{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:H74PVXSHUDJDHSNTIJ73US7F6V","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":"05f59411bd7b71c8038051c09d80d08317a840ba27ef6255f7e76e947291feee","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T13:21:43Z","title_canon_sha256":"1cae84d075ed6cb05215cd0a7d2f41aeba15ad68b8174bda56fc466414088a69"},"schema_version":"1.0","source":{"id":"2605.13499","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13499","created_at":"2026-05-18T02:44:41Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13499v1","created_at":"2026-05-18T02:44:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13499","created_at":"2026-05-18T02:44:41Z"},{"alias_kind":"pith_short_12","alias_value":"H74PVXSHUDJD","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"H74PVXSHUDJDHSNT","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"H74PVXSH","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:0e51a9dbc6e4da09753149f776df79cb62c4bbdc00efba344d4a46dc2fc9c527","target":"graph","created_at":"2026-05-18T02:44:41Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"we show that its leading order behavior is determined completely by the collisional frequency of the Boltzmann-Nordheim collision operator at equilibrium. This settles a prediction by Lukkarinen-Spohn, and thus gives a justification of the quantum Boltzmann equation from many-body quantum mechanics."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The initial state is close to equilibrium; the interaction strength λ is small, and the analysis is restricted to the kinetic time regime t ∼ λ^{-2}."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The leading-order asymptotic behavior of the two-point correlation function for a weakly interacting Fermi gas at kinetic times is exactly the collisional frequency of the equilibrium Boltzmann-Nordheim collision operator."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"For a weakly interacting Fermi gas starting near equilibrium, the leading decay of two-point time correlations at kinetic times is fixed exactly by the collision frequency of the Boltzmann-Nordheim operator."}],"snapshot_sha256":"797c8b2592fed9cb782be81b7cc42c2c34146586b30c638ac00c462ce5c59eeb"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper is devoted to the dynamics of a weakly interacting Fermi gas at the kinetic time regime $t\\sim \\lambda^{-2}$ where $\\lambda \\ll 1$ is the strength of the interaction potential. We prove that if the initial state is close to equilibrium, then the two-point time correlation function of the many-body quantum dynamics can be computed effectively. In fact, we show that its leading order behavior is determined completely by the collisional frequency of the Boltzmann-Nordheim collision operator at equilibrium. This settles a prediction by Lukkarinen-Spohn, and thus gives a justification of","authors_text":"Herbert Spohn, Minh-Binh Tran, Peter S. Madsen, Phan Th\\`anh Nam","cross_cats":["math.MP"],"headline":"For a weakly interacting Fermi gas starting near equilibrium, the leading decay of two-point time correlations at kinetic times is fixed exactly by the collision frequency of the Boltzmann-Nordheim operator.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T13:21:43Z","title":"On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas"},"references":{"count":21,"internal_anchors":0,"resolved_work":21,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"R. Balescu. Equilibrium and nonequilibrium statistical mechanics.NASA STI Recon Technical Report A, 76, 1975","work_id":"d0710276-b2de-4507-b4ff-cfe60eb0f0fd","year":1975},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Y. Deng and Z. Hani. Full derivation of the wave kinetic equation.Inventiones Mathematicae, 233(2):543–724, 2023","work_id":"5bba6081-39c6-464a-bf1e-594bc80d3b19","year":2023},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Y. Deng and Z. Hani. Long time justification of wave turbulence theory. arXiv e-print, arXiv:2311.10082, 2023","work_id":"34492de4-92c1-42a8-ab55-4035d73130f0","year":2023},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Long time derivation of the boltzmann equation from hard sphere dynamics","work_id":"a505e4c3-d5ab-4437-bff0-13e1bd253fd3","year":2025},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"L. Erd¨ os, M. Salmhofer, and H.-T. Yau. On the quantum boltzmann equation.Journal of Statistical Physics, 116:367–380, 08 2004","work_id":"23e4e7c6-68ef-44b1-9d64-e4d1e18acc2f","year":2004}],"snapshot_sha256":"7c3afb20a18ca28cdcb36418929a29686da8020775340638f5dad93e5674b3b0"},"source":{"id":"2605.13499","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T18:03:30.901948Z","id":"ab77bea6-f944-42db-a7a7-d47bf1941ec0","model_set":{"reader":"grok-4.3"},"one_line_summary":"The leading-order asymptotic behavior of the two-point correlation function for a weakly interacting Fermi gas at kinetic times is exactly the collisional frequency of the equilibrium Boltzmann-Nordheim collision operator.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"For a weakly interacting Fermi gas starting near equilibrium, the leading decay of two-point time correlations at kinetic times is fixed exactly by the collision frequency of the Boltzmann-Nordheim operator.","strongest_claim":"we show that its leading order behavior is determined completely by the collisional frequency of the Boltzmann-Nordheim collision operator at equilibrium. This settles a prediction by Lukkarinen-Spohn, and thus gives a justification of the quantum Boltzmann equation from many-body quantum mechanics.","weakest_assumption":"The initial state is close to equilibrium; the interaction strength λ is small, and the analysis is restricted to the kinetic time regime t ∼ λ^{-2}."}},"verdict_id":"ab77bea6-f944-42db-a7a7-d47bf1941ec0"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1f6e3918b1a643915efc5bb72d1353cb78d63707e32078bdbd2abc7f04c3132f","target":"record","created_at":"2026-05-18T02:44:41Z","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":"05f59411bd7b71c8038051c09d80d08317a840ba27ef6255f7e76e947291feee","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T13:21:43Z","title_canon_sha256":"1cae84d075ed6cb05215cd0a7d2f41aeba15ad68b8174bda56fc466414088a69"},"schema_version":"1.0","source":{"id":"2605.13499","kind":"arxiv","version":1}},"canonical_sha256":"3ff8fade47a0d233c9b3427fba4be5f56839de3ac572183878edbcf8fb031e24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ff8fade47a0d233c9b3427fba4be5f56839de3ac572183878edbcf8fb031e24","first_computed_at":"2026-05-18T02:44:41.028358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:41.028358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1HFNwdMjatT6dYv/Ej3ee9PnIwXN3vzJsK/lilGMWJNpKI4XQ0uNLVbUIv4b2NmwFC4cXM20YAlLJFFOMj5ICg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:41.028985Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13499","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f6e3918b1a643915efc5bb72d1353cb78d63707e32078bdbd2abc7f04c3132f","sha256:0e51a9dbc6e4da09753149f776df79cb62c4bbdc00efba344d4a46dc2fc9c527"],"state_sha256":"154aedcc3cf751adfe7859be3a182c7a20ec221ae8b08f18a81a1f794c949859"}