{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AYOIO6QWFZY7WUTXIRLYQ45U6E","short_pith_number":"pith:AYOIO6QW","canonical_record":{"source":{"id":"1811.00929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-02T15:20:28Z","cross_cats_sorted":[],"title_canon_sha256":"cb5dcb5a6e0702ee220c30dd799bf24e3a3616c1ec313a135d5e23f213781ab8","abstract_canon_sha256":"d262f4948bc7fb13e5ae24052f12edaa759c4fd021f69e74f78f0f56817851de"},"schema_version":"1.0"},"canonical_sha256":"061c877a162e71fb527744578873b4f117f3e244973fa64a15321875cba2e2e0","source":{"kind":"arxiv","id":"1811.00929","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.00929","created_at":"2026-05-18T00:01:41Z"},{"alias_kind":"arxiv_version","alias_value":"1811.00929v1","created_at":"2026-05-18T00:01:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00929","created_at":"2026-05-18T00:01:41Z"},{"alias_kind":"pith_short_12","alias_value":"AYOIO6QWFZY7","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AYOIO6QWFZY7WUTX","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AYOIO6QW","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AYOIO6QWFZY7WUTXIRLYQ45U6E","target":"record","payload":{"canonical_record":{"source":{"id":"1811.00929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-02T15:20:28Z","cross_cats_sorted":[],"title_canon_sha256":"cb5dcb5a6e0702ee220c30dd799bf24e3a3616c1ec313a135d5e23f213781ab8","abstract_canon_sha256":"d262f4948bc7fb13e5ae24052f12edaa759c4fd021f69e74f78f0f56817851de"},"schema_version":"1.0"},"canonical_sha256":"061c877a162e71fb527744578873b4f117f3e244973fa64a15321875cba2e2e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:41.714833Z","signature_b64":"AeDwieNc5/b6o2NBnjrwvmIJtLSdFPZs8p1G6QggqLi76e3HJjoQcZ7QZbSFVY11fmWmiQH4OTBNWL6nZ3tNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"061c877a162e71fb527744578873b4f117f3e244973fa64a15321875cba2e2e0","last_reissued_at":"2026-05-18T00:01:41.714288Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:41.714288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.00929","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":"2026-05-18T00:01:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vRVpxhbZfK3gbL8NSIQGp/uFBv3Ity/V0ERmJC3OM9qEB+8pfCOuwMqdUwJ+uo4a61nfmFHZPCgLwH2bHgtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:54:54.266414Z"},"content_sha256":"7166728dcd14677974d3a73da9f5f5d1e06fb7f23701c53e53b95c7841fd133d","schema_version":"1.0","event_id":"sha256:7166728dcd14677974d3a73da9f5f5d1e06fb7f23701c53e53b95c7841fd133d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AYOIO6QWFZY7WUTXIRLYQ45U6E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Concerning ill-posedness for semilinear wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chengbo Wang, Mengyun Liu","submitted_at":"2018-11-02T15:20:28Z","abstract_excerpt":"In this paper, we investigate the problem of optimal regularity for derivative semilinear wave equations to be locally well-posed in $H^{s}$ with spatial dimension $n \\leq 5$. We show this equation, with power $2\\le p\\le 1+4/(n-1)$, is (strongly) ill-posed in $H^{s}$ with $s = (n+5)/4$ in general. Moreover, when the nonlinearity is quadratic we establish a characterization of the structure of nonlinear terms in terms of the regularity. As a byproduct, we give an alternative proof of the failure of the local in time endpoint scale-invariant $L_{t}^{4/(n-1)}L_{x}^{\\infty}$ Strichartz estimates. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00929","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":""},"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":"2026-05-18T00:01:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jzP7VPvNRJIKGiZUXJUeO5HlsyMBZpDfjBIbIqZQCYtpY6+rg+JuInNOcQazD0kXrVT1i6l6kTkUENNaLjZ3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:54:54.266761Z"},"content_sha256":"63ec713628414ef649e2c76820733547014cea45d0b0005ca5fb2a1ff95f3092","schema_version":"1.0","event_id":"sha256:63ec713628414ef649e2c76820733547014cea45d0b0005ca5fb2a1ff95f3092"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AYOIO6QWFZY7WUTXIRLYQ45U6E/bundle.