{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JZNXE52S7KY2E55LVVLYSF5NSX","short_pith_number":"pith:JZNXE52S","canonical_record":{"source":{"id":"1102.4174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-21T09:58:02Z","cross_cats_sorted":[],"title_canon_sha256":"053e490e0aeba6cea85fc1bf2e6d95c6e686f45ab03511732c29a511a6ead17c","abstract_canon_sha256":"5554e72d84778630a4bfa5953cfd5e68cbdb5096b3f4149ac17598cb0790e2c7"},"schema_version":"1.0"},"canonical_sha256":"4e5b727752fab1a277abad578917ad95cddbc656e1d8537026694e3d4600b00c","source":{"kind":"arxiv","id":"1102.4174","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4174","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4174v1","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4174","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"JZNXE52S7KY2","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JZNXE52S7KY2E55L","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JZNXE52S","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JZNXE52S7KY2E55LVVLYSF5NSX","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-21T09:58:02Z","cross_cats_sorted":[],"title_canon_sha256":"053e490e0aeba6cea85fc1bf2e6d95c6e686f45ab03511732c29a511a6ead17c","abstract_canon_sha256":"5554e72d84778630a4bfa5953cfd5e68cbdb5096b3f4149ac17598cb0790e2c7"},"schema_version":"1.0"},"canonical_sha256":"4e5b727752fab1a277abad578917ad95cddbc656e1d8537026694e3d4600b00c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:42.015453Z","signature_b64":"zfVSxN+OPBoXBeoAU8HnubksciB8aIdeDU9kIcVJuqgY03ggmuUnO3FI7BnJzWkrAEGyTP53zJH/i7f31wSVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e5b727752fab1a277abad578917ad95cddbc656e1d8537026694e3d4600b00c","last_reissued_at":"2026-05-18T01:21:42.014945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:42.014945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4174","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":"2026-05-18T01:21:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9O4a3PjIDTThFAnRXgqSj5aUoLV/QXdrgoXcrTLo6MxB2LS206KE9K3y9veDJik+GCWpECECij6XxhJ0pjzrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T19:14:50.614294Z"},"content_sha256":"131ae6fd5f1b5c606a41409911d513441692058c3936f5338bf0cc3e10edbe69","schema_version":"1.0","event_id":"sha256:131ae6fd5f1b5c606a41409911d513441692058c3936f5338bf0cc3e10edbe69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JZNXE52S7KY2E55LVVLYSF5NSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cauchy problem for semilinear wave equation with time-dependent metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yavar Kian","submitted_at":"2011-02-21T09:58:02Z","abstract_excerpt":"We establish the existence of weak solutions $u$ of the semilinear wave equation $\\partial_t^2 u-\\textrm{div}_x(a(t,x)\\nabla_xu)=f_k(u)$ where $a(t,x)$ is equal to $1$ outside a compact set with respect to $x$ and a non-linear term $f_k$ which satisfies $\\vert f_k(u)\\vert\\leq C\\vert u\\vert^k$. For some non-trapping time-periodic perturbations $a(t,x)$, we obtain the long time existence of solution for small initial data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4174","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":"2026-05-18T01:21:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IlqnvLOWphBQzqh8JdQUOhb6q3nVRBMZwYiL2XtFHCWuZTRvnY/9wVO2azUsVzwQv/o7eDpTP7Lw9e1yYCBwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T19:14:50.614655Z"},"content_sha256":"e3a42cbcea6e1b7ac9e1d45bac314f4177b58c706aaf0be2f6d2c82b4e2d2b58","schema_version":"1.0","event_id":"sha256:e3a42cbcea6e1b7ac9e1d45bac314f4177b58c706aaf0be2f6d2c82b4e2d2b58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZNXE52S7KY2E55LVVLYSF5NSX/bundle.json","state_url":"https://pith.science/pith/JZNXE52S7KY2E55LVVLYSF5NSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZNXE52S7KY2E55LVVLYSF5NSX/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":"2026-06-22T19:14:50Z","links":{"resolver":"https://pith.science/pith/JZNXE52S7KY2E55LVVLYSF5NSX","bundle":"https://pith.science/pith/JZNXE52S7KY2E55LVVLYSF5NSX/bundle.json","state":"https://pith.science/pith/JZNXE52S7KY2E55LVVLYSF5NSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZNXE52S7KY2E55LVVLYSF5NSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JZNXE52S7KY2E55LVVLYSF5NSX","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":"5554e72d84778630a4bfa5953cfd5e68cbdb5096b3f4149ac17598cb0790e2c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-21T09:58:02Z","title_canon_sha256":"053e490e0aeba6cea85fc1bf2e6d95c6e686f45ab03511732c29a511a6ead17c"},"schema_version":"1.0","source":{"id":"1102.4174","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4174","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4174v1","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4174","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"JZNXE52S7KY2","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JZNXE52S7KY2E55L","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JZNXE52S","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:e3a42cbcea6e1b7ac9e1d45bac314f4177b58c706aaf0be2f6d2c82b4e2d2b58","target":"graph","created_at":"2026-05-18T01:21:42Z","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 establish the existence of weak solutions $u$ of the semilinear wave equation $\\partial_t^2 u-\\textrm{div}_x(a(t,x)\\nabla_xu)=f_k(u)$ where $a(t,x)$ is equal to $1$ outside a compact set with respect to $x$ and a non-linear term $f_k$ which satisfies $\\vert f_k(u)\\vert\\leq C\\vert u\\vert^k$. For some non-trapping time-periodic perturbations $a(t,x)$, we obtain the long time existence of solution for small initial data.","authors_text":"Yavar Kian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-21T09:58:02Z","title":"Cauchy problem for semilinear wave equation with time-dependent metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4174","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":"sha256:131ae6fd5f1b5c606a41409911d513441692058c3936f5338bf0cc3e10edbe69","target":"record","created_at":"2026-05-18T01:21:42Z","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":"5554e72d84778630a4bfa5953cfd5e68cbdb5096b3f4149ac17598cb0790e2c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-21T09:58:02Z","title_canon_sha256":"053e490e0aeba6cea85fc1bf2e6d95c6e686f45ab03511732c29a511a6ead17c"},"schema_version":"1.0","source":{"id":"1102.4174","kind":"arxiv","version":1}},"canonical_sha256":"4e5b727752fab1a277abad578917ad95cddbc656e1d8537026694e3d4600b00c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e5b727752fab1a277abad578917ad95cddbc656e1d8537026694e3d4600b00c","first_computed_at":"2026-05-18T01:21:42.014945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:42.014945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zfVSxN+OPBoXBeoAU8HnubksciB8aIdeDU9kIcVJuqgY03ggmuUnO3FI7BnJzWkrAEGyTP53zJH/i7f31wSVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:42.015453Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4174","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:131ae6fd5f1b5c606a41409911d513441692058c3936f5338bf0cc3e10edbe69","sha256:e3a42cbcea6e1b7ac9e1d45bac314f4177b58c706aaf0be2f6d2c82b4e2d2b58"],"state_sha256":"67ef5057bb7e7a72b8767cf47e458e1cba52e701aa6a22057dd984727244c333"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qE0tdLODlITfr85unWpYGyk6eDqJbWmBo+Dl8qQM0i9ToRsXNG96+Vu9dilgCMDsSGXmRliLLSJui5dtEem4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T19:14:50.616616Z","bundle_sha256":"e0ed6266e0448381e20417dd62d17dbe140786050e6b2bdd6e06755e07f0f7ae"}}