{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KKPR7TFRPTNEYZUYMI4LKVMQS5","short_pith_number":"pith:KKPR7TFR","canonical_record":{"source":{"id":"1509.02994","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-10T03:11:33Z","cross_cats_sorted":[],"title_canon_sha256":"5b8e8fe9b19c8bec52fc78406a3beec6ad770126b0363d878b0e517a58dec779","abstract_canon_sha256":"9b2b57ae04b8de43cfb0a3c7bb93e4dd007e05262a608c16da9162b99817eaba"},"schema_version":"1.0"},"canonical_sha256":"529f1fccb17cda4c66986238b555909761da8c7fa15d7de4a36b5f288a903edc","source":{"kind":"arxiv","id":"1509.02994","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02994","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02994v2","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02994","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"pith_short_12","alias_value":"KKPR7TFRPTNE","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KKPR7TFRPTNEYZUY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KKPR7TFR","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KKPR7TFRPTNEYZUYMI4LKVMQS5","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02994","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-10T03:11:33Z","cross_cats_sorted":[],"title_canon_sha256":"5b8e8fe9b19c8bec52fc78406a3beec6ad770126b0363d878b0e517a58dec779","abstract_canon_sha256":"9b2b57ae04b8de43cfb0a3c7bb93e4dd007e05262a608c16da9162b99817eaba"},"schema_version":"1.0"},"canonical_sha256":"529f1fccb17cda4c66986238b555909761da8c7fa15d7de4a36b5f288a903edc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:03.468558Z","signature_b64":"AWHltLFTkSICtg1ImxscW+Yu39QFhqR4OBz2womoss7PVZpWUl/YkpSTcnrjGtSlHUH4oHEhow3AyhIKPN1KCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"529f1fccb17cda4c66986238b555909761da8c7fa15d7de4a36b5f288a903edc","last_reissued_at":"2026-05-18T01:20:03.467951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:03.467951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02994","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"neI0blaCqEwAFSyer0avXRs8V6LeuLyfCn/62W/3G/w7wVVolwb5wHXmB7GE/+6RS4lsOqcqUC0CW8v9e61lBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:31:08.854116Z"},"content_sha256":"9c6d5d4285daa9d58ea71e4f9cfded72f6cab60bc88a414a8e6c7ae202477a54","schema_version":"1.0","event_id":"sha256:9c6d5d4285daa9d58ea71e4f9cfded72f6cab60bc88a414a8e6c7ae202477a54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KKPR7TFRPTNEYZUYMI4LKVMQS5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp weighted Korn and Korn-like inequalities and an application to washers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Davit Harutyunyan","submitted_at":"2015-09-10T03:11:33Z","abstract_excerpt":"In this paper we prove asymptotically sharp weighted \"first-and-a-half\" $2D$ Korn and Korn-like inequalities with a singular weight occurring from Cartesian to cylindrical change of variables. We prove some Hardy and the so-called \"harmonic function gradient separation\" inequalities with the same singular weight. Then we apply the obtained $2D$ inequalities to prove similar inequalities for washers with thickness $h$ subject to vanishing Dirichlet boundary conditions on the inner and outer thin faces of the washer. A washer can be regarded in two ways: As the limit case of a conical shell when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02994","kind":"arxiv","version":2},"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":"2026-05-18T01:20:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ju5rEk6q2fsqYPXaWlMYox+18mmhvZJvfkvrcsz50QFQMYs4JjeQHHQuObqEXcfV3v8DbeJxm/KKqNxafcDFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:31:08.854498Z"},"content_sha256":"138f48ead48300798a8729a31c1665257daa5c497f002a4ece0f76095316ba50","schema_version":"1.0","event_id":"sha256:138f48ead48300798a8729a31c1665257daa5c497f002a4ece0f76095316ba50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KKPR7TFRPTNEYZUYMI4LKVMQS5/bundle.json","state_url":"https://pith.science/pith/KKPR7TFRPTNEYZUYMI4LKVMQS5