{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7DA6RRGWJMH4U4OA64GHYPN3YD","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":"a07547e2b641996f9d51cdb2c5a6541f7ec2491525fd856a9d87699164b160e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-08T01:07:51Z","title_canon_sha256":"758cfd5196cac0856ffa6c0344117b43372d0b4d269f21d89a686f98525f1a5a"},"schema_version":"1.0","source":{"id":"1807.03634","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03634","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03634v2","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03634","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"7DA6RRGWJMH4","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7DA6RRGWJMH4U4OA","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7DA6RRGW","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:498baf1063e17bcf764e8a167a44a03a678ba39efcb10c00555168d70434d0a9","target":"graph","created_at":"2026-05-17T23:46:30Z","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":"Let $\\mathcal{O}\\subset\\mathbb{R}^d$ a bounded domain of class $C^{1,1}$. In $L_2(\\mathcal{O};\\mathbb{C}^n)$, we consider a self-adjoint matrix strongly elliptic second order differential operator $B_{D,\\varepsilon}$, $0<\\varepsilon \\leqslant 1$, with the Dirichlet boundary condition. The coefficients of the operator $B_{D,\\varepsilon}$ are periodic and depend on $\\mathbf{x}/\\varepsilon$. We are interested in the behavior of the operators $\\cos(tB_{D,\\varepsilon}^{1/2})$ and $B_{D,\\varepsilon} ^{-1/2}\\sin (t B_{D,\\varepsilon} ^{1/2})$, $t\\in\\mathbb{R}$, in the small period limit. For these ope","authors_text":"Yulia Meshkova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-08T01:07:51Z","title":"On homogenization of the first initial-boundary value problem for periodic hyperbolic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03634","kind":"arxiv","version":2},"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:f7fded84095847a43f52a6411f07a28e128c7f0faf3996d290720c876c95b71c","target":"record","created_at":"2026-05-17T23:46:30Z","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":"a07547e2b641996f9d51cdb2c5a6541f7ec2491525fd856a9d87699164b160e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-08T01:07:51Z","title_canon_sha256":"758cfd5196cac0856ffa6c0344117b43372d0b4d269f21d89a686f98525f1a5a"},"schema_version":"1.0","source":{"id":"1807.03634","kind":"arxiv","version":2}},"canonical_sha256":"f8c1e8c4d64b0fca71c0f70c7c3dbbc0dee86f3756863fb151230b50c6cf917d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8c1e8c4d64b0fca71c0f70c7c3dbbc0dee86f3756863fb151230b50c6cf917d","first_computed_at":"2026-05-17T23:46:30.224251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:30.224251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kjsBJc6DboGKN3bSRmEYLpsThl+OEX52FbvWgD128sirCKJKi8aqfGSMt7TGNeRilfReZkRdPU8zqgv/d/onDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:30.224984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03634","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7fded84095847a43f52a6411f07a28e128c7f0faf3996d290720c876c95b71c","sha256:498baf1063e17bcf764e8a167a44a03a678ba39efcb10c00555168d70434d0a9"],"state_sha256":"4ff66b370d15abfacf873d957f5423740649cec73494d0169edd3a7458aefa20"}