{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UWGNC2HVKSNLRWM5JTATZPPV3T","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":"9bd6810455cbd25cf968ee2710cb919ac70b3e879aadf68777d547ff3f822685","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-17T11:46:30Z","title_canon_sha256":"7203b32286cd9eb25fcab40546f2426f6783cacd3231c3a06e07c870a0640b97"},"schema_version":"1.0","source":{"id":"2607.15878","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.15878","created_at":"2026-07-20T01:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"2607.15878v1","created_at":"2026-07-20T01:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.15878","created_at":"2026-07-20T01:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"UWGNC2HVKSNL","created_at":"2026-07-20T01:19:15Z"},{"alias_kind":"pith_short_16","alias_value":"UWGNC2HVKSNLRWM5","created_at":"2026-07-20T01:19:15Z"},{"alias_kind":"pith_short_8","alias_value":"UWGNC2HV","created_at":"2026-07-20T01:19:15Z"}],"graph_snapshots":[{"event_id":"sha256:54ce13f33fd4d6292e2ed4ff94d3ebc7c70c74d4e2d4c6cae423c33b15b14159","target":"graph","created_at":"2026-07-20T01:19:15Z","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/2607.15878/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the Cauchy problem for the incompressible Euler-Vlasov-Fokker-Planck (Euler-VFP) system in the whole space \\(\\mathbb R^3\\) near the global Maxwellian equilibrium. The Fokker-Planck operator and the particle-fluid drag dissipate the relative momentum but do not separately control the common particle-fluid momentum; in Fourier variables, this degeneracy occurs in the transverse momentum components. To recover the missing coercivity, we augment the classical four-moment compensator with a finite-rank skew-adjoint correction constructed from second-order Hermite modes. Combined with th","authors_text":"Jinkai Ni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-17T11:46:30Z","title":"Modified compensating functions for the incompressible Euler--Vlasov--Fokker--Planck system: Global classical solutions and pointwise-in-space decay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15878","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":"sha256:220ee62f42be30af1aeec954efd9c921e212c2b065a939a8125a8c54c170391a","target":"record","created_at":"2026-07-20T01:19:15Z","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":"9bd6810455cbd25cf968ee2710cb919ac70b3e879aadf68777d547ff3f822685","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-17T11:46:30Z","title_canon_sha256":"7203b32286cd9eb25fcab40546f2426f6783cacd3231c3a06e07c870a0640b97"},"schema_version":"1.0","source":{"id":"2607.15878","kind":"arxiv","version":1}},"canonical_sha256":"a58cd168f5549ab8d99d4cc13cbdf5dcece6a42717c223778d48852b6cb03e50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a58cd168f5549ab8d99d4cc13cbdf5dcece6a42717c223778d48852b6cb03e50","first_computed_at":"2026-07-20T01:19:15.026765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-20T01:19:15.026765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pEO+UvVkzRT1aCoKq0sIdDgiYuS17hIOoZAo7LfmbPAtOS8DsMWvCC9+BeBE7Pe+aFX5Mc3ozRsOtejP48WMDQ==","signature_status":"signed_v1","signed_at":"2026-07-20T01:19:15.027645Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.15878","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:220ee62f42be30af1aeec954efd9c921e212c2b065a939a8125a8c54c170391a","sha256:54ce13f33fd4d6292e2ed4ff94d3ebc7c70c74d4e2d4c6cae423c33b15b14159"],"state_sha256":"c754a19b5e108775da15d47f9bc0457efdc82b46cae0dbf97f3cb8f89943e6e9"}