{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6WXV7AOJ4DV2JZTBOUNGPEMYAK","short_pith_number":"pith:6WXV7AOJ","canonical_record":{"source":{"id":"1512.03180","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2015-12-10T09:11:59Z","cross_cats_sorted":[],"title_canon_sha256":"99371a43ad619fadab0e540899a82d990e5937aa54eb95f3376cd4814b3d6dd1","abstract_canon_sha256":"7a39547f2ec2e10719bb29ae39d4c09cfdea459dd8b1a1a7711ce6e30600306f"},"schema_version":"1.0"},"canonical_sha256":"f5af5f81c9e0eba4e661751a67919802b919d70eafb3841d6bc3364d7f9295bf","source":{"kind":"arxiv","id":"1512.03180","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03180","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03180v1","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03180","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"6WXV7AOJ4DV2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6WXV7AOJ4DV2JZTB","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6WXV7AOJ","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6WXV7AOJ4DV2JZTBOUNGPEMYAK","target":"record","payload":{"canonical_record":{"source":{"id":"1512.03180","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2015-12-10T09:11:59Z","cross_cats_sorted":[],"title_canon_sha256":"99371a43ad619fadab0e540899a82d990e5937aa54eb95f3376cd4814b3d6dd1","abstract_canon_sha256":"7a39547f2ec2e10719bb29ae39d4c09cfdea459dd8b1a1a7711ce6e30600306f"},"schema_version":"1.0"},"canonical_sha256":"f5af5f81c9e0eba4e661751a67919802b919d70eafb3841d6bc3364d7f9295bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:37.730726Z","signature_b64":"JtPSPElaLdHGsYoYb9fkDfr5J4lO+Vf0QVOkwCTxH8WHpu0LtYPkdL1pA+qnozcuJXj7mvZw0U7LMabgjSAnCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5af5f81c9e0eba4e661751a67919802b919d70eafb3841d6bc3364d7f9295bf","last_reissued_at":"2026-05-18T01:24:37.730240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:37.730240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.03180","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":"2026-05-18T01:24:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TkXaHVJyE2jrmj78JxMRiXfHJacPeYJ67TX+wT7KpSm/fPef0tQYYhcDryVRRGtybtWlSpFpNf3KvtWNnp1GAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:47:03.456032Z"},"content_sha256":"1783c58aba69ccb148d6b2082276ca2b45d13789a08a1cd00c3842fab8acf24a","schema_version":"1.0","event_id":"sha256:1783c58aba69ccb148d6b2082276ca2b45d13789a08a1cd00c3842fab8acf24a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6WXV7AOJ4DV2JZTBOUNGPEMYAK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On semi-linear elliptic equation arising from Micro-Electromechanical Systems with contacting elastic membrane","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Zhou, Huyuan Chen, Ying Wang","submitted_at":"2015-12-10T09:11:59Z","abstract_excerpt":"This paper is concerned with the nonlinear elliptic problem $-\\Delta u=\\frac{\\lambda }{(a-u)^2}$ on a bounded domain $\\Omega$ of $\\mathbb{R}^N$ with Dirichlet boundary conditions. This problem arises from Micro-Electromechanical Systems devices in the case that the elastic membrane contacts the ground plate on the boundary. We analyze the properties of minimal solutions to this equation when $\\lambda>0$ and the function $a:\\bar\\Omega\\to[0,1]$ satisfying $a(x)\\ge \\kappa{\\rm dist}(x,\\partial\\Omega)^\\gamma$ for some $\\kappa>0$ and $\\gamma\\in(0,1)$. Our results show how the boundary decay of the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03180","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":"2026-05-18T01:24:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XF0AEJdyA15pmMd/4DbPpTf9gMqMMbaqQspjMCxsWXqGtKOymb4Z5s2BkbVC2IDmpiQhT4BbNiUAzE+KA31pDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:47:03.456387Z"},"content_sha256":"4dae2b0c3266fb0f2f85a7033f4640fc68e658bccb58a00509b74294ee888b66","schema_version":"1.0","event_id":"sha256:4dae2b0c3266fb0f2f85a7033f4640fc68e658bccb58a00509b74294ee888b66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6WXV7AOJ4DV2JZTBOUNGPEMYAK/bundle.json","