{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GDR6QTUETBL226VLIGTV7OXMFO","short_pith_number":"pith:GDR6QTUE","schema_version":"1.0","canonical_sha256":"30e3e84e849857ad7aab41a75fbaec2b882d5566d3ccfbcc0a4f6c38f58ae358","source":{"kind":"arxiv","id":"2506.02948","version":2},"attestation_state":"computed","paper":{"title":"Rigorous Derivation of the Wave Kinetic Equation for $\\beta$-FPUT System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Boyang Wu","submitted_at":"2025-06-03T14:44:43Z","abstract_excerpt":"Wave kinetic theory has been suggested as a way to understand the longtime statistical behavior of the Fermi-Pasta-Ulam-Tsingou (FPUT) system, with the aim of determining the thermalization time scale. The latter has been a major problem since the model was introduced in the 1950s. In this thesis we establish the wave kinetic equation for a reduced evolution equation obtained from the $\\beta$-FPUT system by removing the non-resonant terms. We work in the kinetic limit $N\\to \\infty$ and $\\beta\\to 0$ under the scaling laws $\\beta=N^{-\\gamma}$ with $0<\\gamma<1$. The result holds up to the sub-kin"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.02948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-03T14:44:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3b000450aaa724e1cac6e3bde99ce5eebea21230ca7b83a547da9b3185576f38","abstract_canon_sha256":"4d065efdb9c06936432d05c78dd461ebaad60f30b5f3d596885478b783b7b91f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:20:12.761882Z","signature_b64":"kWsRjxOcQyqp9SGsAy1mQq0giG4DUSwqGurUNzU6z89089nevxbGgHXuXjBhOjbTjmF1UkxY+/Q6zvwGf7BzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30e3e84e849857ad7aab41a75fbaec2b882d5566d3ccfbcc0a4f6c38f58ae358","last_reissued_at":"2026-07-05T11:20:12.761416Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:20:12.761416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigorous Derivation of the Wave Kinetic Equation for $\\beta$-FPUT System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Boyang Wu","submitted_at":"2025-06-03T14:44:43Z","abstract_excerpt":"Wave kinetic theory has been suggested as a way to understand the longtime statistical behavior of the Fermi-Pasta-Ulam-Tsingou (FPUT) system, with the aim of determining the thermalization time scale. The latter has been a major problem since the model was introduced in the 1950s. In this thesis we establish the wave kinetic equation for a reduced evolution equation obtained from the $\\beta$-FPUT system by removing the non-resonant terms. We work in the kinetic limit $N\\to \\infty$ and $\\beta\\to 0$ under the scaling laws $\\beta=N^{-\\gamma}$ with $0<\\gamma<1$. The result holds up to the sub-kin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02948","kind":"arxiv","version":2},"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/2506.02948/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.02948","created_at":"2026-07-05T11:20:12.761473+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.02948v2","created_at":"2026-07-05T11:20:12.761473+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02948","created_at":"2026-07-05T11:20:12.761473+00:00"},{"alias_kind":"pith_short_12","alias_value":"GDR6QTUETBL2","created_at":"2026-07-05T11:20:12.761473+00:00"},{"alias_kind":"pith_short_16","alias_value":"GDR6QTUETBL226VL","created_at":"2026-07-05T11:20:12.761473+00:00"},{"alias_kind":"pith_short_8","alias_value":"GDR6QTUE","created_at":"2026-07-05T11:20:12.761473+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.07018","citing_title":"A survey on rigorous results for the dynamics of periodic FPU chains","ref_index":38,"is_internal_anchor":false},{"citing_arxiv_id":"2606.01358","citing_title":"A review on the kinetic theory of oscillator chains","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2605.24268","citing_title":"Resonant interactions in the $\\alpha$-FPUT lattice with site-dependent coefficients","ref_index":31,"is_internal_anchor":false},{"citing_arxiv_id":"2605.19308","citing_title":"Rigorous Derivation of the Wave Kinetic Equation for full $\\beta$-FPUT System","ref_index":76,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GDR6QTUETBL226VLIGTV7OXMFO","json":"https://pith.science/pith/GDR6QTUETBL226VLIGTV7OXMFO.json","graph_json":"https://pith.science/api/pith-number/GDR6QTUETBL226VLIGTV7OXMFO/graph.json","events_json":"https://pith.science/api/pith-number/GDR6QTUETBL226VLIGTV7OXMFO/events.json","paper":"https://pith.science/paper/GDR6QTUE"},"agent_actions":{"view_html":"https://pith.science/pith/GDR6QTUETBL226VLIGTV7OXMFO","download_json":"https://pith.science/pith/GDR6QTUETBL226VLIGTV7OXMFO.json","view_paper":"https://pith.science/paper/GDR6QTUE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.02948&json=true","fetch_graph":"https://pith.science/api/pith-number/GDR6QTUETBL226VLIGTV7OXMFO/graph.json","fetch_events":"https://pith.science/api/pith-number/GDR6QTUETBL226VLIGTV7OXMFO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GDR6QTUETBL226VLIGTV7OXMFO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GDR6QTUETBL226VLIGTV7OXMFO/action/storage_attestation","attest_author":"https://pith.science/pith/GDR6QTUETBL226VLIGTV7OXMFO/action/author_attestation","sign_citation":"https://pith.science/pith/GDR6QTUETBL226VLIGTV7OXMFO/action/citation_signature","submit_replication":"https://pith.science/pith/GDR6QTUETBL226VLIGTV7OXMFO/action/replication_record"}},"created_at":"2026-07-05T11:20:12.761473+00:00","updated_at":"2026-07-05T11:20:12.761473+00:00"}