{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YO6LMJAYO6UYKAXQB7CHUYGZAN","short_pith_number":"pith:YO6LMJAY","canonical_record":{"source":{"id":"1409.2812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-09T16:54:57Z","cross_cats_sorted":[],"title_canon_sha256":"e863bd56786e142410cbcdedac894592b885f83beae377881a3e49d8426eab76","abstract_canon_sha256":"3d18aa8f15140116745de5adea9410d6984f5ad1f1c8ec41e31dd524974b505d"},"schema_version":"1.0"},"canonical_sha256":"c3bcb6241877a98502f00fc47a60d90348647eb131e8c1f78ae85986b6862361","source":{"kind":"arxiv","id":"1409.2812","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2812","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2812v1","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2812","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"YO6LMJAYO6UY","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YO6LMJAYO6UYKAXQ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YO6LMJAY","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YO6LMJAYO6UYKAXQB7CHUYGZAN","target":"record","payload":{"canonical_record":{"source":{"id":"1409.2812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-09T16:54:57Z","cross_cats_sorted":[],"title_canon_sha256":"e863bd56786e142410cbcdedac894592b885f83beae377881a3e49d8426eab76","abstract_canon_sha256":"3d18aa8f15140116745de5adea9410d6984f5ad1f1c8ec41e31dd524974b505d"},"schema_version":"1.0"},"canonical_sha256":"c3bcb6241877a98502f00fc47a60d90348647eb131e8c1f78ae85986b6862361","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:09.753106Z","signature_b64":"5QuvwWtPYOH+ze0pUn4rWzS+GSw7C5CUSntLO7RlEUUlKE5jkwfqHNhs6tYiYYOYq1Lp4jQ5/En1C8IftXMaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3bcb6241877a98502f00fc47a60d90348647eb131e8c1f78ae85986b6862361","last_reissued_at":"2026-05-18T02:43:09.752625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:09.752625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.2812","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":"2026-05-18T02:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TI0oJTL25ifW1+6mpUM1re5hsPDxWV6TR7zokeBsaJ/sRchvq8ptRCf1Y+UJFwN28uHFLKTSovDi/0FIauRsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:41:03.803361Z"},"content_sha256":"515e6414afd9055374b36930a594ef2215e3976de04adb5a285cc327f2fa14f9","schema_version":"1.0","event_id":"sha256:515e6414afd9055374b36930a594ef2215e3976de04adb5a285cc327f2fa14f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YO6LMJAYO6UYKAXQB7CHUYGZAN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A variational approach to a stationary free boundary problem modeling MEMS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Walker (IFAM), Philippe Laurencot (IMT)","submitted_at":"2014-09-09T16:54:57Z","abstract_excerpt":"A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid ground plate. The model couples a non-local fourth-order equation for the elastic plate deflection to the harmonic electrostatic potential in the free domain between the elastic and the ground plate. The corresponding energy is non-coercive reflecting an inherent singularity related to a possible touchdown of the elastic plate. Stationary solutions are const"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2812","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":"2026-05-18T02:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0hDgbWmX3jdQsBs4agIxtREMVFqNsFrzhYJgQPAhYqC4dYF0bqABznhnkEzTQpO7N9HNvLVnLb+OIytf8rueCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:41:03.803726Z"},"content_sha256":"c91257dde51150c424127a74c546e8f07a8f1cc8a9d3b782f61bb5d5ea6f5e0a","schema_version":"1.0","event_id":"sha256:c91257dde51150c424127a74c546e8f07a8f1cc8a9d3b782f61bb5d5ea6f5e0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YO6LMJAYO6UYKAXQB7CHUYGZAN/bundle.json","state_url":"https://pith.science/pith/YO6LMJAYO6UYKAXQB7CHUYGZAN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YO6LMJAYO6UYKAXQB7CHUYGZAN/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":"2026-06-02T02:41:03Z","links":{"resolver":"https://pith.science/pith/YO6LMJAYO6UYKAXQB7CHUYGZAN","bundle":"https://pith.science/pith/YO6LMJAYO6UYKAXQB7CHUYGZAN/bundle.json","state":"https://pith.science/pith/YO6LMJAYO6UYKAXQB7CHUYGZAN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YO6LMJAYO6UYKAXQB7CHUYGZAN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YO6LMJAYO6UYKAXQB7CHUYGZAN","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":"3d18aa8f15140116745de5adea9410d6984f5ad1f1c8ec41e31dd524974b505d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-09T16:54:57Z","title_canon_sha256":"e863bd56786e142410cbcdedac894592b885f83beae377881a3e49d8426eab76"},"schema_version":"1.0","source":{"id":"1409.2812","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2812","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2812v1","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2812","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"YO6LMJAYO6UY","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YO6LMJAYO6UYKAXQ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YO6LMJAY","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:c91257dde51150c424127a74c546e8f07a8f1cc8a9d3b782f61bb5d5ea6f5e0a","target":"graph","created_at":"2026-05-18T02:43:09Z","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":"A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid ground plate. The model couples a non-local fourth-order equation for the elastic plate deflection to the harmonic electrostatic potential in the free domain between the elastic and the ground plate. The corresponding energy is non-coercive reflecting an inherent singularity related to a possible touchdown of the elastic plate. Stationary solutions are const","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":"2014-09-09T16:54:57Z","title":"A variational approach to a stationary free boundary problem modeling MEMS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2812","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":"sha256:515e6414afd9055374b36930a594ef2215e3976de04adb5a285cc327f2fa14f9","target":"record","created_at":"2026-05-18T02:43:09Z","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":"3d18aa8f15140116745de5adea9410d6984f5ad1f1c8ec41e31dd524974b505d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-09T16:54:57Z","title_canon_sha256":"e863bd56786e142410cbcdedac894592b885f83beae377881a3e49d8426eab76"},"schema_version":"1.0","source":{"id":"1409.2812","kind":"arxiv","version":1}},"canonical_sha256":"c3bcb6241877a98502f00fc47a60d90348647eb131e8c1f78ae85986b6862361","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3bcb6241877a98502f00fc47a60d90348647eb131e8c1f78ae85986b6862361","first_computed_at":"2026-05-18T02:43:09.752625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:09.752625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5QuvwWtPYOH+ze0pUn4rWzS+GSw7C5CUSntLO7RlEUUlKE5jkwfqHNhs6tYiYYOYq1Lp4jQ5/En1C8IftXMaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:09.753106Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2812","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:515e6414afd9055374b36930a594ef2215e3976de04adb5a285cc327f2fa14f9","sha256:c91257dde51150c424127a74c546e8f07a8f1cc8a9d3b782f61bb5d5ea6f5e0a"],"state_sha256":"47aeb29dcfd38854f12a55fb47401a3a09a05af8930232b39141c7923e705462"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DwrgscNpfEXn8nUoVeaKWBlvjlBVFj+UI5/Q18YkEUpnDCSxc/+T+mRjf/PmfUhj/lyRzPiqxCon5xYz8xp8CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:41:03.805597Z","bundle_sha256":"045949a7c37d55deffee8de94baac0dd42a5359a3746486651a68751e63650b4"}}