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KKPR7TFRPTNEYZUYMI4LKVMQS5/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":"2026-06-25T08:31:08Z","links":{"resolver":"https://pith.science/pith/KKPR7TFRPTNEYZUYMI4LKVMQS5","bundle":"https://pith.science/pith/KKPR7TFRPTNEYZUYMI4LKVMQS5/bundle.json","state":"https://pith.science/pith/KKPR7TFRPTNEYZUYMI4LKVMQS5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KKPR7TFRPTNEYZUYMI4LKVMQS5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KKPR7TFRPTNEYZUYMI4LKVMQS5","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":"9b2b57ae04b8de43cfb0a3c7bb93e4dd007e05262a608c16da9162b99817eaba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-10T03:11:33Z","title_canon_sha256":"5b8e8fe9b19c8bec52fc78406a3beec6ad770126b0363d878b0e517a58dec779"},"schema_version":"1.0","source":{"id":"1509.02994","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02994","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02994v2","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02994","created_at":"2026-05-18T01:20:03Z"},{"alias_kind":"pith_short_12","alias_value":"KKPR7TFRPTNE","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KKPR7TFRPTNEYZUY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KKPR7TFR","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:138f48ead48300798a8729a31c1665257daa5c497f002a4ece0f76095316ba50","target":"graph","created_at":"2026-05-18T01:20:03Z","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 this paper we prove asymptotically sharp weighted \"first-and-a-half\" $2D$ Korn and Korn-like inequalities with a singular weight occurring from Cartesian to cylindrical change of variables. We prove some Hardy and the so-called \"harmonic function gradient separation\" inequalities with the same singular weight. Then we apply the obtained $2D$ inequalities to prove similar inequalities for washers with thickness $h$ subject to vanishing Dirichlet boundary conditions on the inner and outer thin faces of the washer. A washer can be regarded in two ways: As the limit case of a conical shell when","authors_text":"Davit Harutyunyan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-10T03:11:33Z","title":"Sharp weighted Korn and Korn-like inequalities and an application to washers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02994","kind":"arxiv","version":2},"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":"sha256:9c6d5d4285daa9d58ea71e4f9cfded72f6cab60bc88a414a8e6c7ae202477a54","target":"record","created_at":"2026-05-18T01:20:03Z","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":"9b2b57ae04b8de43cfb0a3c7bb93e4dd007e05262a608c16da9162b99817eaba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-10T03:11:33Z","title_canon_sha256":"5b8e8fe9b19c8bec52fc78406a3beec6ad770126b0363d878b0e517a58dec779"},"schema_version":"1.0","source":{"id":"1509.02994","kind":"arxiv","version":2}},"canonical_sha256":"529f1fccb17cda4c66986238b555909761da8c7fa15d7de4a36b5f288a903edc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"529f1fccb17cda4c66986238b555909761da8c7fa15d7de4a36b5f288a903edc","first_computed_at":"2026-05-18T01:20:03.467951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:03.467951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AWHltLFTkSICtg1ImxscW+Yu39QFhqR4OBz2womoss7PVZpWUl/YkpSTcnrjGtSlHUH4oHEhow3AyhIKPN1KCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:03.468558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02994","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c6d5d4285daa9d58ea71e4f9cfded72f6cab60bc88a414a8e6c7ae202477a54","sha256:138f48ead48300798a8729a31c1665257daa5c497f002a4ece0f76095316ba50"],"state_sha256":"3fcb194d95162e5d38354281a48b590d1e1ec43b44f5f894b1b9c8b6751c73f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MEiuTdltGT5qw/fCFKJRsgIt5qtyOnNrGTp7+i1n/iwID+3Wd2YvCiCjFdbSgp2LZjtDUFQX5dxg4c+6ilxRDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:31:08.856546Z","bundle_sha256":"b6b952f9fd5de36eea7db7073927e05fd4f94451067c7fb9625ba5515fc71278"}}