{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DOBNLLEKBS3OI4DEYWUMIRJUAF","short_pith_number":"pith:DOBNLLEK","canonical_record":{"source":{"id":"1706.02959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-09T14:07:21Z","cross_cats_sorted":[],"title_canon_sha256":"74739d1b7b9f2244094b2757dbca8e6365d944f451b5c6e10ef2987fc4dcae88","abstract_canon_sha256":"55433982e796b0be2b2a7bb94124dd77d90cab30e2820aec8f573048c2fb6558"},"schema_version":"1.0"},"canonical_sha256":"1b82d5ac8a0cb6e47064c5a8c44534016c0040786a9bba64b116a9a40b799884","source":{"kind":"arxiv","id":"1706.02959","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02959","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02959v1","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02959","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"pith_short_12","alias_value":"DOBNLLEKBS3O","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DOBNLLEKBS3OI4DE","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DOBNLLEK","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DOBNLLEKBS3OI4DEYWUMIRJUAF","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-09T14:07:21Z","cross_cats_sorted":[],"title_canon_sha256":"74739d1b7b9f2244094b2757dbca8e6365d944f451b5c6e10ef2987fc4dcae88","abstract_canon_sha256":"55433982e796b0be2b2a7bb94124dd77d90cab30e2820aec8f573048c2fb6558"},"schema_version":"1.0"},"canonical_sha256":"1b82d5ac8a0cb6e47064c5a8c44534016c0040786a9bba64b116a9a40b799884","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:40.448795Z","signature_b64":"P8d6hWTt4R+OObLFDKTiKbubDThK9U0WQwMx+pNBq/bTAMkSFC9YNiZvDHnhTCeFrmJ55B9hIPBKQr9BD++KBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b82d5ac8a0cb6e47064c5a8c44534016c0040786a9bba64b116a9a40b799884","last_reissued_at":"2026-05-18T00:42:40.448093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:40.448093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02959","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":"2026-05-18T00:42:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j2Hwf1eIHZXu93HlIvUFjJbkfAUw6l/CZCcCnnc4ZtAdroNxynvyuJeDxds3r4QZTsFxNX9FRoIwqdD+TSquDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:13:40.125690Z"},"content_sha256":"dfcf1726e09f99710e6a93fe65e62579d45ed307715f8bccefad463fc321dd90","schema_version":"1.0","event_id":"sha256:dfcf1726e09f99710e6a93fe65e62579d45ed307715f8bccefad463fc321dd90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DOBNLLEKBS3OI4DEYWUMIRJUAF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some singular equations 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":"2017-06-09T14:07:21Z","abstract_excerpt":"In the past fifteen years mathematical models for microelectromechanical systems (MEMS) have been the subject of several studies, in particular due to the interesting qualitative properties they feature. Still most research is devoted to an illustrative, but simplified model which is deduced from a more complex model when the aspect ratio of the device vanishes, the so-called vanishing (or small) aspect ratio model. The analysis of the aforementioned complex model involving a moving boundary has started only recently and an outlook of the results obtained so far in this direction is provided i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02959","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":"2026-05-18T00:42:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ij7oB8CkMtk45fvP+SZ3lm9nI9zY2N619iWYBq/FNL+kGzu6t0BIOaLwoRsAEgqI56bzOuT2Z/4LLcmqrniOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:13:40.126042Z"},"content_sha256":"f5f7e58e35f5d3abaaefe88c241942ff43e8d7e7ff7d35b42bb653308eeef6f5","schema_version":"1.0","event_id":"sha256:f5f7e58e35f5d3abaaefe88c241942ff43e8d7e7ff7d35b42bb653308eeef6f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOBNLLEKBS3OI4DEYWUMIRJUAF/bundle.json","state_url":"https://pith.science/pith/DOBNLLEKBS3OI4DEYWUMIRJUAF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOBNLLEKBS3OI4DEYWUMIRJUAF/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":"2026-06-01T21:13:40Z","links":{"resolver":"https://pith.science/pith/DOBNLLEKBS3OI4DEYWUMIRJUAF","bundle":"https://pith.science/pith/DOBNLLEKBS3OI4DEYWUMIRJUAF/bundle.json","state":"https://pith.science/pith/DOBNLLEKBS3OI4DEYWUMIRJUAF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOBNLLEKBS3OI4DEYWUMIRJUAF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DOBNLLEKBS3OI4DEYWUMIRJUAF","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":"55433982e796b0be2b2a7bb94124dd77d90cab30e2820aec8f573048c2fb6558","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-09T14:07:21Z","title_canon_sha256":"74739d1b7b9f2244094b2757dbca8e6365d944f451b5c6e10ef2987fc4dcae88"},"schema_version":"1.0","source":{"id":"1706.02959","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02959","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02959v1","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02959","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"pith_short_12","alias_value":"DOBNLLEKBS3O","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DOBNLLEKBS3OI4DE","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DOBNLLEK","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:f5f7e58e35f5d3abaaefe88c241942ff43e8d7e7ff7d35b42bb653308eeef6f5","target":"graph","created_at":"2026-05-18T00:42:40Z","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 the past fifteen years mathematical models for microelectromechanical systems (MEMS) have been the subject of several studies, in particular due to the interesting qualitative properties they feature. Still most research is devoted to an illustrative, but simplified model which is deduced from a more complex model when the aspect ratio of the device vanishes, the so-called vanishing (or small) aspect ratio model. The analysis of the aforementioned complex model involving a moving boundary has started only recently and an outlook of the results obtained so far in this direction is provided i","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":"2017-06-09T14:07:21Z","title":"Some singular equations modeling MEMS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02959","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:dfcf1726e09f99710e6a93fe65e62579d45ed307715f8bccefad463fc321dd90","target":"record","created_at":"2026-05-18T00:42:40Z","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":"55433982e796b0be2b2a7bb94124dd77d90cab30e2820aec8f573048c2fb6558","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-09T14:07:21Z","title_canon_sha256":"74739d1b7b9f2244094b2757dbca8e6365d944f451b5c6e10ef2987fc4dcae88"},"schema_version":"1.0","source":{"id":"1706.02959","kind":"arxiv","version":1}},"canonical_sha256":"1b82d5ac8a0cb6e47064c5a8c44534016c0040786a9bba64b116a9a40b799884","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b82d5ac8a0cb6e47064c5a8c44534016c0040786a9bba64b116a9a40b799884","first_computed_at":"2026-05-18T00:42:40.448093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:40.448093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P8d6hWTt4R+OObLFDKTiKbubDThK9U0WQwMx+pNBq/bTAMkSFC9YNiZvDHnhTCeFrmJ55B9hIPBKQr9BD++KBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:40.448795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02959","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfcf1726e09f99710e6a93fe65e62579d45ed307715f8bccefad463fc321dd90","sha256:f5f7e58e35f5d3abaaefe88c241942ff43e8d7e7ff7d35b42bb653308eeef6f5"],"state_sha256":"60040060601e06817c5e3df3f80e9bdc9e1f13b18455eda19fff493a1959fe56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gkM3KbbYk4Quto0P1CAiET+/gUaMYPYsdYoaD8CdUCARqaoO2uVSBMLoYHF2i227mCdmWkE+mKcrRUS8XysuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:13:40.128034Z","bundle_sha256":"483c55f3b8a70381a1a50d1650fbe9e3e40806126381dad66d33f620b61b0307"}}