{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5UMJOHHEG2OVZ4HIOT6WOG62SK","short_pith_number":"pith:5UMJOHHE","canonical_record":{"source":{"id":"1101.2545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-13T12:37:03Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"e1ef57615cb00115b2ae6d1e4646bc147249cd5958c2dbc80413e371883e4fc5","abstract_canon_sha256":"867f6e3d24c3fbed93ce525efb75172b9014ecfddaaac27fd99982ee60bccd96"},"schema_version":"1.0"},"canonical_sha256":"ed18971ce4369d5cf0e874fd671bda92a33463bda34ffd7e07b31a1ce8690469","source":{"kind":"arxiv","id":"1101.2545","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2545","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2545v1","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2545","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"5UMJOHHEG2OV","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5UMJOHHEG2OVZ4HI","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5UMJOHHE","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5UMJOHHEG2OVZ4HIOT6WOG62SK","target":"record","payload":{"canonical_record":{"source":{"id":"1101.2545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-13T12:37:03Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"e1ef57615cb00115b2ae6d1e4646bc147249cd5958c2dbc80413e371883e4fc5","abstract_canon_sha256":"867f6e3d24c3fbed93ce525efb75172b9014ecfddaaac27fd99982ee60bccd96"},"schema_version":"1.0"},"canonical_sha256":"ed18971ce4369d5cf0e874fd671bda92a33463bda34ffd7e07b31a1ce8690469","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:44.278113Z","signature_b64":"lIocV7tnXGVViUbCkB1CNVG/yzsD7/yp91rZrkTqFFP67UmCdkO211AbVPqO/BNwRPluxNrvGhKLL1mGUwtzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed18971ce4369d5cf0e874fd671bda92a33463bda34ffd7e07b31a1ce8690469","last_reissued_at":"2026-05-18T03:02:44.277445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:44.277445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.2545","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":"2026-05-18T03:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YQDhHJc7g+S9R6F9GAUnLbVy+d2B4s3SJaSpZLnezOvj0ImoyqDo+EeptYZz+G3jUX/nlL5lsaCt9DN/TzrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:39:22.484621Z"},"content_sha256":"2fd7ed9e5b1abba86d702a36e2cef4fac5ff61ddbd5a83a240f50dcc9cc11862","schema_version":"1.0","event_id":"sha256:2fd7ed9e5b1abba86d702a36e2cef4fac5ff61ddbd5a83a240f50dcc9cc11862"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5UMJOHHEG2OVZ4HIOT6WOG62SK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral stability estimates for elliptic operators subject to domain transformations with non-uniformly bounded gradients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Gerassimos Barbatis, Pier Domenico Lamberti","submitted_at":"2011-01-13T12:37:03Z","abstract_excerpt":"We consider uniformly elliptic operators with Dirichlet or Neumann homogeneous boundary conditions on a domain $\\Omega $ in ${\\mathbb{R}}^N$. We consider deformations $\\phi (\\Omega)$ of $\\Omega $ obtained by means of a locally Lipschitz homeomorphism $\\phi $ and we estimate the variation of the eigenfunctions and eigenvalues upon variation of $\\phi $. We prove general stability estimates without using uniform upper bounds for the gradients of the maps $\\phi$. As an application, we obtain estimates on the rate of convergence for eigenvalues and eigenfunctions when a domain with an outward cusp "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2545","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":"2026-05-18T03:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lr/6eOC+XbeBmmqCvj6UUmUwAbHjNNXgu6fRvd+HvHueSp9yfHosoE6Hexqe0utNTET5NtlmJiEFNXR5UXjNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:39:22.484978Z"},"content_sha256":"b64d9d4293a30f91030d4c56eb3b3c1edb9fdc74b33d4857f586d5dc517d1e79","schema_version":"1.0","event_id":"sha256:b64d9d4293a30f91030d4c56eb3b3c1edb9fdc74b33d4857f586d5dc517d1e79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5UMJOHHEG2OVZ4HIOT6WOG62SK/bundle.json","state_url":"https://