{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:E53ZACFCUOZFQPQVMSWHCESDNL","short_pith_number":"pith:E53ZACFC","canonical_record":{"source":{"id":"1812.09182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-21T15:13:46Z","cross_cats_sorted":[],"title_canon_sha256":"9ff249cba5557d02019f6b7d807bb3d06ada22b62d5102b849e7584af7c343f1","abstract_canon_sha256":"a349a4476b81b75ed84eee3524190a973d70c853a75a3de0e71fd195a918f6fd"},"schema_version":"1.0"},"canonical_sha256":"27779008a2a3b2583e1564ac7112436aeebb848f0fce734041e04d849196998c","source":{"kind":"arxiv","id":"1812.09182","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09182","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09182v1","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09182","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"E53ZACFCUOZF","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E53ZACFCUOZFQPQV","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E53ZACFC","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:E53ZACFCUOZFQPQVMSWHCESDNL","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-21T15:13:46Z","cross_cats_sorted":[],"title_canon_sha256":"9ff249cba5557d02019f6b7d807bb3d06ada22b62d5102b849e7584af7c343f1","abstract_canon_sha256":"a349a4476b81b75ed84eee3524190a973d70c853a75a3de0e71fd195a918f6fd"},"schema_version":"1.0"},"canonical_sha256":"27779008a2a3b2583e1564ac7112436aeebb848f0fce734041e04d849196998c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:45.135881Z","signature_b64":"ivcc6+/cVYHJfZ/1ZBchjhTs45JoiRNcUtS10k3OuFppCiKZg/+g5ai+O9R58U9DiBJB3PPwnJP/7jWUDJ9hCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27779008a2a3b2583e1564ac7112436aeebb848f0fce734041e04d849196998c","last_reissued_at":"2026-05-17T23:57:45.135202Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:45.135202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09182","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":"2026-05-17T23:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AtLCfP3R4VGhYDVqJi4vLvEZKS882ypAS0B5yX/YjvG9Z2X+afQvqROpB/sVxRuvUe6wgCI8LmkAOU0JDyHIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:24:57.082263Z"},"content_sha256":"16ea7d12063495c5132181e7012c1a992036fd0ee52399ff1e7d711972295975","schema_version":"1.0","event_id":"sha256:16ea7d12063495c5132181e7012c1a992036fd0ee52399ff1e7d711972295975"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:E53ZACFCUOZFQPQVMSWHCESDNL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite time blowup of solutions to semilinear wave equation in an exterior domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kyouhei Wakasa, Motohiro Sobajima","submitted_at":"2018-12-21T15:13:46Z","abstract_excerpt":"We consider the initial-boundary value problem of semilinear wave equation with nonlinearity $|u|^p$ in exterior domain in $\\mathbf{R}^N$ $(N\\geq 3)$. Especially, the lifespan of blowup solutions with small initial data are studied. The result gives upper bounds of lifespan which is essentially the same as the Cauchy problem in $\\mathbf{R}^N$. At least in the case $N=4$, their estimates are sharp in view of the work by Zha--Zhou (2015). The idea of the proof is to use special solutions to linear wave equation with Dirichlet boundary condition which are constructed via an argument based on Waka"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09182","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":"2026-05-17T23:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y3VhGfh3f/0oCsLWjVNmraE2Uhi28NEbgYFJ8ZX2FgaYicQUwBiHjHnC0g9qKvcQWhzTinhaGDi1YYN25q8SAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:24:57.082637Z"},"content_sha256":"7c5666968913f5527c6bfed19a751dae5a6e1f77cc12373fa0c0cb4e022e54ae","schema_version":"1.0","event_id":"sha256:7c5666968913f5527c6bfed19a751dae5a6e1f77cc12373fa0c0cb4e022e54ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E53ZACFCUOZFQPQVMSWHCESDNL/bundle.json","state_url":"https://pith.science/pith/E53ZACFCUOZFQPQVMSWHCESDNL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E53ZACFCUOZFQPQVMSWHCESDNL/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":"2026-06-22T15:24:57Z","links":{"resolver":"https://pith.science/pith/E53ZACFCUOZFQPQVMSWHCESDNL","bundle":"https://pith.science/pith/E53ZACFCUOZFQPQVMSWHCESDNL/bundle.json","state":"https://pith.science/pith/E53ZACFCUOZFQPQVMSWHCESDNL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E53ZACFCUOZFQPQVMSWHCESDNL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:E53ZACFCUOZFQPQVMSWHCESDNL","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":"a349a4476b81b75ed84eee3524190a973d70c853a75a3de0e71fd195a918f6fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-21T15:13:46Z","title_canon_sha256":"9ff249cba5557d02019f6b7d807bb3d06ada22b62d5102b849e7584af7c343f1"},"schema_version":"1.0","source":{"id":"1812.09182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09182","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09182v1","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09182","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"E53ZACFCUOZF","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E53ZACFCUOZFQPQV","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E53ZACFC","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:7c5666968913f5527c6bfed19a751dae5a6e1f77cc12373fa0c0cb4e022e54ae","target":"graph","created_at":"2026-05-17T23:57:45Z","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"},"paper":{"abstract_excerpt":"We consider the initial-boundary value problem of semilinear wave equation with nonlinearity $|u|^p$ in exterior domain in $\\mathbf{R}^N$ $(N\\geq 3)$. Especially, the lifespan of blowup solutions with small initial data are studied. The result gives upper bounds of lifespan which is essentially the same as the Cauchy problem in $\\mathbf{R}^N$. At least in the case $N=4$, their estimates are sharp in view of the work by Zha--Zhou (2015). The idea of the proof is to use special solutions to linear wave equation with Dirichlet boundary condition which are constructed via an argument based on Waka","authors_text":"Kyouhei Wakasa, Motohiro Sobajima","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-21T15:13:46Z","title":"Finite time blowup of solutions to semilinear wave equation in an exterior domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09182","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":"sha256:16ea7d12063495c5132181e7012c1a992036fd0ee52399ff1e7d711972295975","target":"record","created_at":"2026-05-17T23:57:45Z","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":"a349a4476b81b75ed84eee3524190a973d70c853a75a3de0e71fd195a918f6fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-21T15:13:46Z","title_canon_sha256":"9ff249cba5557d02019f6b7d807bb3d06ada22b62d5102b849e7584af7c343f1"},"schema_version":"1.0","source":{"id":"1812.09182","kind":"arxiv","version":1}},"canonical_sha256":"27779008a2a3b2583e1564ac7112436aeebb848f0fce734041e04d849196998c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27779008a2a3b2583e1564ac7112436aeebb848f0fce734041e04d849196998c","first_computed_at":"2026-05-17T23:57:45.135202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:45.135202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ivcc6+/cVYHJfZ/1ZBchjhTs45JoiRNcUtS10k3OuFppCiKZg/+g5ai+O9R58U9DiBJB3PPwnJP/7jWUDJ9hCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:45.135881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16ea7d12063495c5132181e7012c1a992036fd0ee52399ff1e7d711972295975","sha256:7c5666968913f5527c6bfed19a751dae5a6e1f77cc12373fa0c0cb4e022e54ae"],"state_sha256":"646d8aae811e7ea4179b5db551ea72344ecb261a46bb1b25e3be94aefdc2d715"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8qHH3HbmeqK51rOsAnyIK7aM+nUYmEiYf4aPa9+2irEjccOxpj3xIXYPEMNuin89pm7CeGjt9FEta7zXNuMuDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T15:24:57.084686Z","bundle_sha256":"a53274627b3bc847329cff42b4a454ac4196e56abcbb7b504faac0d7ba5f0354"}}