{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:JX6J5O5HI4HAMSC6ZDYREIOYOT","short_pith_number":"pith:JX6J5O5H","schema_version":"1.0","canonical_sha256":"4dfc9ebba7470e06485ec8f11221d874fe3cd2d08aa1a4297d6874e464dff70a","source":{"kind":"arxiv","id":"2608.04643","version":1},"attestation_state":"computed","paper":{"title":"Almost sure local well-posedness for the nonlinear Schr\\\"odinger equations on $\\Bbb T^d$ with non-algebraic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Yongming Luo","submitted_at":"2026-08-05T10:01:32Z","abstract_excerpt":"We study the Cauchy problem for the nonlinear Schr\\\"odinger equation on $\\mathbb T^d$ with random initial data and a general non-algebraic power-type nonlinearity. We establish almost sure local well-posedness in every spatial dimension and for the whole mass-supercritical range allowed by the natural condition $0<s_{\\mathrm c}<1+a$. The main new ingredient is a frequency-gaining probabilistic refinement of the Galilean bilinear estimates recently developed by Kwak and Kwon \\cite{KwakKwon}. In the random setting, the gauge decomposition gives rise to three new types of terms: a mean-free coeff"},"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":"2608.04643","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-05T10:01:32Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"5b86e91c7a57e49379941d9d8bb6860dfa53a6fdb75891d3f94658e01800636b","abstract_canon_sha256":"6c7b275d1dd8d3463b192b7dbc53f9b566f3d33fe78f0e14a3580e9cda0f70ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:36:27.684792Z","signature_b64":"fJ8xc8U9bYKi+xRQeQ+/3XRZLGZrm3/pZFLPvY1rPLleDUBveahKqw+o+j8VzwYbj+qv6TfHSOGLSVg5zbBuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dfc9ebba7470e06485ec8f11221d874fe3cd2d08aa1a4297d6874e464dff70a","last_reissued_at":"2026-08-06T01:36:27.683217Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:36:27.683217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost sure local well-posedness for the nonlinear Schr\\\"odinger equations on $\\Bbb T^d$ with non-algebraic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Yongming Luo","submitted_at":"2026-08-05T10:01:32Z","abstract_excerpt":"We study the Cauchy problem for the nonlinear Schr\\\"odinger equation on $\\mathbb T^d$ with random initial data and a general non-algebraic power-type nonlinearity. We establish almost sure local well-posedness in every spatial dimension and for the whole mass-supercritical range allowed by the natural condition $0<s_{\\mathrm c}<1+a$. The main new ingredient is a frequency-gaining probabilistic refinement of the Galilean bilinear estimates recently developed by Kwak and Kwon \\cite{KwakKwon}. In the random setting, the gauge decomposition gives rise to three new types of terms: a mean-free coeff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04643","kind":"arxiv","version":1},"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/2608.04643/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":"2608.04643","created_at":"2026-08-06T01:36:27.685102+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.04643v1","created_at":"2026-08-06T01:36:27.685102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04643","created_at":"2026-08-06T01:36:27.685102+00:00"},{"alias_kind":"pith_short_12","alias_value":"JX6J5O5HI4HA","created_at":"2026-08-06T01:36:27.685102+00:00"},{"alias_kind":"pith_short_16","alias_value":"JX6J5O5HI4HAMSC6","created_at":"2026-08-06T01:36:27.685102+00:00"},{"alias_kind":"pith_short_8","alias_value":"JX6J5O5H","created_at":"2026-08-06T01:36:27.685102+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JX6J5O5HI4HAMSC6ZDYREIOYOT","json":"https://pith.science/pith/JX6J5O5HI4HAMSC6ZDYREIOYOT.json","graph_json":"https://pith.science/api/pith-number/JX6J5O5HI4HAMSC6ZDYREIOYOT/graph.json","events_json":"https://pith.science/api/pith-number/JX6J5O5HI4HAMSC6ZDYREIOYOT/events.json","paper":"https://pith.science/paper/JX6J5O5H"},"agent_actions":{"view_html":"https://pith.science/pith/JX6J5O5HI4HAMSC6ZDYREIOYOT","download_json":"https://pith.science/pith/JX6J5O5HI4HAMSC6ZDYREIOYOT.json","view_paper":"https://pith.science/paper/JX6J5O5H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.04643&json=true","fetch_graph":"https://pith.science/api/pith-number/JX6J5O5HI4HAMSC6ZDYREIOYOT/graph.json","fetch_events":"https://pith.science/api/pith-number/JX6J5O5HI4HAMSC6ZDYREIOYOT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JX6J5O5HI4HAMSC6ZDYREIOYOT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JX6J5O5HI4HAMSC6ZDYREIOYOT/action/storage_attestation","attest_author":"https://pith.science/pith/JX6J5O5HI4HAMSC6ZDYREIOYOT/action/author_attestation","sign_citation":"https://pith.science/pith/JX6J5O5HI4HAMSC6ZDYREIOYOT/action/citation_signature","submit_replication":"https://pith.science/pith/JX6J5O5HI4HAMSC6ZDYREIOYOT/action/replication_record"}},"created_at":"2026-08-06T01:36:27.685102+00:00","updated_at":"2026-08-06T01:36:27.685102+00:00"}