{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EWL7AIICMVSDVN2E4ULKSYYY2V","short_pith_number":"pith:EWL7AIIC","canonical_record":{"source":{"id":"1602.00850","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-02T09:39:03Z","cross_cats_sorted":["math.SP","physics.class-ph"],"title_canon_sha256":"2283e3733859cd00d245776e9c9409af5861e06ddadc5cb4a99c566693a8e49a","abstract_canon_sha256":"e6174eb2fc87b0502dc55661a51b1e2c3aa397a95187b31e61604662f0f8e716"},"schema_version":"1.0"},"canonical_sha256":"2597f0210265643ab744e516a96318d57951030e292dda73f1dada466c3c9f5e","source":{"kind":"arxiv","id":"1602.00850","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00850","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00850v3","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00850","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"EWL7AIICMVSD","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EWL7AIICMVSDVN2E","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EWL7AIIC","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EWL7AIICMVSDVN2E4ULKSYYY2V","target":"record","payload":{"canonical_record":{"source":{"id":"1602.00850","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-02T09:39:03Z","cross_cats_sorted":["math.SP","physics.class-ph"],"title_canon_sha256":"2283e3733859cd00d245776e9c9409af5861e06ddadc5cb4a99c566693a8e49a","abstract_canon_sha256":"e6174eb2fc87b0502dc55661a51b1e2c3aa397a95187b31e61604662f0f8e716"},"schema_version":"1.0"},"canonical_sha256":"2597f0210265643ab744e516a96318d57951030e292dda73f1dada466c3c9f5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:52.246900Z","signature_b64":"gOh0DEQtxF6pZR6uivhSofeWWDLktVxlRMXbjgZSOCJ7OPEKHX1Et1QwB31qX8EClp1CFDDelwtxsWD6FppFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2597f0210265643ab744e516a96318d57951030e292dda73f1dada466c3c9f5e","last_reissued_at":"2026-05-18T00:29:52.246403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:52.246403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.00850","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":"2026-05-18T00:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WOBr1kJn8zaxoy9gUo4uNTJoiUPXVdAGOssQLB6o6aaR1a/8nkVpK5ezxne0y5V5W9knz+xXMCoCRwNpG89/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:01:30.969584Z"},"content_sha256":"f4498f9fa0d13f972f02857d30234a35b6b04c959810e132bcdcdb1c152b32c9","schema_version":"1.0","event_id":"sha256:f4498f9fa0d13f972f02857d30234a35b6b04c959810e132bcdcdb1c152b32c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EWL7AIICMVSDVN2E4ULKSYYY2V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP","physics.class-ph"],"primary_cat":"math.NA","authors_text":"Erwan Faou (IRMAR, IPSO), Marie Chaussade-Beaudouin (IRMAR), Monique Dauge (IRMAR), Zohar Yosibash","submitted_at":"2016-02-02T09:39:03Z","abstract_excerpt":"Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lam{\\'e} system) are determined by an asymptotic analysis as the thickness ($2\\varepsilon$) tends to zero. The departing point is the Koiter shell model that we reduce by asymptotic analysis to a scalar modelthat depends on two parameters: the angular frequency $k$ and the half-thickness $\\varepsilon$. Optimizing $k$ for each chosen $\\varepsilon$, we find power laws for $k$ in function of $\\varepsilon$ that provide the smallest eigenvalues of the scalar reductions.Corresponding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00850","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":"2026-05-18T00:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aNx8TW3cGf7BamfMc87pI/A5IDmVPR4nCzz3E4OappNHxw/Mu4mdrjlHb5D1Y5qRRFlamcmNHf+71EbET8sIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:01:30.970005Z"},"content_sha256":"e3f6a314b608d350082df18efe569e221660e6d05df3468bfc033f5bdbc43ab2","schema_version":"1.0","event_id":"sha256:e3f6a314b608d350082df18efe569e221660e6d05df3468bfc033f5bdbc43ab2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EWL7AIICMVSDVN2E4ULKSYYY2V/bundle.json","state_url