{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5YCAUMIM2TLUKT5X55OFMWU7E4","short_pith_number":"pith:5YCAUMIM","canonical_record":{"source":{"id":"1512.00823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-02T19:55:33Z","cross_cats_sorted":[],"title_canon_sha256":"98c8c9156e26e345a2231a6401eec5bed9e59e72c17feddf2a2b867e68952ff1","abstract_canon_sha256":"23c35800c0d097ac014f97a27a776c0303a42a9799840985f8fcf8f6c71a797f"},"schema_version":"1.0"},"canonical_sha256":"ee040a310cd4d7454fb7ef5c565a9f270f2214d5b270ae224724892b7f2ff512","source":{"kind":"arxiv","id":"1512.00823","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00823","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00823v1","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00823","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"pith_short_12","alias_value":"5YCAUMIM2TLU","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5YCAUMIM2TLUKT5X","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5YCAUMIM","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5YCAUMIM2TLUKT5X55OFMWU7E4","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-02T19:55:33Z","cross_cats_sorted":[],"title_canon_sha256":"98c8c9156e26e345a2231a6401eec5bed9e59e72c17feddf2a2b867e68952ff1","abstract_canon_sha256":"23c35800c0d097ac014f97a27a776c0303a42a9799840985f8fcf8f6c71a797f"},"schema_version":"1.0"},"canonical_sha256":"ee040a310cd4d7454fb7ef5c565a9f270f2214d5b270ae224724892b7f2ff512","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:57.582178Z","signature_b64":"ImFvCMBC7MUqt30DZNerxBngbqsL2pM5A+HVFb8QimHzkIRd1eR8xGJGo5qMIUEQq/1V/Fr1g48P5VimjEcJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee040a310cd4d7454fb7ef5c565a9f270f2214d5b270ae224724892b7f2ff512","last_reissued_at":"2026-05-18T00:50:57.581583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:57.581583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00823","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":"2026-05-18T00:50:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52Cd/izO2e+osd9m0SqIsNstslsd0ThOD5fpJiSWPY8nKt6vlH9gTes0dL54bvhdP9Vw+gXHz/IoU33H11+/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T10:36:33.659726Z"},"content_sha256":"b8c7123791cbccee04639ed036f489fbb7348fd54bfbc3dc0e0b8f6fce29d7a0","schema_version":"1.0","event_id":"sha256:b8c7123791cbccee04639ed036f489fbb7348fd54bfbc3dc0e0b8f6fce29d7a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5YCAUMIM2TLUKT5X55OFMWU7E4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence Rates in Periodic Homogenization of Systems of Elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinping Zhuge, Zhongwei Shen","submitted_at":"2015-12-02T19:55:33Z","abstract_excerpt":"This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00823","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":"2026-05-18T00:50:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06pHbmyRsUMppCtiHFpoLgQS9rlOq6II/u38E80lknSoV+40T7Vfj04PChjLB0QHvkwIy/2a4CWno/JHg44HAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T10:36:33.660486Z"},"content_sha256":"5223c554e7456cb874f5edb328b596d1d718bcfe3190eccea6deaa5422872fea","schema_version":"1.0","event_id":"sha256:5223c554e7456cb874f5edb328b596d1d718bcfe3190eccea6deaa5422872fea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5YCAUMIM2TLUKT5X55OFMWU7E4/bundle.json","state_url":"https://pith.science/pith/5YCAUMIM2TLUKT5X55OFMWU7E4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5YCAUMIM2TLUKT5X55OFMWU7E4/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":"2026-05-26T10:36:33Z","links":{"resolver":"https://pith.science/pith/5YCAUMIM2TLUKT5X55OFMWU7E4","bundle":"https://pith.science/pith/5YCAUMIM2TLUKT5X55OFMWU7E4/bundle.json","state":"https://pith.science/pith/5YCAUMIM2TLUKT5X55OFMWU7E4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5YCAUMIM2TLUKT5X55OFMWU7E4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5YCAUMIM2TLUKT5X55OFMWU7E4","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":"23c35800c0d097ac014f97a27a776c0303a42a9799840985f8fcf8f6c71a797f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-02T19:55:33Z","title_canon_sha256":"98c8c9156e26e345a2231a6401eec5bed9e59e72c17feddf2a2b867e68952ff1"},"schema_version":"1.0","source":{"id":"1512.00823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00823","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00823v1","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00823","created_at":"2026-05-18T00:50:57Z"},{"alias_kind":"pith_short_12","alias_value":"5YCAUMIM2TLU","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5YCAUMIM2TLUKT5X","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5YCAUMIM","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:5223c554e7456cb874f5edb328b596d1d718bcfe3190eccea6deaa5422872fea","target":"graph","created_at":"2026-05-18T00:50:57Z","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":"This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable coefficients.","authors_text":"Jinping Zhuge, Zhongwei Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-02T19:55:33Z","title":"Convergence Rates in Periodic Homogenization of Systems of Elasticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00823","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:b8c7123791cbccee04639ed036f489fbb7348fd54bfbc3dc0e0b8f6fce29d7a0","target":"record","created_at":"2026-05-18T00:50:57Z","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":"23c35800c0d097ac014f97a27a776c0303a42a9799840985f8fcf8f6c71a797f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-02T19:55:33Z","title_canon_sha256":"98c8c9156e26e345a2231a6401eec5bed9e59e72c17feddf2a2b867e68952ff1"},"schema_version":"1.0","source":{"id":"1512.00823","kind":"arxiv","version":1}},"canonical_sha256":"ee040a310cd4d7454fb7ef5c565a9f270f2214d5b270ae224724892b7f2ff512","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee040a310cd4d7454fb7ef5c565a9f270f2214d5b270ae224724892b7f2ff512","first_computed_at":"2026-05-18T00:50:57.581583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:57.581583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ImFvCMBC7MUqt30DZNerxBngbqsL2pM5A+HVFb8QimHzkIRd1eR8xGJGo5qMIUEQq/1V/Fr1g48P5VimjEcJCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:57.582178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8c7123791cbccee04639ed036f489fbb7348fd54bfbc3dc0e0b8f6fce29d7a0","sha256:5223c554e7456cb874f5edb328b596d1d718bcfe3190eccea6deaa5422872fea"],"state_sha256":"adb74372218688a24cfb57fe662069fddcef12ecc66f83985ee4b7aece0dd9d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0KMGEINkQhY6X1wyzr+vNjYxdCXgIg9YMdlV9q2Lll1JWHxydLyd9qqB9sKQEWIvij14+dDrWiVNEXLVGhp/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T10:36:33.663264Z","bundle_sha256":"0cd742a6abb59e955726f6e6d629385ecb38bf10f70a1d5f6c608ea668719c52"}}