{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:W2XGA63EB27EHZGUD4X3SMXUCD","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":"8ee323080b52663924f06055be0a91ca07b1d000a56ce1e44cdccbea83f52fcc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-16T12:09:08Z","title_canon_sha256":"73a1a2fd2485d0cc75dc252e4e521974595c01fbfabe7f5aa60cb2e8e6fdc53b"},"schema_version":"1.0","source":{"id":"2607.14892","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14892","created_at":"2026-07-17T01:21:57Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14892v1","created_at":"2026-07-17T01:21:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14892","created_at":"2026-07-17T01:21:57Z"},{"alias_kind":"pith_short_12","alias_value":"W2XGA63EB27E","created_at":"2026-07-17T01:21:57Z"},{"alias_kind":"pith_short_16","alias_value":"W2XGA63EB27EHZGU","created_at":"2026-07-17T01:21:57Z"},{"alias_kind":"pith_short_8","alias_value":"W2XGA63E","created_at":"2026-07-17T01:21:57Z"}],"graph_snapshots":[{"event_id":"sha256:1960062adeee914716acbfce8fd76b3eda9ad711b20477055e2f8986deac8f56","target":"graph","created_at":"2026-07-17T01:21:57Z","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/2607.14892/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study four-wave kinetic equations in space dimension three with power-law dispersion $\\omega(p)=|p|^a$ and collision kernels with high-frequency growth measured by $\\beta$. In weighted $L^\\infty$ spaces, we identify the sharp decay threshold $$ s_c=4\\beta+3-\\frac a2. $$ For $s>s_c$, we prove local well-posedness by establishing trilinear bounds for the full gain-loss collision operator. For $s<s_c$, we prove ill-posedness by constructing data concentrated near a high-low-low-high resonant configuration. This threshold captures the balance between the high-frequency strength of the kernel an","authors_text":"Xilu Zhu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14892","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":"sha256:38145041a58f5edacaaff85953295cbf16b1be34cb06cc09080ff9735fc95a35","target":"record","created_at":"2026-07-17T01:21:57Z","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":"8ee323080b52663924f06055be0a91ca07b1d000a56ce1e44cdccbea83f52fcc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-16T12:09:08Z","title_canon_sha256":"73a1a2fd2485d0cc75dc252e4e521974595c01fbfabe7f5aa60cb2e8e6fdc53b"},"schema_version":"1.0","source":{"id":"2607.14892","kind":"arxiv","version":1}},"canonical_sha256":"b6ae607b640ebe43e4d41f2fb932f410fd91729dfcd5477fe4d46e55c33be8af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6ae607b640ebe43e4d41f2fb932f410fd91729dfcd5477fe4d46e55c33be8af","first_computed_at":"2026-07-17T01:21:57.260706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T01:21:57.260706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ktcAluWXLCTHbYfwv+o3C9LGjxux5xemVeMZz0Xz9hRpCYGgv2ijhetdhvtTXm+d/7G2Y236wY7m1+nRq5QNCQ==","signature_status":"signed_v1","signed_at":"2026-07-17T01:21:57.261572Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.14892","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38145041a58f5edacaaff85953295cbf16b1be34cb06cc09080ff9735fc95a35","sha256:1960062adeee914716acbfce8fd76b3eda9ad711b20477055e2f8986deac8f56"],"state_sha256":"6d066af3ec53a8e93bd41fd72ccdd96865a8dc61b5d8a440ac10797f84fd0bef"}