{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UQBONUXVS7UXJOTC242KDUZMQ4","short_pith_number":"pith:UQBONUXV","canonical_record":{"source":{"id":"2607.18939","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-21T10:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"fbc9173c3fb141fe0ee1cd8d86e6f60472b1371325b0473d9a58e27d6e386f4f","abstract_canon_sha256":"b3701da2c7dd418a8cc8ce95957925c597a3529a065d62cfd8dda834306a089a"},"schema_version":"1.0"},"canonical_sha256":"a402e6d2f597e974ba62d734a1d32c871a700a36292044e3e2f8ca399f033231","source":{"kind":"arxiv","id":"2607.18939","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18939","created_at":"2026-07-22T01:23:20Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18939v1","created_at":"2026-07-22T01:23:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18939","created_at":"2026-07-22T01:23:20Z"},{"alias_kind":"pith_short_12","alias_value":"UQBONUXVS7UX","created_at":"2026-07-22T01:23:20Z"},{"alias_kind":"pith_short_16","alias_value":"UQBONUXVS7UXJOTC","created_at":"2026-07-22T01:23:20Z"},{"alias_kind":"pith_short_8","alias_value":"UQBONUXV","created_at":"2026-07-22T01:23:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UQBONUXVS7UXJOTC242KDUZMQ4","target":"record","payload":{"canonical_record":{"source":{"id":"2607.18939","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-21T10:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"fbc9173c3fb141fe0ee1cd8d86e6f60472b1371325b0473d9a58e27d6e386f4f","abstract_canon_sha256":"b3701da2c7dd418a8cc8ce95957925c597a3529a065d62cfd8dda834306a089a"},"schema_version":"1.0"},"canonical_sha256":"a402e6d2f597e974ba62d734a1d32c871a700a36292044e3e2f8ca399f033231","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T01:23:20.830777Z","signature_b64":"v6LJWeoSfa2E1iok5MwrBoqRYzIwVWbg8ttldmQam483J3cvCbdCJN1zHwjr1OjBQViPETZmhKy2DAMcYrYGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a402e6d2f597e974ba62d734a1d32c871a700a36292044e3e2f8ca399f033231","last_reissued_at":"2026-07-22T01:23:20.829942Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T01:23:20.829942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.18939","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":"2026-07-22T01:23:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmHZNLKd16ZeNVx2Ufil7bn1qvUsS3ghG0aeTvrIE/4QZqtd2DsPUqXtZyREdfGcIAoCCL2grYmrn0GBmxWSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T17:05:12.359246Z"},"content_sha256":"a6dc7c9e34b954007bcc55a216c2fb9df8a49d3b6ec850ddc945531a13095b7b","schema_version":"1.0","event_id":"sha256:a6dc7c9e34b954007bcc55a216c2fb9df8a49d3b6ec850ddc945531a13095b7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UQBONUXVS7UXJOTC242KDUZMQ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incompressible Navier-Stokes limit of non-bilinear kinetic equations and application to the BGK, nonlinear Fokker-Planck and Boltzmann-Fermi-Dirac equations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pierre Gervais","submitted_at":"2026-07-21T10:22:49Z","abstract_excerpt":"We consider collisional kinetic equations whose collision operator is not necessarily bilinear and prove quantitative convergence to the Navier-Stokes-Fourier system in weighted Sobolev spaces, together with a description of the initial layers. The aim of this paper is to conciliate the conditional convergence result of Bardos-Golse-Levermore for abstract kinetic equations conserving macroscopic quantities and dissipating entropy with the spectral strategy initiated by Bardos-Ukai for the Boltzmann equation. This work extends the abstract approach of Gervais-Lods which was restricted to biline"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18939","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/2607.18939/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":"2026-07-22T01:23:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bYFA7jcG+vY1kFiQuzNKMyFDPQXSiGteAb19U1AXaQQa2AA4L4L0SCy7bxZKpwsnYcJTj0a98yF1tcwUBeHLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T17:05:12.362625Z"},"content_sha256":"e95ed8149995e4a5dcab5ebcae338c29523174c2b81f85b8965dc5d7051793b7","schema_version":"1.0","event_id":"sha256:e95ed8149995e4a5dcab5ebcae338c29523174c2b81f85b8965dc5d7051793b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQBONUXVS7UXJOTC242KDUZMQ4/bundle.json","state_url":"https