{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5VRWGPXZNI3LOTTP3QUTAYBDEY","short_pith_number":"pith:5VRWGPXZ","canonical_record":{"source":{"id":"2405.19674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-30T04:00:35Z","cross_cats_sorted":[],"title_canon_sha256":"dad383be8424a1253b1871e71cc893999d30e4edf8425b5a687f6d93e0f045bb","abstract_canon_sha256":"b30308330953502ca0e79c6daf1f0fa2fd6d122a5f3ac4eddd6b8a5bb6959a82"},"schema_version":"1.0"},"canonical_sha256":"ed63633ef96a36b74e6fdc29306023260719b637dbe018048fa96ceea0fa0c13","source":{"kind":"arxiv","id":"2405.19674","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.19674","created_at":"2026-07-05T10:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"2405.19674v1","created_at":"2026-07-05T10:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19674","created_at":"2026-07-05T10:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"5VRWGPXZNI3L","created_at":"2026-07-05T10:42:35Z"},{"alias_kind":"pith_short_16","alias_value":"5VRWGPXZNI3LOTTP","created_at":"2026-07-05T10:42:35Z"},{"alias_kind":"pith_short_8","alias_value":"5VRWGPXZ","created_at":"2026-07-05T10:42:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5VRWGPXZNI3LOTTP3QUTAYBDEY","target":"record","payload":{"canonical_record":{"source":{"id":"2405.19674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-30T04:00:35Z","cross_cats_sorted":[],"title_canon_sha256":"dad383be8424a1253b1871e71cc893999d30e4edf8425b5a687f6d93e0f045bb","abstract_canon_sha256":"b30308330953502ca0e79c6daf1f0fa2fd6d122a5f3ac4eddd6b8a5bb6959a82"},"schema_version":"1.0"},"canonical_sha256":"ed63633ef96a36b74e6fdc29306023260719b637dbe018048fa96ceea0fa0c13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:42:35.324307Z","signature_b64":"Gz9biiw1SH1LviAq7FcSDlsDgK/13+c9Mw7oiQ4zc1OslUCgy3cNl0Ge9/G0mOAMMvQYNsvSni7geWch7x8BAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed63633ef96a36b74e6fdc29306023260719b637dbe018048fa96ceea0fa0c13","last_reissued_at":"2026-07-05T10:42:35.323812Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:42:35.323812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.19674","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":"2026-07-05T10:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bm27ejWLXgtwXVPvMFobHTZFVFuxZ7bw4wV1M+yrnjMscaSNlBSh3EfaQ7ZxZ6UPzrf44yWLXJ3YCD10hRmEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T18:03:40.180179Z"},"content_sha256":"b73be0af526418dd4b53cb28dc11e7a07e6ed3fe008f1e24f92dea3aaa613ac0","schema_version":"1.0","event_id":"sha256:b73be0af526418dd4b53cb28dc11e7a07e6ed3fe008f1e24f92dea3aaa613ac0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5VRWGPXZNI3LOTTP3QUTAYBDEY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On blow-up for the supercritical defocusing nonlinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongyi Wei, Feng Shao, Zhifei Zhang","submitted_at":"2024-05-30T04:00:35Z","abstract_excerpt":"In this paper, we consider the defocusing nonlinear wave equation $-\\partial_t^2u+\\Delta u=|u|^{p-1}u$ in $\\mathbb R\\times \\mathbb R^d$. Building on our companion work ({\\it \\small Self-similar imploding solutions of the relativistic Euler equations}), we prove that for $d=4, p\\geq 29$ and $d\\geq 5, p\\geq 17$, there exists a smooth complex-valued solution that blows up in finite time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19674","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/2405.19674/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":"2026-07-05T10:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BZuk0myk+ESeXZFur98uUV7qw5OqvWB+DWRU8LvavijrdZK8IxF7FQY0xZ3kJRv83w+iaWqj3YH/CGP9gy+eDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T18:03:40.181041Z"},"content_sha256":"628b0c1c66e2177b674948c2f06c381f912be71487c40fc1232eae81a13ed9e7","schema_version":"1.0","event_id":"sha256:628b0c1c66e2177b674948c2f06c381f912be71487c40fc1232eae81a13ed9e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5VRWGPXZNI3LOTTP3QUTAYBDEY/bundle.json","state_url":"https://