json","state_url":"https://pith.science/pith/AYOIO6QWFZY7WUTXIRLYQ45U6E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AYOIO6QWFZY7WUTXIRLYQ45U6E/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":"2026-06-27T12:54:54Z","links":{"resolver":"https://pith.science/pith/AYOIO6QWFZY7WUTXIRLYQ45U6E","bundle":"https://pith.science/pith/AYOIO6QWFZY7WUTXIRLYQ45U6E/bundle.json","state":"https://pith.science/pith/AYOIO6QWFZY7WUTXIRLYQ45U6E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AYOIO6QWFZY7WUTXIRLYQ45U6E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AYOIO6QWFZY7WUTXIRLYQ45U6E","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":"d262f4948bc7fb13e5ae24052f12edaa759c4fd021f69e74f78f0f56817851de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-02T15:20:28Z","title_canon_sha256":"cb5dcb5a6e0702ee220c30dd799bf24e3a3616c1ec313a135d5e23f213781ab8"},"schema_version":"1.0","source":{"id":"1811.00929","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.00929","created_at":"2026-05-18T00:01:41Z"},{"alias_kind":"arxiv_version","alias_value":"1811.00929v1","created_at":"2026-05-18T00:01:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00929","created_at":"2026-05-18T00:01:41Z"},{"alias_kind":"pith_short_12","alias_value":"AYOIO6QWFZY7","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AYOIO6QWFZY7WUTX","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AYOIO6QW","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:63ec713628414ef649e2c76820733547014cea45d0b0005ca5fb2a1ff95f3092","target":"graph","created_at":"2026-05-18T00:01:41Z","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 investigate the problem of optimal regularity for derivative semilinear wave equations to be locally well-posed in $H^{s}$ with spatial dimension $n \\leq 5$. We show this equation, with power $2\\le p\\le 1+4/(n-1)$, is (strongly) ill-posed in $H^{s}$ with $s = (n+5)/4$ in general. Moreover, when the nonlinearity is quadratic we establish a characterization of the structure of nonlinear terms in terms of the regularity. As a byproduct, we give an alternative proof of the failure of the local in time endpoint scale-invariant $L_{t}^{4/(n-1)}L_{x}^{\\infty}$ Strichartz estimates. ","authors_text":"Chengbo Wang, Mengyun Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-02T15:20:28Z","title":"Concerning ill-posedness for semilinear wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00929","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":"sha256:7166728dcd14677974d3a73da9f5f5d1e06fb7f23701c53e53b95c7841fd133d","target":"record","created_at":"2026-05-18T00:01:41Z","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":"d262f4948bc7fb13e5ae24052f12edaa759c4fd021f69e74f78f0f56817851de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-02T15:20:28Z","title_canon_sha256":"cb5dcb5a6e0702ee220c30dd799bf24e3a3616c1ec313a135d5e23f213781ab8"},"schema_version":"1.0","source":{"id":"1811.00929","kind":"arxiv","version":1}},"canonical_sha256":"061c877a162e71fb527744578873b4f117f3e244973fa64a15321875cba2e2e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"061c877a162e71fb527744578873b4f117f3e244973fa64a15321875cba2e2e0","first_computed_at":"2026-05-18T00:01:41.714288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:41.714288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AeDwieNc5/b6o2NBnjrwvmIJtLSdFPZs8p1G6QggqLi76e3HJjoQcZ7QZbSFVY11fmWmiQH4OTBNWL6nZ3tNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:41.714833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.00929","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7166728dcd14677974d3a73da9f5f5d1e06fb7f23701c53e53b95c7841fd133d","sha256:63ec713628414ef649e2c76820733547014cea45d0b0005ca5fb2a1ff95f3092"],"state_sha256":"783d4ffbd4d72b3e6dc66374d0ccb4bd03c53e3c06602b8cfaa2523ebf474daf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9c6UTqRNU3vJbf+k/ljuQogpb1TpLkeq7komMvY2ynnQW8bK/d3YRyVtXXaGR8B6fw76Or438FI6S/ubDyCMAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:54:54.268784Z","bundle_sha256":"222d8f69688ab5cb4bcb59131f68cb3d205ee66c73e9190af2835df7f8988796"}}