{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4EPNPXQBNDOGNUHUEWOQIUCOHE","short_pith_number":"pith:4EPNPXQB","canonical_record":{"source":{"id":"1705.02531","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-06T21:58:33Z","cross_cats_sorted":[],"title_canon_sha256":"4417c140b3de195d16279e9e8356e22a110078bfcdc7feeb468d43cf34f7b9ce","abstract_canon_sha256":"67de5e99566b3e61f1bc072f4e4b90785fb08babdab4e52970913601f94cd1d0"},"schema_version":"1.0"},"canonical_sha256":"e11ed7de0168dc66d0f4259d04504e3909afa91e078299d4bb86e4371eb2c117","source":{"kind":"arxiv","id":"1705.02531","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02531","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02531v4","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02531","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"4EPNPXQBNDOG","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4EPNPXQBNDOGNUHU","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4EPNPXQB","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4EPNPXQBNDOGNUHUEWOQIUCOHE","target":"record","payload":{"canonical_record":{"source":{"id":"1705.02531","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-06T21:58:33Z","cross_cats_sorted":[],"title_canon_sha256":"4417c140b3de195d16279e9e8356e22a110078bfcdc7feeb468d43cf34f7b9ce","abstract_canon_sha256":"67de5e99566b3e61f1bc072f4e4b90785fb08babdab4e52970913601f94cd1d0"},"schema_version":"1.0"},"canonical_sha256":"e11ed7de0168dc66d0f4259d04504e3909afa91e078299d4bb86e4371eb2c117","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:04.103435Z","signature_b64":"dEwiAleFNxRbsKVQLFBrHOI/8AyajHIP45yo61t4VZhQtjeTxD0a1KL/8uyYXkOqO0wdYoi5Tnop+WZcxqb8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e11ed7de0168dc66d0f4259d04504e3909afa91e078299d4bb86e4371eb2c117","last_reissued_at":"2026-05-18T00:19:04.102893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:04.102893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.02531","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zw8YO6/wpzPuI1TzJVl6LoxA5TOa/MrqcvlVvcVpLO0fCwadPn1Ub4EbgD7rgsp7qQvmVrhZ3gSINcswV06jCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:54:27.051641Z"},"content_sha256":"8cb98f7cbb07b2d9a80b00371812c25d744609f6443e54f311a9fc2ef00d9ed4","schema_version":"1.0","event_id":"sha256:8cb98f7cbb07b2d9a80b00371812c25d744609f6443e54f311a9fc2ef00d9ed4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4EPNPXQBNDOGNUHUEWOQIUCOHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On operator error estimates for homogenization of hyperbolic systems with periodic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yulia Meshkova","submitted_at":"2017-05-06T21:58:33Z","abstract_excerpt":"In $L_2(\\mathbb{R}^d;\\mathbb{C}^n)$, we consider a selfadjoint matrix strongly elliptic second order differential operator $\\mathcal{A}_\\varepsilon$, $\\varepsilon >0$. The coefficients of the operator $\\mathcal{A}_\\varepsilon$ are periodic and depend on $\\mathbf{x}/\\varepsilon$. We study the behavior of the operator $\\mathcal{A}_\\varepsilon ^{-1/2}\\sin (\\tau \\mathcal{A}_\\varepsilon ^{1/2})$, $\\tau\\in\\mathbb{R}$, in the small period limit. The principal term of approximation in the $(H^1\\rightarrow L_2)$-norm for this operator is found. Approximation in the $(H^2\\rightarrow H^1)$-operator norm "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02531","kind":"arxiv","version":4},"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":"2026-05-18T00:19:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BKkKkJYBGyVXcYXnfys+p10nOkn+/xny+ELDutzyQfuqGDiC7gF/hAPSOwg+aKCN+QW1PduvGAMVLpl5lt0wAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:54:27.051983Z"},"content_sha256":"a474066af5798a45a3b850a115cdd9920b209d2e2a37ffc50a1b237782a39c21","schema_version":"1.0","event_id":"sha256:a474066af5798a45a3b850a115cdd9920b209d2e2a37ffc50a1b237782a39c21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/bundle.json