{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RXMNZSPHPCC5FL4HY3FNXJHM3I","short_pith_number":"pith:RXMNZSPH","canonical_record":{"source":{"id":"2407.19505","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-28T14:36:50Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"5cd0210318e15186c1542f3aab81aed3236f18c255c5e6ae2cc92b31cab040b6","abstract_canon_sha256":"d3bb03bbe235a4eaaf8c325762609b4f690ce5253de57a75067a3d7f8b8b271b"},"schema_version":"1.0"},"canonical_sha256":"8dd8dcc9e77885d2af87c6cadba4ecda20d15668e589bd3068cb3af047fda27c","source":{"kind":"arxiv","id":"2407.19505","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.19505","created_at":"2026-07-05T11:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"2407.19505v2","created_at":"2026-07-05T11:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.19505","created_at":"2026-07-05T11:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"RXMNZSPHPCC5","created_at":"2026-07-05T11:35:50Z"},{"alias_kind":"pith_short_16","alias_value":"RXMNZSPHPCC5FL4H","created_at":"2026-07-05T11:35:50Z"},{"alias_kind":"pith_short_8","alias_value":"RXMNZSPH","created_at":"2026-07-05T11:35:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RXMNZSPHPCC5FL4HY3FNXJHM3I","target":"record","payload":{"canonical_record":{"source":{"id":"2407.19505","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-28T14:36:50Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"5cd0210318e15186c1542f3aab81aed3236f18c255c5e6ae2cc92b31cab040b6","abstract_canon_sha256":"d3bb03bbe235a4eaaf8c325762609b4f690ce5253de57a75067a3d7f8b8b271b"},"schema_version":"1.0"},"canonical_sha256":"8dd8dcc9e77885d2af87c6cadba4ecda20d15668e589bd3068cb3af047fda27c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:35:50.430092Z","signature_b64":"EqUGNgGY/qmZJaW4aARje1ln4gFe35oE0MOZOzIOI/bdfXpIOgNZHdW8oHAVZY9yS3Lb0tul7k1d8P8oHmd6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dd8dcc9e77885d2af87c6cadba4ecda20d15668e589bd3068cb3af047fda27c","last_reissued_at":"2026-07-05T11:35:50.429610Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:35:50.429610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.19505","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":"2026-07-05T11:35:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SpV2yo1jT75WOVTPYLLdAE7Wr7jWBXBgvhLmFjjIOdZxokyJqAVqH0F9DRBkFD88P3GdHg9AIx8sD7glnUlaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:27:46.343497Z"},"content_sha256":"2666785110e2c43bfe7e6a8d7d61da202e3d746e27f603fb639799d087da41b6","schema_version":"1.0","event_id":"sha256:2666785110e2c43bfe7e6a8d7d61da202e3d746e27f603fb639799d087da41b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RXMNZSPHPCC5FL4HY3FNXJHM3I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On asymptotics of Robin eigenvalues in the Dirichlet limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Roberto Ognibene","submitted_at":"2024-07-28T14:36:50Z","abstract_excerpt":"We investigate the asymptotic behavior of the eigenvalues of the Laplacian with homogeneous Robin boundary conditions, when the (positive) Robin parameter is diverging. In this framework, since the convergence of the Robin eigenvalues to the Dirichlet ones is known, we address the question of quantifying the rate of such convergence. More precisely, in this work we identify the proper geometric quantity representing (asymptotically) the first term in the expansion of the eigenvalue variation: it is a novel notion of torsional rigidity. Then, by performing a suitable asymptotic analysis of both"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.19505","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.19505/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:35:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qe+MUX6xuZNfW9LAadZA6rD5etmgVilYh9Gt4CFrCzSn5bt+UnOu4I54nrCJ66NSWWTrirfXCEsnUy3aGYhrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:27:46.344417Z"},"content_sha256":"fa59c4af307213be588c127e7f37e0bae6c4619296b47cb4465f11b84608d8d7","schema_version":"1.0","event_id":"sha256:fa59c4af307213be588c127e7f37e0bae6c4619296b47cb4465f11b84608d8d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RXMNZSPHPCC5FL4HY3FNXJHM3I/bundle.json","state_url":"https://pith.science