pith.science/pith/5VRWGPXZNI3LOTTP3QUTAYBDEY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5VRWGPXZNI3LOTTP3QUTAYBDEY/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":"2026-08-11T18:03:40Z","links":{"resolver":"https://pith.science/pith/5VRWGPXZNI3LOTTP3QUTAYBDEY","bundle":"https://pith.science/pith/5VRWGPXZNI3LOTTP3QUTAYBDEY/bundle.json","state":"https://pith.science/pith/5VRWGPXZNI3LOTTP3QUTAYBDEY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5VRWGPXZNI3LOTTP3QUTAYBDEY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5VRWGPXZNI3LOTTP3QUTAYBDEY","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":"b30308330953502ca0e79c6daf1f0fa2fd6d122a5f3ac4eddd6b8a5bb6959a82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-30T04:00:35Z","title_canon_sha256":"dad383be8424a1253b1871e71cc893999d30e4edf8425b5a687f6d93e0f045bb"},"schema_version":"1.0","source":{"id":"2405.19674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.19674","created_at":"2026-07-05T10:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"2405.19674v1","created_at":"2026-07-05T10:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19674","created_at":"2026-07-05T10:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"5VRWGPXZNI3L","created_at":"2026-07-05T10:42:35Z"},{"alias_kind":"pith_short_16","alias_value":"5VRWGPXZNI3LOTTP","created_at":"2026-07-05T10:42:35Z"},{"alias_kind":"pith_short_8","alias_value":"5VRWGPXZ","created_at":"2026-07-05T10:42:35Z"}],"graph_snapshots":[{"event_id":"sha256:628b0c1c66e2177b674948c2f06c381f912be71487c40fc1232eae81a13ed9e7","target":"graph","created_at":"2026-07-05T10:42:35Z","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/2405.19674/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider the defocusing nonlinear wave equation $-\\partial_t^2u+\\Delta u=|u|^{p-1}u$ in $\\mathbb R\\times \\mathbb R^d$. Building on our companion work ({\\it \\small Self-similar imploding solutions of the relativistic Euler equations}), we prove that for $d=4, p\\geq 29$ and $d\\geq 5, p\\geq 17$, there exists a smooth complex-valued solution that blows up in finite time.","authors_text":"Dongyi Wei, Feng Shao, Zhifei Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-30T04:00:35Z","title":"On blow-up for the supercritical defocusing nonlinear wave equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19674","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:b73be0af526418dd4b53cb28dc11e7a07e6ed3fe008f1e24f92dea3aaa613ac0","target":"record","created_at":"2026-07-05T10:42:35Z","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":"b30308330953502ca0e79c6daf1f0fa2fd6d122a5f3ac4eddd6b8a5bb6959a82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-05-30T04:00:35Z","title_canon_sha256":"dad383be8424a1253b1871e71cc893999d30e4edf8425b5a687f6d93e0f045bb"},"schema_version":"1.0","source":{"id":"2405.19674","kind":"arxiv","version":1}},"canonical_sha256":"ed63633ef96a36b74e6fdc29306023260719b637dbe018048fa96ceea0fa0c13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed63633ef96a36b74e6fdc29306023260719b637dbe018048fa96ceea0fa0c13","first_computed_at":"2026-07-05T10:42:35.323812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:42:35.323812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gz9biiw1SH1LviAq7FcSDlsDgK/13+c9Mw7oiQ4zc1OslUCgy3cNl0Ge9/G0mOAMMvQYNsvSni7geWch7x8BAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:42:35.324307Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.19674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b73be0af526418dd4b53cb28dc11e7a07e6ed3fe008f1e24f92dea3aaa613ac0","sha256:628b0c1c66e2177b674948c2f06c381f912be71487c40fc1232eae81a13ed9e7"],"state_sha256":"aa353ab6f755c42b83981fb5b074df0c0ccc89fb294954d9faa943dcfc577be5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gikOMNRD1NUw9prNubktKxE8+3AWbm8ecKzy5npX2fqRFuP5LftJ60yM7peLTrWui3JrNIxmynyz9cxmHfvBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T18:03:40.202922Z","bundle_sha256":"04604a7610635177892d6b48efeaa771d91a9eeb721cc4a7929b4aa3441f02ef"}}