{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:C47I7OZRT3L5F4L3EWE75GGEBI","short_pith_number":"pith:C47I7OZR","canonical_record":{"source":{"id":"1806.10066","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-26T15:37:05Z","cross_cats_sorted":[],"title_canon_sha256":"1f7e11c74ef57fc04744857a16627d84c5c91975de46c7c3d6e456cb62190639","abstract_canon_sha256":"a23ec1ce40bf4396d535827a50bfa42301ffeb8b87fcd0970fc15de64701c3a6"},"schema_version":"1.0"},"canonical_sha256":"173e8fbb319ed7d2f17b2589fe98c40a281f0250ef0dd2a28a64c09251d5bb12","source":{"kind":"arxiv","id":"1806.10066","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10066","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10066v3","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10066","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"C47I7OZRT3L5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C47I7OZRT3L5F4L3","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C47I7OZR","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:C47I7OZRT3L5F4L3EWE75GGEBI","target":"record","payload":{"canonical_record":{"source":{"id":"1806.10066","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-26T15:37:05Z","cross_cats_sorted":[],"title_canon_sha256":"1f7e11c74ef57fc04744857a16627d84c5c91975de46c7c3d6e456cb62190639","abstract_canon_sha256":"a23ec1ce40bf4396d535827a50bfa42301ffeb8b87fcd0970fc15de64701c3a6"},"schema_version":"1.0"},"canonical_sha256":"173e8fbb319ed7d2f17b2589fe98c40a281f0250ef0dd2a28a64c09251d5bb12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:23.353027Z","signature_b64":"lnBjtDlLrTQK8IiS3t1QrAK4nReEcbYfldXP87OwU/jD+2KhSCvm0UOZt8+aR6CJB4iUu3g/Xqwxre3FksSNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"173e8fbb319ed7d2f17b2589fe98c40a281f0250ef0dd2a28a64c09251d5bb12","last_reissued_at":"2026-05-18T00:07:23.352569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:23.352569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.10066","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aojCAN0MhfF6xXedoYfrQlW1L/GP+5uk5Ck9LTR3Z3HkB0mf3hUsAqKvKPPDPoh9YEWfzKZJBh9xLNTGnm4VAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:09:46.690727Z"},"content_sha256":"50f4adb5cdb5837f53f32ccd4a358d0b13ada83047a7b456099391ba8c530a93","schema_version":"1.0","event_id":"sha256:50f4adb5cdb5837f53f32ccd4a358d0b13ada83047a7b456099391ba8c530a93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:C47I7OZRT3L5F4L3EWE75GGEBI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on norm inflation for nonlinear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nobu Kishimoto","submitted_at":"2018-06-26T15:37:05Z","abstract_excerpt":"We consider semilinear Schr\\\"odinger equations with nonlinearity that is a polynomial in the unknown function and its complex conjugate, on $\\mathbb{R}^d$ or on the torus. Norm inflation (ill-posedness) of the associated initial value problem is proved in Sobolev spaces of negative indices. To this end, we apply the argument of Iwabuchi and Ogawa (2012), who treated quadratic nonlinearities. This method can be applied whether the spatial domain is non-periodic or periodic and whether the nonlinearity is gauge/scale-invariant or not."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10066","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXEEXhgnoZsQkyPpJxEABw750wtVEFQwkmJuIJ5lodtobihDecJSfXWij/1z++A6P6BB1PgwG4GrdUOhs4mWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:09:46.691343Z"},"content_sha256":"a9647dcd16fd05b00f6c0436b94a3bea47fff2712c8aac87d12d3b5d31c3e522","schema_version":"1.0","event_id":"sha256:a9647dcd16fd05b00f6c0436b94a3bea47fff2712c8aac87d12d3b5d31c3e522"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C47I7OZRT3L5F4L3EWE75GGEBI/bundle.json","state_url":"https://pith.science/pith/C47I7OZRT3L5F4L3EWE75GGEBI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C47I7OZRT3L5F4L3EWE75GGEBI/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":"2026-06-05T22:09:46Z","links":{"resolver":"https://pith.science/pith/C47I7OZRT3L5F4L3EWE75GGEBI","bundle":"https://pith.science/pith/C47I7OZRT3L5F4L3EWE75GGEBI/bundle.json","state":"https://pith.science/pith/C47I7OZRT3L5F4L3EWE75GGEBI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C47I7OZRT3L5F4L3EWE75GGEBI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C47I7OZRT3L5F4L3EWE75GGEBI","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":"a23ec1ce40bf4396d535827a50bfa42301ffeb8b87fcd0970fc15de64701c3a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-26T15:37:05Z","title_canon_sha256":"1f7e11c74ef57fc04744857a16627d84c5c91975de46c7c3d6e456cb62190639"},"schema_version":"1.0","source":{"id":"1806.10066","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10066","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10066v3","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10066","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"C47I7OZRT3L5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C47I7OZRT3L5F4L3","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C47I7OZR","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:a9647dcd16fd05b00f6c0436b94a3bea47fff2712c8aac87d12d3b5d31c3e522","target":"graph","created_at":"2026-05-18T00:07:23Z","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":"We consider semilinear Schr\\\"odinger equations with nonlinearity that is a polynomial in the unknown function and its complex conjugate, on $\\mathbb{R}^d$ or on the torus. Norm inflation (ill-posedness) of the associated initial value problem is proved in Sobolev spaces of negative indices. To this end, we apply the argument of Iwabuchi and Ogawa (2012), who treated quadratic nonlinearities. This method can be applied whether the spatial domain is non-periodic or periodic and whether the nonlinearity is gauge/scale-invariant or not.","authors_text":"Nobu Kishimoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-26T15:37:05Z","title":"A remark on norm inflation for nonlinear Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10066","kind":"arxiv","version":3},"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":"sha256:50f4adb5cdb5837f53f32ccd4a358d0b13ada83047a7b456099391ba8c530a93","target":"record","created_at":"2026-05-18T00:07:23Z","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":"a23ec1ce40bf4396d535827a50bfa42301ffeb8b87fcd0970fc15de64701c3a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-26T15:37:05Z","title_canon_sha256":"1f7e11c74ef57fc04744857a16627d84c5c91975de46c7c3d6e456cb62190639"},"schema_version":"1.0","source":{"id":"1806.10066","kind":"arxiv","version":3}},"canonical_sha256":"173e8fbb319ed7d2f17b2589fe98c40a281f0250ef0dd2a28a64c09251d5bb12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"173e8fbb319ed7d2f17b2589fe98c40a281f0250ef0dd2a28a64c09251d5bb12","first_computed_at":"2026-05-18T00:07:23.352569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:23.352569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lnBjtDlLrTQK8IiS3t1QrAK4nReEcbYfldXP87OwU/jD+2KhSCvm0UOZt8+aR6CJB4iUu3g/Xqwxre3FksSNAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:23.353027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10066","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50f4adb5cdb5837f53f32ccd4a358d0b13ada83047a7b456099391ba8c530a93","sha256:a9647dcd16fd05b00f6c0436b94a3bea47fff2712c8aac87d12d3b5d31c3e522"],"state_sha256":"a55942d55435ec81f1013c8b814ff998cdb2e892276a5c7a3c8330e41f80a597"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f8+BW9aGBwnEdgUG+O03QPK2yR9dH79UEwRDO0chUO9e7NUn0RHPhSkdMsNW+05oybhLepjh0gvm43T6qhmrDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:09:46.694998Z","bundle_sha256":"c889cf961e36a9fe9a4834393714d0551ac3ecde4d74dbf9616dd1462e85c5e6"}}