/pith/RXMNZSPHPCC5FL4HY3FNXJHM3I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RXMNZSPHPCC5FL4HY3FNXJHM3I/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":"2026-08-08T15:27:46Z","links":{"resolver":"https://pith.science/pith/RXMNZSPHPCC5FL4HY3FNXJHM3I","bundle":"https://pith.science/pith/RXMNZSPHPCC5FL4HY3FNXJHM3I/bundle.json","state":"https://pith.science/pith/RXMNZSPHPCC5FL4HY3FNXJHM3I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RXMNZSPHPCC5FL4HY3FNXJHM3I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RXMNZSPHPCC5FL4HY3FNXJHM3I","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":"d3bb03bbe235a4eaaf8c325762609b4f690ce5253de57a75067a3d7f8b8b271b","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-28T14:36:50Z","title_canon_sha256":"5cd0210318e15186c1542f3aab81aed3236f18c255c5e6ae2cc92b31cab040b6"},"schema_version":"1.0","source":{"id":"2407.19505","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.19505","created_at":"2026-07-05T11:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"2407.19505v2","created_at":"2026-07-05T11:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.19505","created_at":"2026-07-05T11:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"RXMNZSPHPCC5","created_at":"2026-07-05T11:35:50Z"},{"alias_kind":"pith_short_16","alias_value":"RXMNZSPHPCC5FL4H","created_at":"2026-07-05T11:35:50Z"},{"alias_kind":"pith_short_8","alias_value":"RXMNZSPH","created_at":"2026-07-05T11:35:50Z"}],"graph_snapshots":[{"event_id":"sha256:fa59c4af307213be588c127e7f37e0bae6c4619296b47cb4465f11b84608d8d7","target":"graph","created_at":"2026-07-05T11:35:50Z","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/2407.19505/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the asymptotic behavior of the eigenvalues of the Laplacian with homogeneous Robin boundary conditions, when the (positive) Robin parameter is diverging. In this framework, since the convergence of the Robin eigenvalues to the Dirichlet ones is known, we address the question of quantifying the rate of such convergence. More precisely, in this work we identify the proper geometric quantity representing (asymptotically) the first term in the expansion of the eigenvalue variation: it is a novel notion of torsional rigidity. Then, by performing a suitable asymptotic analysis of both","authors_text":"Roberto Ognibene","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-28T14:36:50Z","title":"On asymptotics of Robin eigenvalues in the Dirichlet limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.19505","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":"sha256:2666785110e2c43bfe7e6a8d7d61da202e3d746e27f603fb639799d087da41b6","target":"record","created_at":"2026-07-05T11:35:50Z","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":"d3bb03bbe235a4eaaf8c325762609b4f690ce5253de57a75067a3d7f8b8b271b","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-28T14:36:50Z","title_canon_sha256":"5cd0210318e15186c1542f3aab81aed3236f18c255c5e6ae2cc92b31cab040b6"},"schema_version":"1.0","source":{"id":"2407.19505","kind":"arxiv","version":2}},"canonical_sha256":"8dd8dcc9e77885d2af87c6cadba4ecda20d15668e589bd3068cb3af047fda27c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dd8dcc9e77885d2af87c6cadba4ecda20d15668e589bd3068cb3af047fda27c","first_computed_at":"2026-07-05T11:35:50.429610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:35:50.429610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EqUGNgGY/qmZJaW4aARje1ln4gFe35oE0MOZOzIOI/bdfXpIOgNZHdW8oHAVZY9yS3Lb0tul7k1d8P8oHmd6Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:35:50.430092Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.19505","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2666785110e2c43bfe7e6a8d7d61da202e3d746e27f603fb639799d087da41b6","sha256:fa59c4af307213be588c127e7f37e0bae6c4619296b47cb4465f11b84608d8d7"],"state_sha256":"8034d6c1b060c75b00f5d15bb5e382cee65a445e6072c36fa239a182b01a5063"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USsr0C6prvf7ImnjetOvsVRP4O8PWz7v7GQK6N4KsJymPf2EmA8dKuJ2VwMPvlM7Cx1D3G0GChqeD3GFlFrCBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T15:27:46.349781Z","bundle_sha256":"68660f858e33ff39a4842daa7ea5eb771fcc6ac135e7274c441e7728eebc52f3"}}