":"https://pith.science/pith/EWL7AIICMVSDVN2E4ULKSYYY2V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EWL7AIICMVSDVN2E4ULKSYYY2V/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":"2026-06-21T06:01:30Z","links":{"resolver":"https://pith.science/pith/EWL7AIICMVSDVN2E4ULKSYYY2V","bundle":"https://pith.science/pith/EWL7AIICMVSDVN2E4ULKSYYY2V/bundle.json","state":"https://pith.science/pith/EWL7AIICMVSDVN2E4ULKSYYY2V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EWL7AIICMVSDVN2E4ULKSYYY2V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EWL7AIICMVSDVN2E4ULKSYYY2V","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":"e6174eb2fc87b0502dc55661a51b1e2c3aa397a95187b31e61604662f0f8e716","cross_cats_sorted":["math.SP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-02T09:39:03Z","title_canon_sha256":"2283e3733859cd00d245776e9c9409af5861e06ddadc5cb4a99c566693a8e49a"},"schema_version":"1.0","source":{"id":"1602.00850","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00850","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00850v3","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00850","created_at":"2026-05-18T00:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"EWL7AIICMVSD","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EWL7AIICMVSDVN2E","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EWL7AIIC","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:e3f6a314b608d350082df18efe569e221660e6d05df3468bfc033f5bdbc43ab2","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":"Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lam{\\'e} system) are determined by an asymptotic analysis as the thickness ($2\\varepsilon$) tends to zero. The departing point is the Koiter shell model that we reduce by asymptotic analysis to a scalar modelthat depends on two parameters: the angular frequency $k$ and the half-thickness $\\varepsilon$. Optimizing $k$ for each chosen $\\varepsilon$, we find power laws for $k$ in function of $\\varepsilon$ that provide the smallest eigenvalues of the scalar reductions.Corresponding ","authors_text":"Erwan Faou (IRMAR, IPSO), Marie Chaussade-Beaudouin (IRMAR), Monique Dauge (IRMAR), Zohar Yosibash","cross_cats":["math.SP","physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-02T09:39:03Z","title":"Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00850","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:f4498f9fa0d13f972f02857d30234a35b6b04c959810e132bcdcdb1c152b32c9","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":"e6174eb2fc87b0502dc55661a51b1e2c3aa397a95187b31e61604662f0f8e716","cross_cats_sorted":["math.SP","physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-02T09:39:03Z","title_canon_sha256":"2283e3733859cd00d245776e9c9409af5861e06ddadc5cb4a99c566693a8e49a"},"schema_version":"1.0","source":{"id":"1602.00850","kind":"arxiv","version":3}},"canonical_sha256":"2597f0210265643ab744e516a96318d57951030e292dda73f1dada466c3c9f5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2597f0210265643ab744e516a96318d57951030e292dda73f1dada466c3c9f5e","first_computed_at":"2026-05-18T00:29:52.246403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:52.246403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gOh0DEQtxF6pZR6uivhSofeWWDLktVxlRMXbjgZSOCJ7OPEKHX1Et1QwB31qX8EClp1CFDDelwtxsWD6FppFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:52.246900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00850","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4498f9fa0d13f972f02857d30234a35b6b04c959810e132bcdcdb1c152b32c9","sha256:e3f6a314b608d350082df18efe569e221660e6d05df3468bfc033f5bdbc43ab2"],"state_sha256":"d592d4a87f3095452cee94e38683accaa3a7917c6cd813a614119ba0a7a8972c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LBvBJk6B2wPbP75ACJ2vNqG9UsIfN36kAEhQstGGRoA0az6RkLfYhytTJsXNTsHzCRK4ENbo8hg9ZESl2pubCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T06:01:30.971954Z","bundle_sha256":"ffc1d69e29e34cae178daa2ed50378b63ec5c299a68beabb1bf4dc4088b8f087"}}