{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RTI74JUUBWILH6XQZUHR6QTKWG","short_pith_number":"pith:RTI74JUU","canonical_record":{"source":{"id":"1807.05908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-16T15:03:49Z","cross_cats_sorted":[],"title_canon_sha256":"76e6477738a6a7ad9e6ba0b4c93cf242a1fd6cf6653f1a5ec94dfcf39ab5db8e","abstract_canon_sha256":"ed0d0aca16078444904585f80b2c163fe9a0724ec0456ce1d74a0c1382a74fe5"},"schema_version":"1.0"},"canonical_sha256":"8cd1fe26940d90b3faf0cd0f1f426ab1883bbd75b036048eb6b3d023816a9e42","source":{"kind":"arxiv","id":"1807.05908","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05908","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05908v1","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05908","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"pith_short_12","alias_value":"RTI74JUUBWIL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RTI74JUUBWILH6XQ","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RTI74JUU","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RTI74JUUBWILH6XQZUHR6QTKWG","target":"record","payload":{"canonical_record":{"source":{"id":"1807.05908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-16T15:03:49Z","cross_cats_sorted":[],"title_canon_sha256":"76e6477738a6a7ad9e6ba0b4c93cf242a1fd6cf6653f1a5ec94dfcf39ab5db8e","abstract_canon_sha256":"ed0d0aca16078444904585f80b2c163fe9a0724ec0456ce1d74a0c1382a74fe5"},"schema_version":"1.0"},"canonical_sha256":"8cd1fe26940d90b3faf0cd0f1f426ab1883bbd75b036048eb6b3d023816a9e42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:42.256010Z","signature_b64":"T7FCQXwInhCV+7m6jeQEeZ5YFJLK0Tw5bGbcYmXfvVbcO8e5z/FDEanr3Qh34rPE2i0FboCEvFzStXn6aYSMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cd1fe26940d90b3faf0cd0f1f426ab1883bbd75b036048eb6b3d023816a9e42","last_reissued_at":"2026-05-18T00:10:42.255281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:42.255281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.05908","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":"2026-05-18T00:10:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qe7m6fUHy2m53Fis5Dvt2PoXaS7BG6NZ9SwlgMyLUVcsp9ZGrEM2ZyYSyryX1FvqnXGTKJn+1eZ8A9r0VQX1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:18:26.137491Z"},"content_sha256":"ae91c95f318afe136e8583bebd289cd4a9fc1cff18348e9817e541d9b8c42a0e","schema_version":"1.0","event_id":"sha256:ae91c95f318afe136e8583bebd289cd4a9fc1cff18348e9817e541d9b8c42a0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RTI74JUUBWILH6XQZUHR6QTKWG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global existence for semilinear damped wave equations in relation with the Strauss conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chengbo Wang, Mengyun Liu","submitted_at":"2018-07-16T15:03:49Z","abstract_excerpt":"We study the global existence of solutions to semilinear wave equations with power-type nonlinearity and general lower order terms on $n$ dimensional nontrapping asymptotically Euclidean manifolds, when $n=3, 4$. In addition, we prove almost global existence with sharp lower bound of the lifespan for the four dimensional critical problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05908","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":"2026-05-18T00:10:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nxrmc54to1vx0Gp+CE+2PbqWn9utfk/MI857bHx5nusP5my6BjOsoIUt3d2sJ3F22oxWdcDT28l94BX5MLZaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:18:26.137832Z"},"content_sha256":"c88d7713710524336acaa7de9bcf8b2ec942fd3c83708fd43d580cd5677be2b7","schema_version":"1.0","event_id":"sha256:c88d7713710524336acaa7de9bcf8b2ec942fd3c83708fd43d580cd5677be2b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RTI74JUUBWILH6XQZUHR6QTKWG/bundle.json","state_url":"https://pith.science/pith/RTI74JUUBWILH6XQZUHR6QTKWG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RTI74JUUBWILH6XQZUHR6QTKWG/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":"2026-06-27T16:18:26Z","links":{"resolver":"https://pith.science/pith/RTI74JUUBWILH6XQZUHR6QTKWG","bundle":"https://pith.science/pith/RTI74JUUBWILH6XQZUHR6QTKWG/bundle.json","state":"https://pith.science/pith/RTI74JUUBWILH6XQZUHR6QTKWG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RTI74JUUBWILH6XQZUHR6QTKWG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RTI74JUUBWILH6XQZUHR6QTKWG","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":"ed0d0aca16078444904585f80b2c163fe9a0724ec0456ce1d74a0c1382a74fe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-16T15:03:49Z","title_canon_sha256":"76e6477738a6a7ad9e6ba0b4c93cf242a1fd6cf6653f1a5ec94dfcf39ab5db8e"},"schema_version":"1.0","source":{"id":"1807.05908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05908","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05908v1","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05908","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"pith_short_12","alias_value":"RTI74JUUBWIL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RTI74JUUBWILH6XQ","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RTI74JUU","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:c88d7713710524336acaa7de9bcf8b2ec942fd3c83708fd43d580cd5677be2b7","target":"graph","created_at":"2026-05-18T00:10:42Z","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 study the global existence of solutions to semilinear wave equations with power-type nonlinearity and general lower order terms on $n$ dimensional nontrapping asymptotically Euclidean manifolds, when $n=3, 4$. In addition, we prove almost global existence with sharp lower bound of the lifespan for the four dimensional critical problem.","authors_text":"Chengbo Wang, Mengyun Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-16T15:03:49Z","title":"Global existence for semilinear damped wave equations in relation with the Strauss conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05908","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:ae91c95f318afe136e8583bebd289cd4a9fc1cff18348e9817e541d9b8c42a0e","target":"record","created_at":"2026-05-18T00:10:42Z","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":"ed0d0aca16078444904585f80b2c163fe9a0724ec0456ce1d74a0c1382a74fe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-16T15:03:49Z","title_canon_sha256":"76e6477738a6a7ad9e6ba0b4c93cf242a1fd6cf6653f1a5ec94dfcf39ab5db8e"},"schema_version":"1.0","source":{"id":"1807.05908","kind":"arxiv","version":1}},"canonical_sha256":"8cd1fe26940d90b3faf0cd0f1f426ab1883bbd75b036048eb6b3d023816a9e42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cd1fe26940d90b3faf0cd0f1f426ab1883bbd75b036048eb6b3d023816a9e42","first_computed_at":"2026-05-18T00:10:42.255281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:42.255281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T7FCQXwInhCV+7m6jeQEeZ5YFJLK0Tw5bGbcYmXfvVbcO8e5z/FDEanr3Qh34rPE2i0FboCEvFzStXn6aYSMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:42.256010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.05908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae91c95f318afe136e8583bebd289cd4a9fc1cff18348e9817e541d9b8c42a0e","sha256:c88d7713710524336acaa7de9bcf8b2ec942fd3c83708fd43d580cd5677be2b7"],"state_sha256":"2cb59a6591549e2efa126de018293b18084ddb134ed84614508e0286a3cc7235"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nh4OBsFvTeOZZuFgh5s2sCi+KliFipB4KXC0RFvwvEJjJ9n8Utn69z1Zd4Zr63z6tjgqnUcchifGUwqwbSBLCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:18:26.140041Z","bundle_sha256":"0302fba4603c8ea2eef5aeafb79b8c5a8a000c4c53d512bf97ec830b4766494a"}}