{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YXCAQGW756N6SAVJVO3NJSVGPE","short_pith_number":"pith:YXCAQGW7","canonical_record":{"source":{"id":"1503.01103","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-03T20:59:38Z","cross_cats_sorted":[],"title_canon_sha256":"ec5ac22b3f4f75f4a1adf1f667dd02143eef7f097e8fb1bf0ea2a108626105ae","abstract_canon_sha256":"8463d6bfa2a38089979e8fd06326a5cb0f96326540bcc66e87410c59b35abea1"},"schema_version":"1.0"},"canonical_sha256":"c5c4081adfef9be902a9abb6d4caa6793a89af30fb197c15303f9c5981fb416f","source":{"kind":"arxiv","id":"1503.01103","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01103","created_at":"2026-05-18T01:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01103v3","created_at":"2026-05-18T01:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01103","created_at":"2026-05-18T01:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"YXCAQGW756N6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YXCAQGW756N6SAVJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YXCAQGW7","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YXCAQGW756N6SAVJVO3NJSVGPE","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01103","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-03T20:59:38Z","cross_cats_sorted":[],"title_canon_sha256":"ec5ac22b3f4f75f4a1adf1f667dd02143eef7f097e8fb1bf0ea2a108626105ae","abstract_canon_sha256":"8463d6bfa2a38089979e8fd06326a5cb0f96326540bcc66e87410c59b35abea1"},"schema_version":"1.0"},"canonical_sha256":"c5c4081adfef9be902a9abb6d4caa6793a89af30fb197c15303f9c5981fb416f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:03.224507Z","signature_b64":"Ojgw/xeFXUKgpXh3VqV3Lp50Kxg4K0aVBlBur/z5vzAEfQ3KPeunqv8sdg73ARpeKbULfJK/IPblltxUSDR3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5c4081adfef9be902a9abb6d4caa6793a89af30fb197c15303f9c5981fb416f","last_reissued_at":"2026-05-18T01:31:03.224073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:03.224073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01103","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aDG/iov/jynckjqXDJn4NYqDWdJl339PcziprLt296w0mg4oBpoEi89h3NC4AR3EbXDRaX0LQKFx/hVT/vYeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:15:35.794089Z"},"content_sha256":"a4b63d06f84d6f6512b907045acde61ddb76b5aa1558b929c081821b4347152c","schema_version":"1.0","event_id":"sha256:a4b63d06f84d6f6512b907045acde61ddb76b5aa1558b929c081821b4347152c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YXCAQGW756N6SAVJVO3NJSVGPE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On uniform estimates for Laplace equation in balls with small holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yong Lu","submitted_at":"2015-03-03T20:59:38Z","abstract_excerpt":"In this paper, we consider the Dirichlet problem of the three-dimensional Laplace equation in the unit ball with a shrinking hole. The problem typically arises from homogenization problems in domains perforated with tiny holes. We give an almost complete description concerning the uniform $W^{1,p}$ estimates: for any $3/2<p<3$ there hold the uniform $W^{1,p}$ estimates; for any $1<p<3/2$ or $3<p<\\infty $, there are counterexamples indicating that the uniform $W^{1,p}$ estimates do not hold. The results can be generalized to higher dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01103","kind":"arxiv","version":3},"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":"2026-05-18T01:31:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L38W2V1N5ByPzssFeM89He5V3j9qhd2xEqGHAlJ5tS+zgh/rxDgM4Y+J7ShKGdybA4wRAGljYH4BUQ2xJ77iCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:15:35.794746Z"},"content_sha256":"10c156f42217385beb2a085f3674047f6efc1f3488574f55a169850a8d6dc7d4","schema_version":"1.0","event_id":"sha256:10c156f42217385beb2a085f3674047f6efc1f3488574f55a169850a8d6dc7d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXCAQGW756N6SAVJVO3NJSVGPE/bundle.json","state_url":"https://pith.science/pith/YXCAQGW756N6SAVJVO3NJSVGPE