{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HYON3J3LUUCABRPM54IZIDK6LU","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":"1ed693a422c311fda994d9d337733a8bcfc8dce790a2df5a348b34237a6c4615","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-10T23:05:35Z","title_canon_sha256":"8a7cec204c43e8b139ca85f68db2060c6c3fbd95a7f9b5b6b0e22fddc9130acc"},"schema_version":"1.0","source":{"id":"2409.06905","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.06905","created_at":"2026-07-05T09:05:42Z"},{"alias_kind":"arxiv_version","alias_value":"2409.06905v1","created_at":"2026-07-05T09:05:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.06905","created_at":"2026-07-05T09:05:42Z"},{"alias_kind":"pith_short_12","alias_value":"HYON3J3LUUCA","created_at":"2026-07-05T09:05:42Z"},{"alias_kind":"pith_short_16","alias_value":"HYON3J3LUUCABRPM","created_at":"2026-07-05T09:05:42Z"},{"alias_kind":"pith_short_8","alias_value":"HYON3J3L","created_at":"2026-07-05T09:05:42Z"}],"graph_snapshots":[{"event_id":"sha256:283efe1b1da646719eb55ade2695d93a930fe6dfd99d3d5b6d381ffcbdf121fb","target":"graph","created_at":"2026-07-05T09:05:42Z","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/2409.06905/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the construction of invariant measures associated with higher order conservation laws of the intermediate long wave equation (ILW) and their convergence properties in the deep-water and shallow-water limits. By exploiting its complete integrability, we first carry out detailed analysis on the construction of appropriate conservation laws of ILW at the $H^\\frac k2$-level for each $k \\in \\mathbb{N}$, and establish their convergence to those of the Benjamin-Ono equation (BO) in the deep-water limit and to those of the Korteweg-de Vries equation (KdV) in the shallow-water limit. In partic","authors_text":"Andreia Chapouto, Guopeng Li, Tadahiro Oh","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-10T23:05:35Z","title":"Deep-water and shallow-water limits of statistical equilibria for the intermediate long wave equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.06905","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:bd0feacf277fdf36f7b86e2be7abdadd08a821c422963f547a0faf3fce366bd2","target":"record","created_at":"2026-07-05T09:05:42Z","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":"1ed693a422c311fda994d9d337733a8bcfc8dce790a2df5a348b34237a6c4615","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-10T23:05:35Z","title_canon_sha256":"8a7cec204c43e8b139ca85f68db2060c6c3fbd95a7f9b5b6b0e22fddc9130acc"},"schema_version":"1.0","source":{"id":"2409.06905","kind":"arxiv","version":1}},"canonical_sha256":"3e1cdda76ba50400c5ecef11940d5e5d2cc8c1d5b2d0ab92d63f15fb26312c18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e1cdda76ba50400c5ecef11940d5e5d2cc8c1d5b2d0ab92d63f15fb26312c18","first_computed_at":"2026-07-05T09:05:42.954925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:05:42.954925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gcrsQpbFihRSrOqDwNGbir+dL6Vj50c1O6cTB5K99Tn5H/kNb8wl6SbljCwDchidqvzgEEnn0SbX36Bws07WDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:05:42.955341Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.06905","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd0feacf277fdf36f7b86e2be7abdadd08a821c422963f547a0faf3fce366bd2","sha256:283efe1b1da646719eb55ade2695d93a930fe6dfd99d3d5b6d381ffcbdf121fb"],"state_sha256":"8c439e954f40192e4ed6a4ca3b90de90f5717a94d96416195bc20f9b3eb9cc26"}