{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DXA2ME5CFS5ORUX6BKX3J4OC3U","short_pith_number":"pith:DXA2ME5C","canonical_record":{"source":{"id":"1707.03160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T08:04:44Z","cross_cats_sorted":[],"title_canon_sha256":"f046deedd7e45402d283b5e4c11cf8df543bad7cfab7c2177bba58b5b2c83c5a","abstract_canon_sha256":"8a6d47ca98c81a7a37d650d0dbfc448916e220981e993a40fe3235928bc773b8"},"schema_version":"1.0"},"canonical_sha256":"1dc1a613a22cbae8d2fe0aafb4f1c2dd37e31ee9ef3f7d7ebad7021e4dd876aa","source":{"kind":"arxiv","id":"1707.03160","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03160","created_at":"2026-05-18T00:40:29Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03160v1","created_at":"2026-05-18T00:40:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03160","created_at":"2026-05-18T00:40:29Z"},{"alias_kind":"pith_short_12","alias_value":"DXA2ME5CFS5O","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DXA2ME5CFS5ORUX6","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DXA2ME5C","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DXA2ME5CFS5ORUX6BKX3J4OC3U","target":"record","payload":{"canonical_record":{"source":{"id":"1707.03160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T08:04:44Z","cross_cats_sorted":[],"title_canon_sha256":"f046deedd7e45402d283b5e4c11cf8df543bad7cfab7c2177bba58b5b2c83c5a","abstract_canon_sha256":"8a6d47ca98c81a7a37d650d0dbfc448916e220981e993a40fe3235928bc773b8"},"schema_version":"1.0"},"canonical_sha256":"1dc1a613a22cbae8d2fe0aafb4f1c2dd37e31ee9ef3f7d7ebad7021e4dd876aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:29.742423Z","signature_b64":"iJ5fmTH9QCJhHQ5V9fXXZY+4br+whVMGWx4ljoi21OGCUitc7/3fSUkiM9SEJstO0Uzswn2cWkjzl2tAiIc7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dc1a613a22cbae8d2fe0aafb4f1c2dd37e31ee9ef3f7d7ebad7021e4dd876aa","last_reissued_at":"2026-05-18T00:40:29.741882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:29.741882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.03160","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":"2026-05-18T00:40:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OaidGgEjcqltk39TJU+2x3UJNo4t/Cv5c4cAjLyw1noDu7FpnocQ/p5Lc7t9VYc/GxtBKKlw4s5jaf4ipjBZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:33:21.502627Z"},"content_sha256":"26e92b4c1dab6c59b0247b92c1a57a5564667bb9231682057cf0560e49d17712","schema_version":"1.0","event_id":"sha256:26e92b4c1dab6c59b0247b92c1a57a5564667bb9231682057cf0560e49d17712"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DXA2ME5CFS5ORUX6BKX3J4OC3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of Homogenized Boundary Data in Periodic Homogenization of Elliptic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinping Zhuge, Zhongwei Shen","submitted_at":"2017-07-11T08:04:44Z","abstract_excerpt":"This paper is concerned with periodic homogenization of second-order elliptic systems in divergence form with oscillating Dirichlet data or Neumann data of first order. We prove that the homogenized boundary data belong to $W^{1, p}$ for any $1<p<\\infty$. In particular, this implies that the boundary layer tails are H\\\"older continuous of order $\\alpha$ for any $\\alpha \\in (0,1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03160","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":"2026-05-18T00:40:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MR7Is4otc61noicIJInhSfQ/PBNo4PkfsFV2UG3VYIGafV/KOtliNk11Kk3ocTajOahDifL1KVb6PV5JN5UTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:33:21.503254Z"},"content_sha256":"ad9af08a86f143832bced737fa18ecb18efd456b9086be1d362b3a11b2a047a3","schema_version":"1.0","event_id":"sha256:ad9af08a86f143832bced737fa18ecb18efd456b9086be1d362b3a11b2a047a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/bundle.json","state_url":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/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":"2026-05-26T02:33:21Z","links":{"resolver":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U","bundle":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/bundle.json","state":"https://pith.science/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DXA2ME5CFS5ORUX6BKX3J4OC3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DXA2ME5CFS5ORUX6BKX3J4OC3U","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":"8a6d47ca98c81a7a37d650d0dbfc448916e220981e993a40fe3235928bc773b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T08:04:44Z","title_canon_sha256":"f046deedd7e45402d283b5e4c11cf8df543bad7cfab7c2177bba58b5b2c83c5a"},"schema_version":"1.0","source":{"id":"1707.03160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03160","created_at":"2026-05-18T00:40:29Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03160v1","created_at":"2026-05-18T00:40:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03160","created_at":"2026-05-18T00:40:29Z"},{"alias_kind":"pith_short_12","alias_value":"DXA2ME5CFS5O","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DXA2ME5CFS5ORUX6","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DXA2ME5C","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:ad9af08a86f143832bced737fa18ecb18efd456b9086be1d362b3a11b2a047a3","target":"graph","created_at":"2026-05-18T00:40:29Z","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 periodic homogenization of second-order elliptic systems in divergence form with oscillating Dirichlet data or Neumann data of first order. We prove that the homogenized boundary data belong to $W^{1, p}$ for any $1<p<\\infty$. In particular, this implies that the boundary layer tails are H\\\"older continuous of order $\\alpha$ for any $\\alpha \\in (0,1)$.","authors_text":"Jinping Zhuge, Zhongwei Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T08:04:44Z","title":"Regularity of Homogenized Boundary Data in Periodic Homogenization of Elliptic Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03160","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":"sha256:26e92b4c1dab6c59b0247b92c1a57a5564667bb9231682057cf0560e49d17712","target":"record","created_at":"2026-05-18T00:40:29Z","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":"8a6d47ca98c81a7a37d650d0dbfc448916e220981e993a40fe3235928bc773b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-11T08:04:44Z","title_canon_sha256":"f046deedd7e45402d283b5e4c11cf8df543bad7cfab7c2177bba58b5b2c83c5a"},"schema_version":"1.0","source":{"id":"1707.03160","kind":"arxiv","version":1}},"canonical_sha256":"1dc1a613a22cbae8d2fe0aafb4f1c2dd37e31ee9ef3f7d7ebad7021e4dd876aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dc1a613a22cbae8d2fe0aafb4f1c2dd37e31ee9ef3f7d7ebad7021e4dd876aa","first_computed_at":"2026-05-18T00:40:29.741882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:29.741882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iJ5fmTH9QCJhHQ5V9fXXZY+4br+whVMGWx4ljoi21OGCUitc7/3fSUkiM9SEJstO0Uzswn2cWkjzl2tAiIc7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:29.742423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26e92b4c1dab6c59b0247b92c1a57a5564667bb9231682057cf0560e49d17712","sha256:ad9af08a86f143832bced737fa18ecb18efd456b9086be1d362b3a11b2a047a3"],"state_sha256":"8e3a5192c09388da0c82ca9ac70b9f38ee519fc9ffd57f3779d84afeaedc1b3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VbURAEGsDlx8TOBgKHxIttzbfrLUq1Kswyz0jCsWo6Ov22ExJFhlTbMkY1+xmQRjElRj5gsOIob9AUOrrN1EAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T02:33:21.505812Z","bundle_sha256":"88b79eb8ed4704eb5856498beb57714a82ca1f1104a4080aca08cf0024957e30"}}