schema_version":"1.0","source":{"id":"2505.19222","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.19222","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"arxiv_version","alias_value":"2505.19222v3","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.19222","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_12","alias_value":"7XRU3RQ2XL7B","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_16","alias_value":"7XRU3RQ2XL7B6LZY","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_8","alias_value":"7XRU3RQ2","created_at":"2026-06-19T16:10:29Z"}],"graph_snapshots":[{"event_id":"sha256:6423f72ed87c93b4d5bc02efef3b9f3f51c1d183e6635d1945e057c6b9866a0d","target":"graph","created_at":"2026-06-19T16:10:29Z","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/2505.19222/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We are concerned with discretisations of the classical Kolmogorov equation by a standard space-time discontinuous Galerkin method. {The} Kolmogorov equation serves as simple, yet rich enough in the present context, model problem for a wide range of kinetic-type equations: although it involves diffusion in one of the two spatial dimensions only, the combined nature of the first order transport/drift term and the degenerate diffusion are sufficient to `propagate dissipation' across the spatial domain in its entirety. This is a manifestation of the celebrated concept of hypocoercivity, a term coi","authors_text":"Emmanuil H. Georgoulis, Philip J. Herbert, Zhaonan Dong","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-25T16:36:09Z","title":"Asymptotic numerical hypocoercivity of the space-time discontinuous Galerkin method for the Kolmogorov equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19222","kind":"arxiv","version":3},"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:b5b554bd5becd5483054291740d3bd8edaa044f80338ee0d8f52baed5be79f56","target":"record","created_at":"2026-06-19T16:10:29Z","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":"7166741885934dee9e1890f4417c62e497b401fda56293015f3ef2c780ab312a","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-05-25T16:36:09Z","title_canon_sha256":"b024e42b5a2f68f51826957c9d9e57305659f4f564f4242eb97442d5e4048131"},"schema_version":"1.0","source":{"id":"2505.19222","kind":"arxiv","version":3}},"canonical_sha256":"fde34dc61abafe1f2f387edcde15e436a1a146a4c9d457bfe0ea46f50c69b9a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fde34dc61abafe1f2f387edcde15e436a1a146a4c9d457bfe0ea46f50c69b9a4","first_computed_at":"2026-06-19T16:10:29.867617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:29.867617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QgpnWDZRleGAkerLFSdH+sBxOrUYIn78bO3uxzscognoOg2wuioxZl6K6IitjXW8nVhCeVggUctBk9bkE2YKAg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:29.868015Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.19222","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5b554bd5becd5483054291740d3bd8edaa044f80338ee0d8f52baed5be79f56","sha256:6423f72ed87c93b4d5bc02efef3b9f3f51c1d183e6635d1945e057c6b9866a0d"],"state_sha256":"4a0e98e8cab7c2bad2085f3ef189f81a3d084b050eb2a223893d5090144f8191"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTvH9vbE19gWcXV83ZNpd5ifDSipdDc8yedgX0O+5rj4SZRXBbqSyUXSYUIEYn3GK1y19+EyQ0bUExBAcp3iAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T21:15:51.763370Z","bundle_sha256":"a8be21b16b7991b49512b79672f570e3f1e146debb2948d5a6adb3648c7ebd09"}}