state_url":"https://pith.science/pith/6WXV7AOJ4DV2JZTBOUNGPEMYAK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6WXV7AOJ4DV2JZTBOUNGPEMYAK/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":"2026-06-04T10:47:03Z","links":{"resolver":"https://pith.science/pith/6WXV7AOJ4DV2JZTBOUNGPEMYAK","bundle":"https://pith.science/pith/6WXV7AOJ4DV2JZTBOUNGPEMYAK/bundle.json","state":"https://pith.science/pith/6WXV7AOJ4DV2JZTBOUNGPEMYAK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6WXV7AOJ4DV2JZTBOUNGPEMYAK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6WXV7AOJ4DV2JZTBOUNGPEMYAK","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":"7a39547f2ec2e10719bb29ae39d4c09cfdea459dd8b1a1a7711ce6e30600306f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2015-12-10T09:11:59Z","title_canon_sha256":"99371a43ad619fadab0e540899a82d990e5937aa54eb95f3376cd4814b3d6dd1"},"schema_version":"1.0","source":{"id":"1512.03180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03180","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03180v1","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03180","created_at":"2026-05-18T01:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"6WXV7AOJ4DV2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6WXV7AOJ4DV2JZTB","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6WXV7AOJ","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:4dae2b0c3266fb0f2f85a7033f4640fc68e658bccb58a00509b74294ee888b66","target":"graph","created_at":"2026-05-18T01:24:37Z","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 the nonlinear elliptic problem $-\\Delta u=\\frac{\\lambda }{(a-u)^2}$ on a bounded domain $\\Omega$ of $\\mathbb{R}^N$ with Dirichlet boundary conditions. This problem arises from Micro-Electromechanical Systems devices in the case that the elastic membrane contacts the ground plate on the boundary. We analyze the properties of minimal solutions to this equation when $\\lambda>0$ and the function $a:\\bar\\Omega\\to[0,1]$ satisfying $a(x)\\ge \\kappa{\\rm dist}(x,\\partial\\Omega)^\\gamma$ for some $\\kappa>0$ and $\\gamma\\in(0,1)$. Our results show how the boundary decay of the m","authors_text":"Feng Zhou, Huyuan Chen, Ying Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2015-12-10T09:11:59Z","title":"On semi-linear elliptic equation arising from Micro-Electromechanical Systems with contacting elastic membrane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03180","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":"sha256:1783c58aba69ccb148d6b2082276ca2b45d13789a08a1cd00c3842fab8acf24a","target":"record","created_at":"2026-05-18T01:24:37Z","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":"7a39547f2ec2e10719bb29ae39d4c09cfdea459dd8b1a1a7711ce6e30600306f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2015-12-10T09:11:59Z","title_canon_sha256":"99371a43ad619fadab0e540899a82d990e5937aa54eb95f3376cd4814b3d6dd1"},"schema_version":"1.0","source":{"id":"1512.03180","kind":"arxiv","version":1}},"canonical_sha256":"f5af5f81c9e0eba4e661751a67919802b919d70eafb3841d6bc3364d7f9295bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5af5f81c9e0eba4e661751a67919802b919d70eafb3841d6bc3364d7f9295bf","first_computed_at":"2026-05-18T01:24:37.730240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:37.730240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JtPSPElaLdHGsYoYb9fkDfr5J4lO+Vf0QVOkwCTxH8WHpu0LtYPkdL1pA+qnozcuJXj7mvZw0U7LMabgjSAnCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:37.730726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1783c58aba69ccb148d6b2082276ca2b45d13789a08a1cd00c3842fab8acf24a","sha256:4dae2b0c3266fb0f2f85a7033f4640fc68e658bccb58a00509b74294ee888b66"],"state_sha256":"2980158b3300a82aaad3a04ad76e8d85bd18e2c92a76d79390b9b9318d92fdfb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"193zI2X6y+lZl0VylQySxtm7fnR3wkYaQbM/Q0TjkkecNKGAozhQBRg0oyKq0AcxQ2MK/ptiQ8nhbtrTcpLYBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:47:03.458380Z","bundle_sha256":"de329b631d464ceb95cd3706fc379cb302e4c9963315f66ba1a20e01b89d0d6a"}}