","state_url":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/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":"2026-06-03T06:54:27Z","links":{"resolver":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE","bundle":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/bundle.json","state":"https://pith.science/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4EPNPXQBNDOGNUHUEWOQIUCOHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4EPNPXQBNDOGNUHUEWOQIUCOHE","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":"67de5e99566b3e61f1bc072f4e4b90785fb08babdab4e52970913601f94cd1d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-06T21:58:33Z","title_canon_sha256":"4417c140b3de195d16279e9e8356e22a110078bfcdc7feeb468d43cf34f7b9ce"},"schema_version":"1.0","source":{"id":"1705.02531","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02531","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02531v4","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02531","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"4EPNPXQBNDOG","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4EPNPXQBNDOGNUHU","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4EPNPXQB","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:a474066af5798a45a3b850a115cdd9920b209d2e2a37ffc50a1b237782a39c21","target":"graph","created_at":"2026-05-18T00:19:04Z","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 a selfadjoint matrix strongly elliptic second order differential operator $\\mathcal{A}_\\varepsilon$, $\\varepsilon >0$. The coefficients of the operator $\\mathcal{A}_\\varepsilon$ are periodic and depend on $\\mathbf{x}/\\varepsilon$. We study the behavior of the operator $\\mathcal{A}_\\varepsilon ^{-1/2}\\sin (\\tau \\mathcal{A}_\\varepsilon ^{1/2})$, $\\tau\\in\\mathbb{R}$, in the small period limit. The principal term of approximation in the $(H^1\\rightarrow L_2)$-norm for this operator is found. Approximation in the $(H^2\\rightarrow H^1)$-operator norm ","authors_text":"Yulia Meshkova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-06T21:58:33Z","title":"On operator error estimates for homogenization of hyperbolic systems with periodic coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02531","kind":"arxiv","version":4},"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":"sha256:8cb98f7cbb07b2d9a80b00371812c25d744609f6443e54f311a9fc2ef00d9ed4","target":"record","created_at":"2026-05-18T00:19:04Z","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":"67de5e99566b3e61f1bc072f4e4b90785fb08babdab4e52970913601f94cd1d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-06T21:58:33Z","title_canon_sha256":"4417c140b3de195d16279e9e8356e22a110078bfcdc7feeb468d43cf34f7b9ce"},"schema_version":"1.0","source":{"id":"1705.02531","kind":"arxiv","version":4}},"canonical_sha256":"e11ed7de0168dc66d0f4259d04504e3909afa91e078299d4bb86e4371eb2c117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e11ed7de0168dc66d0f4259d04504e3909afa91e078299d4bb86e4371eb2c117","first_computed_at":"2026-05-18T00:19:04.102893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:04.102893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dEwiAleFNxRbsKVQLFBrHOI/8AyajHIP45yo61t4VZhQtjeTxD0a1KL/8uyYXkOqO0wdYoi5Tnop+WZcxqb8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:04.103435Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02531","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cb98f7cbb07b2d9a80b00371812c25d744609f6443e54f311a9fc2ef00d9ed4","sha256:a474066af5798a45a3b850a115cdd9920b209d2e2a37ffc50a1b237782a39c21"],"state_sha256":"bdb07bc1c0a9c3ddb2268829dcca3cdee9758f89e21684785238c47422ab2923"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q41fzsl6MrxyRoLkTkMwL1bXL7oxWFSt7quM1KdJ1BC2n9hnrtDAqdmBd9ffTRpFCLnsg1phh/2idfmTiZ1WCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:54:27.053916Z","bundle_sha256":"9e1b885e8a98010a82f490bdfb85449635a5dcd20cb2815c4b856412f5bca0cb"}}