{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WXEWUKKWI5377OPT3OQ3VFBZGJ","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":"cdc9b31541f2446eaac6b1df680170891f48b9d0754ccbde70e371e99a306c02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-08T18:26:37Z","title_canon_sha256":"7f4c3184c8a994e60fa675d8ac044ff2ca448b4e21b4f936b3987a58705a52d8"},"schema_version":"1.0","source":{"id":"1304.2296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2296","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2296v1","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2296","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"WXEWUKKWI537","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WXEWUKKWI5377OPT","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WXEWUKKW","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:971994d88e141709b8aae5e210d8d7aa8a7f12c011149cc7871632ef05eafab0","target":"graph","created_at":"2026-05-18T00:44:29Z","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":"The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems (MEMS) and includes a positive voltage parameter $\\lambda$. It is shown that there is a threshold value $\\lambda_*>0$ of the voltage parameter such that no radially symmetric stationary solution exists for $\\lambda>\\lambda_*$, while at least two such solutions exist for $\\lambda\\in (0,\\lambda_*)$. Local and global well-posedness results are obtained for the corresp","authors_text":"Christoph Walker (IFAM), Philippe Laurencot (IMT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-08T18:26:37Z","title":"A fourth-order model for MEMS with clamped boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2296","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":"sha256:545525463df2e54b21a3b2a1f2ccd94530668d42a8950e806943c93fb16f9da4","target":"record","created_at":"2026-05-18T00:44:29Z","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":"cdc9b31541f2446eaac6b1df680170891f48b9d0754ccbde70e371e99a306c02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-08T18:26:37Z","title_canon_sha256":"7f4c3184c8a994e60fa675d8ac044ff2ca448b4e21b4f936b3987a58705a52d8"},"schema_version":"1.0","source":{"id":"1304.2296","kind":"arxiv","version":1}},"canonical_sha256":"b5c96a29564777ffb9f3dba1ba94393264fa69382ec3b22fa14024a0c22ce5ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5c96a29564777ffb9f3dba1ba94393264fa69382ec3b22fa14024a0c22ce5ef","first_computed_at":"2026-05-18T00:44:29.893370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:29.893370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vB69D7N5YWEkJyRVQmIi31nnnbv6SIp9H+g+0H6CEKPwPt8eqWLrxSdoXtRt9bv1L67x2fT447WCna/TYgvRDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:29.893839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:545525463df2e54b21a3b2a1f2ccd94530668d42a8950e806943c93fb16f9da4","sha256:971994d88e141709b8aae5e210d8d7aa8a7f12c011149cc7871632ef05eafab0"],"state_sha256":"9e52c5a2e1d2e0c4848bde78396ab293d071845ded9ef389a790092b47b2c71e"}