{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EKCZJY2H3PA6DMSW5ZJ3ZUZTW7","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":"d38d9dbaaab6e32ac20278c5793bc5d0638e86734c4d6fe698ebf9870bc82745","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-29T21:59:26Z","title_canon_sha256":"0ab2027ffba8d20996461a5591fb92fb2e34d5b4cead18c92dca413de8038e80"},"schema_version":"1.0","source":{"id":"1807.11114","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11114","created_at":"2026-07-05T00:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11114v4","created_at":"2026-07-05T00:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11114","created_at":"2026-07-05T00:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"EKCZJY2H3PA6","created_at":"2026-07-05T00:03:12Z"},{"alias_kind":"pith_short_16","alias_value":"EKCZJY2H3PA6DMSW","created_at":"2026-07-05T00:03:12Z"},{"alias_kind":"pith_short_8","alias_value":"EKCZJY2H","created_at":"2026-07-05T00:03:12Z"}],"graph_snapshots":[{"event_id":"sha256:784a55a225481be547be96e9e136b2dd1ac2bcde6770fb3fbe0676a94de2fb82","target":"graph","created_at":"2026-07-05T00:03:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1807.11114/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish Korn's interpolation inequalities and the rigidity results of the strain tensor of the middle surface for the parabolic and elliptic shells and show that the best constant in Korn's inequalities scales like $h^{3/2}$ for the parabolic shell and $h$ for the elliptic shell, removing the main assumption that the middle surface of the shell is given by one single principal coordinate in the literature and, in particular, including the closed elliptic shell.","authors_text":"Pengfei Yao","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-29T21:59:26Z","title":"Optimal exponentials of thickness in Korn's inequalities for parabolic and elliptic shells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11114","kind":"arxiv","version":4},"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":"sha256:255d3944734be272a9fe729a8affc751f698f52a5d646b728e8e90283742e9e9","target":"record","created_at":"2026-07-05T00:03:12Z","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":"d38d9dbaaab6e32ac20278c5793bc5d0638e86734c4d6fe698ebf9870bc82745","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2018-07-29T21:59:26Z","title_canon_sha256":"0ab2027ffba8d20996461a5591fb92fb2e34d5b4cead18c92dca413de8038e80"},"schema_version":"1.0","source":{"id":"1807.11114","kind":"arxiv","version":4}},"canonical_sha256":"228594e347dbc1e1b256ee53bcd333b7cbe2f7624e844153e089c8d400ee1552","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"228594e347dbc1e1b256ee53bcd333b7cbe2f7624e844153e089c8d400ee1552","first_computed_at":"2026-07-05T00:03:12.278427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:03:12.278427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"68HXGmTRjE4oIFcf2+Z6uc3IrBgttEpoyvNBIwSgPz8nhBm5kI0U6++BuF0XRxvxdFIK2YL8XfKf+FXnPe2aDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:03:12.278920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11114","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:255d3944734be272a9fe729a8affc751f698f52a5d646b728e8e90283742e9e9","sha256:784a55a225481be547be96e9e136b2dd1ac2bcde6770fb3fbe0676a94de2fb82"],"state_sha256":"bbb6ed244a62ea979386105e0d6550402e00f0cbfb055de1f8567c4b3e4b2b48"}