{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SPRMA3P4SPG7L6TBGE26MTRUOK","short_pith_number":"pith:SPRMA3P4","canonical_record":{"source":{"id":"1310.7967","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T21:00:34Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"cf69504374956df3543e56c3f7d0a72f4e9d3b695addd9e8c032d3b1b4bee309","abstract_canon_sha256":"d87110e2666622e69e8257f14a527f350392845ac210f003f324fd163d6c56fd"},"schema_version":"1.0"},"canonical_sha256":"93e2c06dfc93cdf5fa613135e64e3472a69d635531d541c5e5b654a3b8ed7c52","source":{"kind":"arxiv","id":"1310.7967","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7967","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7967v3","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7967","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"SPRMA3P4SPG7","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SPRMA3P4SPG7L6TB","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SPRMA3P4","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SPRMA3P4SPG7L6TBGE26MTRUOK","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7967","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T21:00:34Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"cf69504374956df3543e56c3f7d0a72f4e9d3b695addd9e8c032d3b1b4bee309","abstract_canon_sha256":"d87110e2666622e69e8257f14a527f350392845ac210f003f324fd163d6c56fd"},"schema_version":"1.0"},"canonical_sha256":"93e2c06dfc93cdf5fa613135e64e3472a69d635531d541c5e5b654a3b8ed7c52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:02.387973Z","signature_b64":"UxDEnTHHc+NaCdIcbrmW6bBLZ77yJ/y0pcWtJGQt10ZwxSZoOlTX96y6n+zFZ48GgyubqqKzJ88KZdNDv5p3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93e2c06dfc93cdf5fa613135e64e3472a69d635531d541c5e5b654a3b8ed7c52","last_reissued_at":"2026-05-18T02:31:02.387425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:02.387425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7967","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qXGW3E0vujHzGNYHrWPLSIqn/w0Ekz1SbWaOv0JXroFQ7wyvCge+ea1y3q5TGwGjLmpbAe5oefQ7zaWV9rfoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:18:03.219118Z"},"content_sha256":"aeac59ddb2bdd14a60968d04ef8ea7e880cd203616cfb02900c17415da0d2d8a","schema_version":"1.0","event_id":"sha256:aeac59ddb2bdd14a60968d04ef8ea7e880cd203616cfb02900c17415da0d2d8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SPRMA3P4SPG7L6TBGE26MTRUOK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hadamard Type Asymptotics for Eigenvalues of the Neumann Problem for Elliptic Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Johan Thim, Vladimir Kozlov","submitted_at":"2013-10-29T21:00:34Z","abstract_excerpt":"This paper considers how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain. The proximity of two domains is measured in terms of the norm of the difference between the two resolvents corresponding to the reference domain and the perturbed domain, and the size of eigenfunctions outside the intersection of the two domains. This construction enables the possibility of comparing both nonsmooth domains and domains with different topology. An abstract framework is presented, where the main result is an asymptotic formula where the remainder is expressed in terms of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7967","kind":"arxiv","version":3},"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":"2026-05-18T02:31:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MkUj6sDY16Rmx4Y3lMEiTI9SFTf6eHog8i6nENgkffCJ/tLQK9sEr9k1m4PQCSV3fxs9Xo4A16DMoaW6t3ayBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:18:03.219593Z"},"content_sha256":"5b91b8cc31d3d0a8523d572de6c24f652bc48f33c618b253c8530065aaafebd0","schema_version":"1.0","event_id":"sha256:5b91b8cc31d3d0a8523d572de6c24f652bc48f33c618b253c8530065aaafebd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SPRMA3P4SPG7L6TBGE26MTRUOK/bundle.json","state_url":"https://pith.science/pith/SPRMA3P4SPG7L6TBGE26MTRUOK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SPRMA3P4SPG7L6TBGE26MTRUOK/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":"2026-06-24T06:18:03Z","links":{"resolver":"https://pith.science/pith/SPRMA3P4SPG7L6TBGE26MTRUOK","bundle":"https://pith.science/pith/SPRMA3P4SPG7L6TBGE26MTRUOK/bundle.json","state":"https://pith.science/pith/SPRMA3P4SPG7L6TBGE26MTRUOK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SPRMA3P4SPG7L6TBGE26MTRUOK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SPRMA3P4SPG7L6TBGE26MTRUOK","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":"d87110e2666622e69e8257f14a527f350392845ac210f003f324fd163d6c56fd","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T21:00:34Z","title_canon_sha256":"cf69504374956df3543e56c3f7d0a72f4e9d3b695addd9e8c032d3b1b4bee309"},"schema_version":"1.0","source":{"id":"1310.7967","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7967","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7967v3","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7967","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"SPRMA3P4SPG7","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SPRMA3P4SPG7L6TB","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SPRMA3P4","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:5b91b8cc31d3d0a8523d572de6c24f652bc48f33c618b253c8530065aaafebd0","target":"graph","created_at":"2026-05-18T02:31:02Z","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":"This paper considers how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain. The proximity of two domains is measured in terms of the norm of the difference between the two resolvents corresponding to the reference domain and the perturbed domain, and the size of eigenfunctions outside the intersection of the two domains. This construction enables the possibility of comparing both nonsmooth domains and domains with different topology. An abstract framework is presented, where the main result is an asymptotic formula where the remainder is expressed in terms of","authors_text":"Johan Thim, Vladimir Kozlov","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T21:00:34Z","title":"Hadamard Type Asymptotics for Eigenvalues of the Neumann Problem for Elliptic Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7967","kind":"arxiv","version":3},"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:aeac59ddb2bdd14a60968d04ef8ea7e880cd203616cfb02900c17415da0d2d8a","target":"record","created_at":"2026-05-18T02:31:02Z","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":"d87110e2666622e69e8257f14a527f350392845ac210f003f324fd163d6c56fd","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T21:00:34Z","title_canon_sha256":"cf69504374956df3543e56c3f7d0a72f4e9d3b695addd9e8c032d3b1b4bee309"},"schema_version":"1.0","source":{"id":"1310.7967","kind":"arxiv","version":3}},"canonical_sha256":"93e2c06dfc93cdf5fa613135e64e3472a69d635531d541c5e5b654a3b8ed7c52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93e2c06dfc93cdf5fa613135e64e3472a69d635531d541c5e5b654a3b8ed7c52","first_computed_at":"2026-05-18T02:31:02.387425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:02.387425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UxDEnTHHc+NaCdIcbrmW6bBLZ77yJ/y0pcWtJGQt10ZwxSZoOlTX96y6n+zFZ48GgyubqqKzJ88KZdNDv5p3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:02.387973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7967","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeac59ddb2bdd14a60968d04ef8ea7e880cd203616cfb02900c17415da0d2d8a","sha256:5b91b8cc31d3d0a8523d572de6c24f652bc48f33c618b253c8530065aaafebd0"],"state_sha256":"0327ddd3142d229adf1a665936988e9117a54159e8418485998b116659042bcb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WyN45eXZGuZNKbWyrU4HAnKK5oPRQkZK1qubWemLGeJ3/bp1WBLY96ydNsqueX1mFr89RKTKx372vlkcCjWVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:18:03.222064Z","bundle_sha256":"2feb5334e38c6c833189da1010a6c728cbc484913d46c7749d517973bec0a0bc"}}