{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FI4LL3BDLBMPDGFGL6FPDW5X7N","short_pith_number":"pith:FI4LL3BD","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"},"canonical_sha256":"2a38b5ec235858f198a65f8af1dbb7fb7654c5932e15bcb65fb158a1f9fce7b4","source":{"kind":"arxiv","id":"2608.07866","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.07866","created_at":"2026-08-11T01:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"2608.07866v1","created_at":"2026-08-11T01:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07866","created_at":"2026-08-11T01:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"FI4LL3BDLBMP","created_at":"2026-08-11T01:18:45Z"},{"alias_kind":"pith_short_16","alias_value":"FI4LL3BDLBMPDGFG","created_at":"2026-08-11T01:18:45Z"},{"alias_kind":"pith_short_8","alias_value":"FI4LL3BD","created_at":"2026-08-11T01:18:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FI4LL3BDLBMPDGFGL6FPDW5X7N","target":"record","payload":{"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"},"canonical_sha256":"2a38b5ec235858f198a65f8af1dbb7fb7654c5932e15bcb65fb158a1f9fce7b4","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"},"source_kind":"arxiv","source_id":"2608.07866","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-11T01:18:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"19yyPhYJmO2w+KNc7BbdrUvz7q1WbcS7Sf8f+gjxU91yr/bHdqBNtmzEs3dJiKbrAOgFIxsCrUqIfnCUU7SUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:20:17.354403Z"},"content_sha256":"633d02eaa13dc0bb93ad056d7eb7a442644422f7280b6f3607e9c9b13a31f5d7","schema_version":"1.0","event_id":"sha256:633d02eaa13dc0bb93ad056d7eb7a442644422f7280b6f3607e9c9b13a31f5d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FI4LL3BDLBMPDGFGL6FPDW5X7N","target":"graph","payload":{"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. We overcome this zero-output obstruction with a two-carrier perturbation: its unique zero-carrier"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07866","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/2608.07866/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-11T01:18:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m6MuRNC3Rf3ZcTJKu6GhVAXiFtO70W3hEbCdEzF0bSkGyJnHTaPY7y3mdg+Ab/bi6JQzx+02bimxWIQ9jxf7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T13:20:17.355158Z"},"content_sha256":"ea0f259d0710680d508f850fc0858db4539fd0d7be19e9ee5d597e143591ed82","schema_version":"1.0","event_id":"sha256:ea0f259d0710680d508f850fc0858db4539fd0d7be19e9ee5d597e143591ed82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FI4LL3BDLBMPDGFGL6FPDW5X7N/bundle.json","state_url":"https://pith.science/pith/FI4LL3BDLBMPDGFGL6FPDW5X7N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FI4LL3BDLBMPDGFGL6FPDW5X7N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T13:20:17Z","links":{"resolver":"https://pith.science/pith/FI4LL3BDLBMPDGFGL6FPDW5X7N","bundle":"https://pith.science/pith/FI4LL3BDLBMPDGFGL6FPDW5X7N/bundle.json","state":"https://pith.science/pith/FI4LL3BDLBMPDGFGL6FPDW5X7N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FI4LL3BDLBMPDGFGL6FPDW5X7N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FI4LL3BDLBMPDGFGL6FPDW5X7N","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":"56953687c20eb16f8ac36b3bc285a9d367cc73e3b24edddb7e46376b90f8ca6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-08T02:37:42Z","title_canon_sha256":"d51570d137259638ba8d838fe2012ae53e3b465921fb973d93bf24a947fac741"},"schema_version":"1.0","source":{"id":"2608.07866","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.07866","created_at":"2026-08-11T01:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"2608.07866v1","created_at":"2026-08-11T01:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07866","created_at":"2026-08-11T01:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"FI4LL3BDLBMP","created_at":"2026-08-11T01:18:45Z"},{"alias_kind":"pith_short_16","alias_value":"FI4LL3BDLBMPDGFG","created_at":"2026-08-11T01:18:45Z"},{"alias_kind":"pith_short_8","alias_value":"FI4LL3BD","created_at":"2026-08-11T01:18:45Z"}],"graph_snapshots":[{"event_id":"sha256:ea0f259d0710680d508f850fc0858db4539fd0d7be19e9ee5d597e143591ed82","target":"graph","created_at":"2026-08-11T01:18:45Z","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/2608.07866/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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. We overcome this zero-output obstruction with a two-carrier perturbation: its unique zero-carrier","authors_text":"Qirui Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-08T02:37:42Z","title":"Sharp non-uniqueness of singular solutions to the one-dimensional periodic cubic nonlinear Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07866","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":"sha256:633d02eaa13dc0bb93ad056d7eb7a442644422f7280b6f3607e9c9b13a31f5d7","target":"record","created_at":"2026-08-11T01:18:45Z","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":"56953687c20eb16f8ac36b3bc285a9d367cc73e3b24edddb7e46376b90f8ca6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-08T02:37:42Z","title_canon_sha256":"d51570d137259638ba8d838fe2012ae53e3b465921fb973d93bf24a947fac741"},"schema_version":"1.0","source":{"id":"2608.07866","kind":"arxiv","version":1}},"canonical_sha256":"2a38b5ec235858f198a65f8af1dbb7fb7654c5932e15bcb65fb158a1f9fce7b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a38b5ec235858f198a65f8af1dbb7fb7654c5932e15bcb65fb158a1f9fce7b4","first_computed_at":"2026-08-11T01:18:45.911124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T01:18:45.911124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U6fPV/hqA9oNEa3h2ub+FwU/NnUr3O0WbOilCxv3HpGVzE5CzViD5Exug/W0lw76lsiSrP309oTts6q/cq1EAw==","signature_status":"signed_v1","signed_at":"2026-08-11T01:18:45.914042Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.07866","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:633d02eaa13dc0bb93ad056d7eb7a442644422f7280b6f3607e9c9b13a31f5d7","sha256:ea0f259d0710680d508f850fc0858db4539fd0d7be19e9ee5d597e143591ed82"],"state_sha256":"429df1009daf2876c3596ebb6c36cc9be565d1b8665edf4546490845a34a592e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NdhxwRKrD4zGoYJNzRtJtjKdda9cfpwHcEVEyUTB3B2qxCtrhyOlJeF38bVB4BZguULG3Ric6lal4RF+/F36AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T13:20:17.361452Z","bundle_sha256":"145fe089820a3fddbd5981d339dfac4f4028d15caaeb81692c107fedbb937d63"}}