{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:3WA4DFWRD4FY2ORTJ7FSSMTSN5","short_pith_number":"pith:3WA4DFWR","canonical_record":{"source":{"id":"2407.17782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-25T05:22:12Z","cross_cats_sorted":[],"title_canon_sha256":"b4bea3d47b4e81af58776de15957b41e51beef11c4498c45f105485ede12491c","abstract_canon_sha256":"e1b771b0a2f8b464e2d8e2880457643cd4373803adfb5e058bfbddd5c9f02e41"},"schema_version":"1.0"},"canonical_sha256":"dd81c196d11f0b8d3a334fcb2932726f59986b7baa130a0ee77194f64e30067e","source":{"kind":"arxiv","id":"2407.17782","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.17782","created_at":"2026-07-05T11:55:36Z"},{"alias_kind":"arxiv_version","alias_value":"2407.17782v1","created_at":"2026-07-05T11:55:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.17782","created_at":"2026-07-05T11:55:36Z"},{"alias_kind":"pith_short_12","alias_value":"3WA4DFWRD4FY","created_at":"2026-07-05T11:55:36Z"},{"alias_kind":"pith_short_16","alias_value":"3WA4DFWRD4FY2ORT","created_at":"2026-07-05T11:55:36Z"},{"alias_kind":"pith_short_8","alias_value":"3WA4DFWR","created_at":"2026-07-05T11:55:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:3WA4DFWRD4FY2ORTJ7FSSMTSN5","target":"record","payload":{"canonical_record":{"source":{"id":"2407.17782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-25T05:22:12Z","cross_cats_sorted":[],"title_canon_sha256":"b4bea3d47b4e81af58776de15957b41e51beef11c4498c45f105485ede12491c","abstract_canon_sha256":"e1b771b0a2f8b464e2d8e2880457643cd4373803adfb5e058bfbddd5c9f02e41"},"schema_version":"1.0"},"canonical_sha256":"dd81c196d11f0b8d3a334fcb2932726f59986b7baa130a0ee77194f64e30067e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:55:36.002639Z","signature_b64":"09WMfhbPqAG5Ize5T57d3A2u04tPDa8e4mrHYsboay3tqgH6A5cpWsC8Z99IY20qaOrYnCKxTGHIy0w7tX96Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd81c196d11f0b8d3a334fcb2932726f59986b7baa130a0ee77194f64e30067e","last_reissued_at":"2026-07-05T11:55:36.001825Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:55:36.001825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.17782","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":"2026-07-05T11:55:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gkghPlQ9mRLI/aNb6UQLjbovwWOPEJsVKNuKeJnVaalUvkuMUmXUIX/joV0Hazc4ngv+8yqDkmDEGwvRYrFRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T19:46:12.615041Z"},"content_sha256":"bfec4bbc5b7fa065b2068a391c0eaeccce0380aa3ce437497ddec7c08132716d","schema_version":"1.0","event_id":"sha256:bfec4bbc5b7fa065b2068a391c0eaeccce0380aa3ce437497ddec7c08132716d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:3WA4DFWRD4FY2ORTJ7FSSMTSN5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Norm inflation for a higher-order nonlinear Schr\\\"odinger equation with a derivative on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mamoru Okamoto, Toshiki Kondo","submitted_at":"2024-07-25T05:22:12Z","abstract_excerpt":"We consider a periodic higher-order nonlinear Schr\\\"odinger equation with the nonlinearity $u^k \\partial_x u$, where $k$ is a natural number. We prove the norm inflation in a subspace of the Sobolev space $H^s(\\mathbb{T})$ for any $s \\in \\mathbb{R}$. In particular, the Cauchy problem is ill-posed in $H^s(\\mathbb{T})$ for any $s \\in \\mathbb{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17782","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/2407.17782/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":"2026-07-05T11:55:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0sDjX5G1UUimUPsGdxUqvmQWcuLaw9hEJuNU9AvE3S1ht9VH1BTIVDhCDyBH36lkPx40lnlu9Vgo73j/rxjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T19:46:12.615511Z"},"content_sha256":"315a05a85c379bc415ed7245e08735dffe56e3d79bbe4d8a436d90d370aaa3dd","schema_version":"1.0","event_id":"sha256:315a05a85c379bc415ed7245e08735dffe56e3d79bbe4d8a436d90d370aaa3dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WA4DFWRD4FY2ORTJ7FSSMTSN5/bundle.json","state_url":"https