://pith.science/pith/UQBONUXVS7UXJOTC242KDUZMQ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQBONUXVS7UXJOTC242KDUZMQ4/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":"2026-08-11T17:05:12Z","links":{"resolver":"https://pith.science/pith/UQBONUXVS7UXJOTC242KDUZMQ4","bundle":"https://pith.science/pith/UQBONUXVS7UXJOTC242KDUZMQ4/bundle.json","state":"https://pith.science/pith/UQBONUXVS7UXJOTC242KDUZMQ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQBONUXVS7UXJOTC242KDUZMQ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UQBONUXVS7UXJOTC242KDUZMQ4","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":"b3701da2c7dd418a8cc8ce95957925c597a3529a065d62cfd8dda834306a089a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-21T10:22:49Z","title_canon_sha256":"fbc9173c3fb141fe0ee1cd8d86e6f60472b1371325b0473d9a58e27d6e386f4f"},"schema_version":"1.0","source":{"id":"2607.18939","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18939","created_at":"2026-07-22T01:23:20Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18939v1","created_at":"2026-07-22T01:23:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18939","created_at":"2026-07-22T01:23:20Z"},{"alias_kind":"pith_short_12","alias_value":"UQBONUXVS7UX","created_at":"2026-07-22T01:23:20Z"},{"alias_kind":"pith_short_16","alias_value":"UQBONUXVS7UXJOTC","created_at":"2026-07-22T01:23:20Z"},{"alias_kind":"pith_short_8","alias_value":"UQBONUXV","created_at":"2026-07-22T01:23:20Z"}],"graph_snapshots":[{"event_id":"sha256:e95ed8149995e4a5dcab5ebcae338c29523174c2b81f85b8965dc5d7051793b7","target":"graph","created_at":"2026-07-22T01:23:20Z","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/2607.18939/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider collisional kinetic equations whose collision operator is not necessarily bilinear and prove quantitative convergence to the Navier-Stokes-Fourier system in weighted Sobolev spaces, together with a description of the initial layers. The aim of this paper is to conciliate the conditional convergence result of Bardos-Golse-Levermore for abstract kinetic equations conserving macroscopic quantities and dissipating entropy with the spectral strategy initiated by Bardos-Ukai for the Boltzmann equation. This work extends the abstract approach of Gervais-Lods which was restricted to biline","authors_text":"Pierre Gervais","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-21T10:22:49Z","title":"Incompressible Navier-Stokes limit of non-bilinear kinetic equations and application to the BGK, nonlinear Fokker-Planck and Boltzmann-Fermi-Dirac equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18939","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:a6dc7c9e34b954007bcc55a216c2fb9df8a49d3b6ec850ddc945531a13095b7b","target":"record","created_at":"2026-07-22T01:23:20Z","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":"b3701da2c7dd418a8cc8ce95957925c597a3529a065d62cfd8dda834306a089a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-21T10:22:49Z","title_canon_sha256":"fbc9173c3fb141fe0ee1cd8d86e6f60472b1371325b0473d9a58e27d6e386f4f"},"schema_version":"1.0","source":{"id":"2607.18939","kind":"arxiv","version":1}},"canonical_sha256":"a402e6d2f597e974ba62d734a1d32c871a700a36292044e3e2f8ca399f033231","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a402e6d2f597e974ba62d734a1d32c871a700a36292044e3e2f8ca399f033231","first_computed_at":"2026-07-22T01:23:20.829942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T01:23:20.829942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v6LJWeoSfa2E1iok5MwrBoqRYzIwVWbg8ttldmQam483J3cvCbdCJN1zHwjr1OjBQViPETZmhKy2DAMcYrYGBg==","signature_status":"signed_v1","signed_at":"2026-07-22T01:23:20.830777Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18939","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6dc7c9e34b954007bcc55a216c2fb9df8a49d3b6ec850ddc945531a13095b7b","sha256:e95ed8149995e4a5dcab5ebcae338c29523174c2b81f85b8965dc5d7051793b7"],"state_sha256":"267e6b1f0108d12f06e5346606de7f6f9cdf17ad35ee1e55f3bde36f74efabaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNO4kxNgaby8WX+dPRPLlKIDlvYe9Xyreq6tgLdoGNlYNXAi49jJiicEyea566h1wahj2d1L3vN0rpX04AdaAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T17:05:12.378512Z","bundle_sha256":"87fc834705875267d6f1bd1d4f9839a33761d05b121b6da92be54417f0800415"}}