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The construction adapts the intermittent slab building block of Gismondi, Ma, Pathak, and Radu. For the full cubic NLS, the spatially constant component generated by the nonlinearity cannot be discarded. We overcome this zero-output obstruction with a two-carrier perturbation: its unique zero-carrier"},"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":"2608.07866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-08T02:37:42Z","cross_cats_sorted":[],"title_canon_sha256":"d51570d137259638ba8d838fe2012ae53e3b465921fb973d93bf24a947fac741","abstract_canon_sha256":"56953687c20eb16f8ac36b3bc285a9d367cc73e3b24edddb7e46376b90f8ca6d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:18:45.914042Z","signature_b64":"U6fPV/hqA9oNEa3h2ub+FwU/NnUr3O0WbOilCxv3HpGVzE5CzViD5Exug/W0lw76lsiSrP309oTts6q/cq1EAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a38b5ec235858f198a65f8af1dbb7fb7654c5932e15bcb65fb158a1f9fce7b4","last_reissued_at":"2026-08-11T01:18:45.911124Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:18:45.911124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp non-uniqueness of singular solutions to the one-dimensional periodic cubic nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qirui Peng","submitted_at":"2026-08-08T02:37:42Z","abstract_excerpt":"We construct, via convex integration, a nonzero singular weak solution of the one-dimensional periodic cubic nonlinear Schr\\\"odinger equation that is compactly supported in time, has zero initial datum, and satisfies $u\\in\\bigcap_{\\alpha<1/6} C_t^0 H_x^\\alpha \\cap \\bigcap_{1\\leq p<3} C_t^0 L_x^p$. The construction adapts the intermittent slab building block of Gismondi, Ma, Pathak, and Radu. For the full cubic NLS, the spatially constant component generated by the nonlinearity cannot be discarded. 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