{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XBEZ47GDVALWYUDRG7MBJAFPEO","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":"7e279478977c14323b15283e61e48be22b570b866ab15d72171a11c20f2cf9b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-21T09:33:58Z","title_canon_sha256":"5ae73af1f2b265b73c7d854ec0254f6467baf80cf5fdcde9a7f9f7cf96cc8571"},"schema_version":"1.0","source":{"id":"1102.4169","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4169","created_at":"2026-05-18T04:28:18Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4169v1","created_at":"2026-05-18T04:28:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4169","created_at":"2026-05-18T04:28:18Z"},{"alias_kind":"pith_short_12","alias_value":"XBEZ47GDVALW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XBEZ47GDVALWYUDR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XBEZ47GD","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:66943616c38b05a7b72a03478551ee5c5de9aa3f2303234d0455458f5f36629b","target":"graph","created_at":"2026-05-18T04:28:18Z","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 obtain global Strichartz estimates for the solution $u$ of the wave equation $\\partial_t^2 u-\\Div_x(a(t,x)\\nabla_xu)=0$ with time-periodic metric $a(t,x)$ equal to 1 outside a compact set with respect to $x$. We assume $a(t,x)$ is a non-trapping perturbation and moreover, we suppose that there are no resonances $z_j\\in\\mathbb{C}$ with $|z_j|\\geq1$.","authors_text":"Yavar Kian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-21T09:33:58Z","title":"Global Strichartz estimates for the wave equation with a time-periodic non-trapping metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4169","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:a6791a5766a3483a5cc638ca7b52c6ead266f53350787c0ce9a044547b24a73e","target":"record","created_at":"2026-05-18T04:28:18Z","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":"7e279478977c14323b15283e61e48be22b570b866ab15d72171a11c20f2cf9b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-21T09:33:58Z","title_canon_sha256":"5ae73af1f2b265b73c7d854ec0254f6467baf80cf5fdcde9a7f9f7cf96cc8571"},"schema_version":"1.0","source":{"id":"1102.4169","kind":"arxiv","version":1}},"canonical_sha256":"b8499e7cc3a8176c507137d81480af23b745b3fb4bb6464becf2739049b7faaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8499e7cc3a8176c507137d81480af23b745b3fb4bb6464becf2739049b7faaf","first_computed_at":"2026-05-18T04:28:18.848973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:18.848973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NF1uTNEJagdkjyj/tm9Ld3cre3P7QR28cnEX/9RBE7BSlMxjStmipQtc29Qazb5Ko3b7/Ozwxt+DN7xOaL17Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:18.849632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4169","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6791a5766a3483a5cc638ca7b52c6ead266f53350787c0ce9a044547b24a73e","sha256:66943616c38b05a7b72a03478551ee5c5de9aa3f2303234d0455458f5f36629b"],"state_sha256":"8585e697c75de7ad88348765d8bda632970c7124456c93dc3462705dbfd3a901"}