pith.science/pith/5UMJOHHEG2OVZ4HIOT6WOG62SK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5UMJOHHEG2OVZ4HIOT6WOG62SK/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":"2026-06-26T00:39:22Z","links":{"resolver":"https://pith.science/pith/5UMJOHHEG2OVZ4HIOT6WOG62SK","bundle":"https://pith.science/pith/5UMJOHHEG2OVZ4HIOT6WOG62SK/bundle.json","state":"https://pith.science/pith/5UMJOHHEG2OVZ4HIOT6WOG62SK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5UMJOHHEG2OVZ4HIOT6WOG62SK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5UMJOHHEG2OVZ4HIOT6WOG62SK","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":"867f6e3d24c3fbed93ce525efb75172b9014ecfddaaac27fd99982ee60bccd96","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-13T12:37:03Z","title_canon_sha256":"e1ef57615cb00115b2ae6d1e4646bc147249cd5958c2dbc80413e371883e4fc5"},"schema_version":"1.0","source":{"id":"1101.2545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2545","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2545v1","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2545","created_at":"2026-05-18T03:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"5UMJOHHEG2OV","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5UMJOHHEG2OVZ4HI","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5UMJOHHE","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:b64d9d4293a30f91030d4c56eb3b3c1edb9fdc74b33d4857f586d5dc517d1e79","target":"graph","created_at":"2026-05-18T03:02:44Z","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":"We consider uniformly elliptic operators with Dirichlet or Neumann homogeneous boundary conditions on a domain $\\Omega $ in ${\\mathbb{R}}^N$. We consider deformations $\\phi (\\Omega)$ of $\\Omega $ obtained by means of a locally Lipschitz homeomorphism $\\phi $ and we estimate the variation of the eigenfunctions and eigenvalues upon variation of $\\phi $. We prove general stability estimates without using uniform upper bounds for the gradients of the maps $\\phi$. As an application, we obtain estimates on the rate of convergence for eigenvalues and eigenfunctions when a domain with an outward cusp ","authors_text":"Gerassimos Barbatis, Pier Domenico Lamberti","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-13T12:37:03Z","title":"Spectral stability estimates for elliptic operators subject to domain transformations with non-uniformly bounded gradients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2545","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":"sha256:2fd7ed9e5b1abba86d702a36e2cef4fac5ff61ddbd5a83a240f50dcc9cc11862","target":"record","created_at":"2026-05-18T03:02:44Z","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":"867f6e3d24c3fbed93ce525efb75172b9014ecfddaaac27fd99982ee60bccd96","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-13T12:37:03Z","title_canon_sha256":"e1ef57615cb00115b2ae6d1e4646bc147249cd5958c2dbc80413e371883e4fc5"},"schema_version":"1.0","source":{"id":"1101.2545","kind":"arxiv","version":1}},"canonical_sha256":"ed18971ce4369d5cf0e874fd671bda92a33463bda34ffd7e07b31a1ce8690469","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed18971ce4369d5cf0e874fd671bda92a33463bda34ffd7e07b31a1ce8690469","first_computed_at":"2026-05-18T03:02:44.277445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:44.277445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lIocV7tnXGVViUbCkB1CNVG/yzsD7/yp91rZrkTqFFP67UmCdkO211AbVPqO/BNwRPluxNrvGhKLL1mGUwtzBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:44.278113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fd7ed9e5b1abba86d702a36e2cef4fac5ff61ddbd5a83a240f50dcc9cc11862","sha256:b64d9d4293a30f91030d4c56eb3b3c1edb9fdc74b33d4857f586d5dc517d1e79"],"state_sha256":"638dc237401cfb021b78afcd86070cfa1e07ec63bb77519bff9cf613705859aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5z3p/XFDE4+i2FDgQTqk/QX6eHuj+oNJ4UO/qKxn+WuKjCr1PEAuKRp5QiaC+wdJ7c5sBwqM6NSmvYKy2GvAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:39:22.487121Z","bundle_sha256":"84700452c57177069e5a1524a1727b2f0d5fbc1c8b12f2bcf9618b4253ef1095"}}