://pith.science/pith/3WA4DFWRD4FY2ORTJ7FSSMTSN5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WA4DFWRD4FY2ORTJ7FSSMTSN5/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":"2026-08-11T19:46:12Z","links":{"resolver":"https://pith.science/pith/3WA4DFWRD4FY2ORTJ7FSSMTSN5","bundle":"https://pith.science/pith/3WA4DFWRD4FY2ORTJ7FSSMTSN5/bundle.json","state":"https://pith.science/pith/3WA4DFWRD4FY2ORTJ7FSSMTSN5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WA4DFWRD4FY2ORTJ7FSSMTSN5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:3WA4DFWRD4FY2ORTJ7FSSMTSN5","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":"e1b771b0a2f8b464e2d8e2880457643cd4373803adfb5e058bfbddd5c9f02e41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-25T05:22:12Z","title_canon_sha256":"b4bea3d47b4e81af58776de15957b41e51beef11c4498c45f105485ede12491c"},"schema_version":"1.0","source":{"id":"2407.17782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.17782","created_at":"2026-07-05T11:55:36Z"},{"alias_kind":"arxiv_version","alias_value":"2407.17782v1","created_at":"2026-07-05T11:55:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.17782","created_at":"2026-07-05T11:55:36Z"},{"alias_kind":"pith_short_12","alias_value":"3WA4DFWRD4FY","created_at":"2026-07-05T11:55:36Z"},{"alias_kind":"pith_short_16","alias_value":"3WA4DFWRD4FY2ORT","created_at":"2026-07-05T11:55:36Z"},{"alias_kind":"pith_short_8","alias_value":"3WA4DFWR","created_at":"2026-07-05T11:55:36Z"}],"graph_snapshots":[{"event_id":"sha256:315a05a85c379bc415ed7245e08735dffe56e3d79bbe4d8a436d90d370aaa3dd","target":"graph","created_at":"2026-07-05T11:55:36Z","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/2407.17782/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a periodic higher-order nonlinear Schr\\\"odinger equation with the nonlinearity $u^k \\partial_x u$, where $k$ is a natural number. We prove the norm inflation in a subspace of the Sobolev space $H^s(\\mathbb{T})$ for any $s \\in \\mathbb{R}$. In particular, the Cauchy problem is ill-posed in $H^s(\\mathbb{T})$ for any $s \\in \\mathbb{R}$.","authors_text":"Mamoru Okamoto, Toshiki Kondo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-25T05:22:12Z","title":"Norm inflation for a higher-order nonlinear Schr\\\"odinger equation with a derivative on the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17782","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:bfec4bbc5b7fa065b2068a391c0eaeccce0380aa3ce437497ddec7c08132716d","target":"record","created_at":"2026-07-05T11:55:36Z","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":"e1b771b0a2f8b464e2d8e2880457643cd4373803adfb5e058bfbddd5c9f02e41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-25T05:22:12Z","title_canon_sha256":"b4bea3d47b4e81af58776de15957b41e51beef11c4498c45f105485ede12491c"},"schema_version":"1.0","source":{"id":"2407.17782","kind":"arxiv","version":1}},"canonical_sha256":"dd81c196d11f0b8d3a334fcb2932726f59986b7baa130a0ee77194f64e30067e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd81c196d11f0b8d3a334fcb2932726f59986b7baa130a0ee77194f64e30067e","first_computed_at":"2026-07-05T11:55:36.001825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:55:36.001825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"09WMfhbPqAG5Ize5T57d3A2u04tPDa8e4mrHYsboay3tqgH6A5cpWsC8Z99IY20qaOrYnCKxTGHIy0w7tX96Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:55:36.002639Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.17782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfec4bbc5b7fa065b2068a391c0eaeccce0380aa3ce437497ddec7c08132716d","sha256:315a05a85c379bc415ed7245e08735dffe56e3d79bbe4d8a436d90d370aaa3dd"],"state_sha256":"1f5eacbcc9ec3e43131ddb5a669a08e830b0157284c586024728fd6c1767541d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t4X2gpmhYjqZ4Alt4VpLrbwDUT3rG1DwR3/rePZLhnnOBvU0e80Jvmh15uIku6eGHjZYIzDCVKZ+BOe5qjWvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T19:46:12.618634Z","bundle_sha256":"ca1154dd985c51e9ed5e41b9f3d698c593b56624323ef725ed6552e42ccda732"}}