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXCAQGW756N6SAVJVO3NJSVGPE/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":"2026-06-06T17:15:35Z","links":{"resolver":"https://pith.science/pith/YXCAQGW756N6SAVJVO3NJSVGPE","bundle":"https://pith.science/pith/YXCAQGW756N6SAVJVO3NJSVGPE/bundle.json","state":"https://pith.science/pith/YXCAQGW756N6SAVJVO3NJSVGPE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXCAQGW756N6SAVJVO3NJSVGPE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YXCAQGW756N6SAVJVO3NJSVGPE","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":"8463d6bfa2a38089979e8fd06326a5cb0f96326540bcc66e87410c59b35abea1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-03T20:59:38Z","title_canon_sha256":"ec5ac22b3f4f75f4a1adf1f667dd02143eef7f097e8fb1bf0ea2a108626105ae"},"schema_version":"1.0","source":{"id":"1503.01103","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01103","created_at":"2026-05-18T01:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01103v3","created_at":"2026-05-18T01:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01103","created_at":"2026-05-18T01:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"YXCAQGW756N6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YXCAQGW756N6SAVJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YXCAQGW7","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:10c156f42217385beb2a085f3674047f6efc1f3488574f55a169850a8d6dc7d4","target":"graph","created_at":"2026-05-18T01:31:03Z","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 this paper, we consider the Dirichlet problem of the three-dimensional Laplace equation in the unit ball with a shrinking hole. The problem typically arises from homogenization problems in domains perforated with tiny holes. We give an almost complete description concerning the uniform $W^{1,p}$ estimates: for any $3/2<p<3$ there hold the uniform $W^{1,p}$ estimates; for any $1<p<3/2$ or $3<p<\\infty $, there are counterexamples indicating that the uniform $W^{1,p}$ estimates do not hold. The results can be generalized to higher dimensions.","authors_text":"Yong Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-03T20:59:38Z","title":"On uniform estimates for Laplace equation in balls with small holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01103","kind":"arxiv","version":3},"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:a4b63d06f84d6f6512b907045acde61ddb76b5aa1558b929c081821b4347152c","target":"record","created_at":"2026-05-18T01:31:03Z","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":"8463d6bfa2a38089979e8fd06326a5cb0f96326540bcc66e87410c59b35abea1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-03T20:59:38Z","title_canon_sha256":"ec5ac22b3f4f75f4a1adf1f667dd02143eef7f097e8fb1bf0ea2a108626105ae"},"schema_version":"1.0","source":{"id":"1503.01103","kind":"arxiv","version":3}},"canonical_sha256":"c5c4081adfef9be902a9abb6d4caa6793a89af30fb197c15303f9c5981fb416f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5c4081adfef9be902a9abb6d4caa6793a89af30fb197c15303f9c5981fb416f","first_computed_at":"2026-05-18T01:31:03.224073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:03.224073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ojgw/xeFXUKgpXh3VqV3Lp50Kxg4K0aVBlBur/z5vzAEfQ3KPeunqv8sdg73ARpeKbULfJK/IPblltxUSDR3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:03.224507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01103","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4b63d06f84d6f6512b907045acde61ddb76b5aa1558b929c081821b4347152c","sha256:10c156f42217385beb2a085f3674047f6efc1f3488574f55a169850a8d6dc7d4"],"state_sha256":"59c424f90d49386ef1cd7d1060d609ade15193fb6fc26eaf62d68cd6c835a593"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HAK9tcPIED0OrtYF8nSVWhP330CngsLdVbZaxJgxApwPXIrEVwJ/nnNuGZBUSL7wY7hW77ZZqjOMVv10MI1zDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T17:15:35.798403Z","bundle_sha256":"ca42cd4db5d12fdf5304ae19e84d31194191c71853ed2dc040fd71dfec1806c2"}}