{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CVO7QICYHUXTGN5CIOPNWMQPEW","short_pith_number":"pith:CVO7QICY","canonical_record":{"source":{"id":"1307.7930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T11:58:50Z","cross_cats_sorted":[],"title_canon_sha256":"a80b291551c42202a78e118907e900bf3dad805bb094c15718e2d011b9ed2228","abstract_canon_sha256":"e83aa9ad99577916bb37b163e707a1cf37e21af40d241afc976faf1f32a709a8"},"schema_version":"1.0"},"canonical_sha256":"155df820583d2f3337a2439edb320f259627e3bcb238ae125b3392ceaed16428","source":{"kind":"arxiv","id":"1307.7930","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7930","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7930v1","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7930","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"CVO7QICYHUXT","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CVO7QICYHUXTGN5C","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CVO7QICY","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CVO7QICYHUXTGN5CIOPNWMQPEW","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T11:58:50Z","cross_cats_sorted":[],"title_canon_sha256":"a80b291551c42202a78e118907e900bf3dad805bb094c15718e2d011b9ed2228","abstract_canon_sha256":"e83aa9ad99577916bb37b163e707a1cf37e21af40d241afc976faf1f32a709a8"},"schema_version":"1.0"},"canonical_sha256":"155df820583d2f3337a2439edb320f259627e3bcb238ae125b3392ceaed16428","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:13.014856Z","signature_b64":"HRQ6Ee8QJuZGDJHnTJMpl8jrA1/lJpxc0+CmWY0DqT6sex+5H6K8vcBX+PV1BDgv9EIlpVnUNx09HOcXtM+LDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"155df820583d2f3337a2439edb320f259627e3bcb238ae125b3392ceaed16428","last_reissued_at":"2026-05-18T03:17:13.014080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:13.014080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7930","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":"2026-05-18T03:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SBWEXq/om527XG6GPlQi/J9Xd8muF/YFtloGdvlrAgJj8YgoOkf1nDKkkdK715hfyegvXg3UoUiHOUV/UrdqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:56:29.930076Z"},"content_sha256":"e8b5741c5bb0bea1c813480a0f4d0c222e1e87b69f86f2cfa8dd3749f7affb61","schema_version":"1.0","event_id":"sha256:e8b5741c5bb0bea1c813480a0f4d0c222e1e87b69f86f2cfa8dd3749f7affb61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CVO7QICYHUXTGN5CIOPNWMQPEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the sharp effect of attaching a thin handle on the spectral rate of convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laura Abatangelo, Susanna Terracini, Veronica Felli","submitted_at":"2013-07-30T11:58:50Z","abstract_excerpt":"Consider two domains connected by a thin tube: it can be shown that the resolvent of the Dirichlet Laplacian is continuous with respect to the channel section parameter. This in particular implies the continuity of isolated simple eigenvalues and the corresponding eigenfunctions with respect to domain perturbation. Under an explicit nondegeneracy condition, we improve this information providing a sharp control of the rate of convergence of the eigenvalues and eigenfunctions in the perturbed domain to the relative eigenvalue and eigenfunction in the limit domain. As an application, we prove tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7930","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":"2026-05-18T03:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QEmDmNMaGhLPxsTSNDTxtx6uPiLVtQU0MWyxjSZLv5oIGqz33bA5H+phK4Lwj0lrJaJ+Tqs1KNXGmMJcNU7XCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:56:29.930686Z"},"content_sha256":"740874e903c5d51206795422354a1bb6597da98fc7340a60a7bcec856f7a5b4d","schema_version":"1.0","event_id":"sha256:740874e903c5d51206795422354a1bb6597da98fc7340a60a7bcec856f7a5b4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CVO7QICYHUXTGN5CIOPNWMQPEW/bundle.json","state_url":"https://pith.science/pith/CVO7QICYHUXTGN5CIOPNWMQPEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CVO7QICYHUXTGN5CIOPNWMQPEW/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":"2026-05-27T14:56:29Z","links":{"resolver":"https://pith.science/pith/CVO7QICYHUXTGN5CIOPNWMQPEW","bundle":"https://pith.science/pith/CVO7QICYHUXTGN5CIOPNWMQPEW/bundle.json","state":"https://pith.science/pith/CVO7QICYHUXTGN5CIOPNWMQPEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CVO7QICYHUXTGN5CIOPNWMQPEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CVO7QICYHUXTGN5CIOPNWMQPEW","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":"e83aa9ad99577916bb37b163e707a1cf37e21af40d241afc976faf1f32a709a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T11:58:50Z","title_canon_sha256":"a80b291551c42202a78e118907e900bf3dad805bb094c15718e2d011b9ed2228"},"schema_version":"1.0","source":{"id":"1307.7930","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7930","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7930v1","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7930","created_at":"2026-05-18T03:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"CVO7QICYHUXT","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CVO7QICYHUXTGN5C","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CVO7QICY","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:740874e903c5d51206795422354a1bb6597da98fc7340a60a7bcec856f7a5b4d","target":"graph","created_at":"2026-05-18T03:17:13Z","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":"Consider two domains connected by a thin tube: it can be shown that the resolvent of the Dirichlet Laplacian is continuous with respect to the channel section parameter. This in particular implies the continuity of isolated simple eigenvalues and the corresponding eigenfunctions with respect to domain perturbation. Under an explicit nondegeneracy condition, we improve this information providing a sharp control of the rate of convergence of the eigenvalues and eigenfunctions in the perturbed domain to the relative eigenvalue and eigenfunction in the limit domain. As an application, we prove tha","authors_text":"Laura Abatangelo, Susanna Terracini, Veronica Felli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T11:58:50Z","title":"On the sharp effect of attaching a thin handle on the spectral rate of convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7930","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:e8b5741c5bb0bea1c813480a0f4d0c222e1e87b69f86f2cfa8dd3749f7affb61","target":"record","created_at":"2026-05-18T03:17:13Z","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":"e83aa9ad99577916bb37b163e707a1cf37e21af40d241afc976faf1f32a709a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-30T11:58:50Z","title_canon_sha256":"a80b291551c42202a78e118907e900bf3dad805bb094c15718e2d011b9ed2228"},"schema_version":"1.0","source":{"id":"1307.7930","kind":"arxiv","version":1}},"canonical_sha256":"155df820583d2f3337a2439edb320f259627e3bcb238ae125b3392ceaed16428","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"155df820583d2f3337a2439edb320f259627e3bcb238ae125b3392ceaed16428","first_computed_at":"2026-05-18T03:17:13.014080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:13.014080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HRQ6Ee8QJuZGDJHnTJMpl8jrA1/lJpxc0+CmWY0DqT6sex+5H6K8vcBX+PV1BDgv9EIlpVnUNx09HOcXtM+LDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:13.014856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7930","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8b5741c5bb0bea1c813480a0f4d0c222e1e87b69f86f2cfa8dd3749f7affb61","sha256:740874e903c5d51206795422354a1bb6597da98fc7340a60a7bcec856f7a5b4d"],"state_sha256":"7ed36944ff167317b08ecfcd9bb198dd80bfe14d19d7400dc77c766d0f2f7c04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"96mb0YjB9XCKNAg1A6xV6A+lepPFb+DHsFBlwFwXY1QE8EGy9uDdX2WMEZsAQ6tAeA+cqdY6Q55UrHtZa4IRBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:56:29.932894Z","bundle_sha256":"63a9619b88c2f8ac4278b7804a138ea304ec05fefac37f048fc48a33262ac086"}}