{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q4JPR2USPGAQGQ42FQAPVHEE3K","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":"1e07db1e74327b78625b44eb2dfce4c7d36e742681e6b9277eea0a551ee7a87f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-02T03:49:59Z","title_canon_sha256":"d07d50b008c29c4488d25999bf16037efc4049db76db79c9f3910afb0f364f3b"},"schema_version":"1.0","source":{"id":"1808.00657","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00657","created_at":"2026-05-18T00:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00657v1","created_at":"2026-05-18T00:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00657","created_at":"2026-05-18T00:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"Q4JPR2USPGAQ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q4JPR2USPGAQGQ42","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q4JPR2US","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:182b5a76fd02ee3eb2a505661381991b6f860df502023bd9903a01c0cbd0ffed","target":"graph","created_at":"2026-05-18T00:09:04Z","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"},"paper":{"abstract_excerpt":"In this paper we prove almost sure local well-posedness in both atomic spaces $X^s$ and Fourier restriction spaces $X^{s, b}$ for the cubic nonlinear Schr\\\"odinger equation on $\\TTT^d$ ($d\\geq 3$) in the super-critical regime.","authors_text":"Haitian Yue","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-02T03:49:59Z","title":"Almost sure well-posedness for the cubic nonlinear Schr\\\"{o}dinger equation in the super-critical regime on $\\TTT^d$, $d\\geq 3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00657","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:ba3e2fc93f853e77aacbc2b40bd9a1cdb36ec30212312e189c4b89291e546241","target":"record","created_at":"2026-05-18T00:09:04Z","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":"1e07db1e74327b78625b44eb2dfce4c7d36e742681e6b9277eea0a551ee7a87f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-02T03:49:59Z","title_canon_sha256":"d07d50b008c29c4488d25999bf16037efc4049db76db79c9f3910afb0f364f3b"},"schema_version":"1.0","source":{"id":"1808.00657","kind":"arxiv","version":1}},"canonical_sha256":"8712f8ea92798103439a2c00fa9c84daa2fe47c052d57a6a78eb8f1effedeb75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8712f8ea92798103439a2c00fa9c84daa2fe47c052d57a6a78eb8f1effedeb75","first_computed_at":"2026-05-18T00:09:04.604107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:04.604107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggMHitdPEWK+ZPsAtDfB9W/tduhIZ9rCkiHbwGhXsBsWHNqX2vs8AxaLacLIOhZxXYaBrnsLskawaVSpkUwxBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:04.604814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.00657","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba3e2fc93f853e77aacbc2b40bd9a1cdb36ec30212312e189c4b89291e546241","sha256:182b5a76fd02ee3eb2a505661381991b6f860df502023bd9903a01c0cbd0ffed"],"state_sha256":"17592379ceab26ff67865aca25c7a0a44dd52ecce1e7c7d290a055738a842a5e"}