{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VT7JZGY5UXILPTU52X3HIZ7MOH","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":"42249178e23170915322c74f773c5af599cf0ba32e9adca51c0483ad908aab76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-29T13:40:34Z","title_canon_sha256":"7c520ab9ac73d628a9a5d6f88c457420f6e0126460c1d5f9dfdd71a637f5ad42"},"schema_version":"1.0","source":{"id":"2407.20005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.20005","created_at":"2026-07-05T10:45:54Z"},{"alias_kind":"arxiv_version","alias_value":"2407.20005v1","created_at":"2026-07-05T10:45:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.20005","created_at":"2026-07-05T10:45:54Z"},{"alias_kind":"pith_short_12","alias_value":"VT7JZGY5UXIL","created_at":"2026-07-05T10:45:54Z"},{"alias_kind":"pith_short_16","alias_value":"VT7JZGY5UXILPTU5","created_at":"2026-07-05T10:45:54Z"},{"alias_kind":"pith_short_8","alias_value":"VT7JZGY5","created_at":"2026-07-05T10:45:54Z"}],"graph_snapshots":[{"event_id":"sha256:a404d023a0f47a85eee890f887edb946f26d17f89ab326e45ec723a33b3ae2d6","target":"graph","created_at":"2026-07-05T10:45:54Z","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/2407.20005/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the Cauchy problem of the nonlinear Schr\\\"odinger equation with the modulated dispersion and power type nonlinearities in any spatial dimensions. We adapt the Young integral theory developed by Chouk-Gubinelli [K. Chouk and M, Gubinelli, Comm. Partial Differential Equations 40 (2015)] and multilinear estimates which are based on divisor counting, and show the local well-posedness. Our result generalizes the result by Chouk-Gubinelli.","authors_text":"Tomoyuki Tanaka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-29T13:40:34Z","title":"Remark on the local well-posedness for NLS with the modulated dispersion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20005","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:a82f35c61f0c87e79151bdec5f88ac9b8040d8bce6182a8cc3173601396ab023","target":"record","created_at":"2026-07-05T10:45:54Z","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":"42249178e23170915322c74f773c5af599cf0ba32e9adca51c0483ad908aab76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-29T13:40:34Z","title_canon_sha256":"7c520ab9ac73d628a9a5d6f88c457420f6e0126460c1d5f9dfdd71a637f5ad42"},"schema_version":"1.0","source":{"id":"2407.20005","kind":"arxiv","version":1}},"canonical_sha256":"acfe9c9b1da5d0b7ce9dd5f67467ec71d8418490541cc527d7a48f96ad12d22e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acfe9c9b1da5d0b7ce9dd5f67467ec71d8418490541cc527d7a48f96ad12d22e","first_computed_at":"2026-07-05T10:45:54.188648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:45:54.188648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ez6xq9+KqD/QW2qIx/UM+sxqMHFw8W+Hpa5mtztPSDyj5kbzJywXXoQUjuGOmjrsNZ8zJl74nqFsdINvFMoBAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:45:54.189065Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.20005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a82f35c61f0c87e79151bdec5f88ac9b8040d8bce6182a8cc3173601396ab023","sha256:a404d023a0f47a85eee890f887edb946f26d17f89ab326e45ec723a33b3ae2d6"],"state_sha256":"25487bdfb82913adecd7b01e3f910963fef202abdf9a50ec83d331d987d62192"}