{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4AS2DSL27YA2ZRX2NQ2SYKFB47","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":"7cbefdc6bc5f5d9ead485e7240200fce8c117cdd327aa7d60ddc2504fcb21c49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-02T07:22:23Z","title_canon_sha256":"88bd2f87e21b5cf9759b39d3cc9c222b8f99031c0327d75a27a3d39c49dea289"},"schema_version":"1.0","source":{"id":"1708.00859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00859","created_at":"2026-05-18T00:38:41Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00859v1","created_at":"2026-05-18T00:38:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00859","created_at":"2026-05-18T00:38:41Z"},{"alias_kind":"pith_short_12","alias_value":"4AS2DSL27YA2","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4AS2DSL27YA2ZRX2","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4AS2DSL2","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:b72cfb7dbf94e5b0ad9a29a9c477af532f0433469690bbdf96ee6d70c6b1cfe6","target":"graph","created_at":"2026-05-18T00:38:41Z","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":"In $L_2(\\mathbb{R}^d;\\mathbb{C}^n)$, we consider selfadjoint strongly elliptic second order differential operators ${\\mathcal A}_\\varepsilon$ with periodic coefficients depending on ${\\mathbf x}/ \\varepsilon$, $\\varepsilon>0$. We study the behavior of the operators $\\cos( {\\mathcal A}^{1/2}_\\varepsilon \\tau)$ and ${\\mathcal A}^{-1/2}_\\varepsilon \\sin( {\\mathcal A}^{1/2}_\\varepsilon \\tau)$, $\\tau \\in \\mathbb{R}$, for small $\\varepsilon$. Approximations for these operators in the $(H^s\\to L_2)$-operator norm with a suitable $s$ are obtained. The results are used to study the behavior of the solu","authors_text":"Mark Dorodnyi, Tatiana Suslina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-02T07:22:23Z","title":"Spectral approach to homogenization of hyperbolic equations with periodic coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00859","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":"sha256:743c61415afc3fedfc3eefced07c70235bd3f37b1578a2930dde8814abb40b7c","target":"record","created_at":"2026-05-18T00:38:41Z","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":"7cbefdc6bc5f5d9ead485e7240200fce8c117cdd327aa7d60ddc2504fcb21c49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-02T07:22:23Z","title_canon_sha256":"88bd2f87e21b5cf9759b39d3cc9c222b8f99031c0327d75a27a3d39c49dea289"},"schema_version":"1.0","source":{"id":"1708.00859","kind":"arxiv","version":1}},"canonical_sha256":"e025a1c97afe01acc6fa6c352c28a1e7cf7caae0da0e52a3c12eef9129d0b6b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e025a1c97afe01acc6fa6c352c28a1e7cf7caae0da0e52a3c12eef9129d0b6b5","first_computed_at":"2026-05-18T00:38:41.307992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:41.307992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zaylhqHsiMjfWcLKLU0lNgOoG5LouWuwKmWDosHyTZOtofz9IOQTTCVjgS9kSUcDOl9onDejG5/eGdHnPIyjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:41.308553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:743c61415afc3fedfc3eefced07c70235bd3f37b1578a2930dde8814abb40b7c","sha256:b72cfb7dbf94e5b0ad9a29a9c477af532f0433469690bbdf96ee6d70c6b1cfe6"],"state_sha256":"8b4d97853b27db82e5e202790b9fd61490ee118a6374a7cc64c2d614a03ba959"}