{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RUQ2C6ZAEBUP3UXA6P2CZTWFJV","short_pith_number":"pith:RUQ2C6ZA","canonical_record":{"source":{"id":"1603.01459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-26T14:46:14Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ff596aed43161486896e3f985b91122013383f9b02d5757ec3d1e063b54161ec","abstract_canon_sha256":"48c868f4237392438f5228572115e2240b9e8b7e797c07bcf8327b22a9714c9c"},"schema_version":"1.0"},"canonical_sha256":"8d21a17b202068fdd2e0f3f42ccec54d5807cd5ffea679164eefc39c89f221c4","source":{"kind":"arxiv","id":"1603.01459","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01459","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01459v1","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01459","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"RUQ2C6ZAEBUP","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RUQ2C6ZAEBUP3UXA","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RUQ2C6ZA","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RUQ2C6ZAEBUP3UXA6P2CZTWFJV","target":"record","payload":{"canonical_record":{"source":{"id":"1603.01459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-26T14:46:14Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ff596aed43161486896e3f985b91122013383f9b02d5757ec3d1e063b54161ec","abstract_canon_sha256":"48c868f4237392438f5228572115e2240b9e8b7e797c07bcf8327b22a9714c9c"},"schema_version":"1.0"},"canonical_sha256":"8d21a17b202068fdd2e0f3f42ccec54d5807cd5ffea679164eefc39c89f221c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:52.233882Z","signature_b64":"lMwV4r51Xys8SWXLUWbcE6HI8zmwSnhWv8y7o5+U+TPq5zdQkEalN55KysZ50xo466VdZ2oCkWvNq9Z+VYf7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d21a17b202068fdd2e0f3f42ccec54d5807cd5ffea679164eefc39c89f221c4","last_reissued_at":"2026-05-18T00:29:52.233383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:52.233383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.01459","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":"2026-05-18T00:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6IPgapA4M48EpFJQzfGw7EMhQhVQK4Ig+STab00ImA2aEVkNuuXBhWMiFHVm81tpXt5QLqRNNYaY1kN3H5uOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:39:39.706212Z"},"content_sha256":"7edf498e31dafdb6e9902b32732935aacd8c2d3b2855b8b95455dfcba42452a7","schema_version":"1.0","event_id":"sha256:7edf498e31dafdb6e9902b32732935aacd8c2d3b2855b8b95455dfcba42452a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RUQ2C6ZAEBUP3UXA6P2CZTWFJV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Erwan Faou (IPSO, IRMAR), Marie Chaussade-Beaudouin (IRMAR), Monique Dauge (IRMAR), Zohar Yosibash","submitted_at":"2016-02-26T14:46:14Z","abstract_excerpt":"The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2$\\epsilon$) tends to zero. Using a novel asymptotic expansion we determine the behavior of the eigenvalue $\\lambda$($\\epsilon$) and the eigenvector angular frequency k($\\epsilon$) for shells with Dirichlet boundary conditions along the lateral boundary, and natural boundary conditions on the other parts. First, the scalar Laplace operator for acoustics is addressed, for which k($\\epsilon$) is always zero. In contrast to it, for the Lam{\\'e} system of line"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01459","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":"2026-05-18T00:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qvBUjZgBT8VZ12cgQ8rAsIJ5xPg17wMiJYI4hMuEvkbfw1AtgW+80E69HapeTFUNULTGEpLyS+h9WcWnQk89Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:39:39.706569Z"},"content_sha256":"bef2c4564892a40000df57f835a65d5eeb847ab6346bea32c466ddaa64ee4eaf","schema_version":"1.0","event_id":"sha256:bef2c4564892a40000df57f835a65d5eeb847ab6346bea32c466ddaa64ee4eaf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUQ2C6ZAEBUP3UXA6P2CZTWFJV/bundle.json","state_url":"https://pith.science/pith/RUQ2C6ZAEBUP3UXA6P2CZTWFJV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUQ2C6ZAEBUP3UXA6P2CZTWFJV/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":"2026-06-21T08:39:39Z","links":{"resolver":"https://pith.science/pith/RUQ2C6ZAEBUP3UXA6P2CZTWFJV","bundle":"https://pith.science/pith/RUQ2C6ZAEBUP3UXA6P2CZTWFJV/bundle.json","state":"https://pith.science/pith/RUQ2C6ZAEBUP3UXA6P2CZTWFJV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUQ2C6ZAEBUP3UXA6P2CZTWFJV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RUQ2C6ZAEBUP3UXA6P2CZTWFJV","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":"48c868f4237392438f5228572115e2240b9e8b7e797c07bcf8327b22a9714c9c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-26T14:46:14Z","title_canon_sha256":"ff596aed43161486896e3f985b91122013383f9b02d5757ec3d1e063b54161ec"},"schema_version":"1.0","source":{"id":"1603.01459","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01459","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01459v1","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01459","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"RUQ2C6ZAEBUP","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RUQ2C6ZAEBUP3UXA","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RUQ2C6ZA","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:bef2c4564892a40000df57f835a65d5eeb847ab6346bea32c466ddaa64ee4eaf","target":"graph","created_at":"2026-05-18T00:29:52Z","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":"The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2$\\epsilon$) tends to zero. Using a novel asymptotic expansion we determine the behavior of the eigenvalue $\\lambda$($\\epsilon$) and the eigenvector angular frequency k($\\epsilon$) for shells with Dirichlet boundary conditions along the lateral boundary, and natural boundary conditions on the other parts. First, the scalar Laplace operator for acoustics is addressed, for which k($\\epsilon$) is always zero. In contrast to it, for the Lam{\\'e} system of line","authors_text":"Erwan Faou (IPSO, IRMAR), Marie Chaussade-Beaudouin (IRMAR), Monique Dauge (IRMAR), Zohar Yosibash","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-26T14:46:14Z","title":"High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01459","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":"sha256:7edf498e31dafdb6e9902b32732935aacd8c2d3b2855b8b95455dfcba42452a7","target":"record","created_at":"2026-05-18T00:29:52Z","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":"48c868f4237392438f5228572115e2240b9e8b7e797c07bcf8327b22a9714c9c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-26T14:46:14Z","title_canon_sha256":"ff596aed43161486896e3f985b91122013383f9b02d5757ec3d1e063b54161ec"},"schema_version":"1.0","source":{"id":"1603.01459","kind":"arxiv","version":1}},"canonical_sha256":"8d21a17b202068fdd2e0f3f42ccec54d5807cd5ffea679164eefc39c89f221c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d21a17b202068fdd2e0f3f42ccec54d5807cd5ffea679164eefc39c89f221c4","first_computed_at":"2026-05-18T00:29:52.233383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:52.233383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lMwV4r51Xys8SWXLUWbcE6HI8zmwSnhWv8y7o5+U+TPq5zdQkEalN55KysZ50xo466VdZ2oCkWvNq9Z+VYf7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:52.233882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01459","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7edf498e31dafdb6e9902b32732935aacd8c2d3b2855b8b95455dfcba42452a7","sha256:bef2c4564892a40000df57f835a65d5eeb847ab6346bea32c466ddaa64ee4eaf"],"state_sha256":"103cb7ee9dd87d389cd716e8778f775b0c9c4ff83ed9ebac9004667c48f6ec46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QUe6eGkNkBVSdJysD73XnglbEv73bp4pT1yk4eJv7OqgcCoq6faI8sHuAwKgQKAoADKfqnvjTVAMhjso8qOkDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T08:39:39.708551Z","bundle_sha256":"d0043ca5b61fee01fb3ba1c7ab4be76955c95959a2438623f6475b9884932049"}}