{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CWF2X6Q3HBNAPE4UWEZVARO6JY","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":"625ff12bc0d119d6c76b4c5a4dc3e85bff2b9e8fac04dcfee31fcfd1ae2c953c","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-03-27T14:56:23Z","title_canon_sha256":"9de06d0972db30da331d771a73aa129f36aa271fca95640ac02512f244c3d500"},"schema_version":"1.0","source":{"id":"2103.14922","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.14922","created_at":"2026-07-05T03:51:26Z"},{"alias_kind":"arxiv_version","alias_value":"2103.14922v1","created_at":"2026-07-05T03:51:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.14922","created_at":"2026-07-05T03:51:26Z"},{"alias_kind":"pith_short_12","alias_value":"CWF2X6Q3HBNA","created_at":"2026-07-05T03:51:26Z"},{"alias_kind":"pith_short_16","alias_value":"CWF2X6Q3HBNAPE4U","created_at":"2026-07-05T03:51:26Z"},{"alias_kind":"pith_short_8","alias_value":"CWF2X6Q3","created_at":"2026-07-05T03:51:26Z"}],"graph_snapshots":[{"event_id":"sha256:8cea7c1a9548e453d119cc2390b7c70e8130b635f1bf33cf5a27e7c0b71a714a","target":"graph","created_at":"2026-07-05T03:51:26Z","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/2103.14922/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The aim of this paper is to give a precise proof of the completeness of Lamb modes and associated modes. This proof is relatively simple and short but relies on two powerful mathematical theorems. The first one is a theorem on elliptic systems with a parameter due to Agranovich and Vishik. The second one is a theorem due to Locker which gives a criterion to show the completeness of the set of generalized eigenvectors of a Hilbert-Schmidt discrete operator.","authors_text":"Jean-Luc Akian","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-03-27T14:56:23Z","title":"A proof of the completeness of Lamb modes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.14922","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:bdfd4c0cd95ab2fa7b492b9b37b7e185e3e4da309f50ecfdc41b912a85ddce7a","target":"record","created_at":"2026-07-05T03:51:26Z","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":"625ff12bc0d119d6c76b4c5a4dc3e85bff2b9e8fac04dcfee31fcfd1ae2c953c","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-03-27T14:56:23Z","title_canon_sha256":"9de06d0972db30da331d771a73aa129f36aa271fca95640ac02512f244c3d500"},"schema_version":"1.0","source":{"id":"2103.14922","kind":"arxiv","version":1}},"canonical_sha256":"158babfa1b385a079394b1335045de4e00973789503f00f05246a9fe0bfc6547","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"158babfa1b385a079394b1335045de4e00973789503f00f05246a9fe0bfc6547","first_computed_at":"2026-07-05T03:51:26.598572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:51:26.598572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zppxqkQ8T5GGeHk/kcdkROqwDB7WQuHKoMYd31n5sI8/YgqpyVYW6DETetwT+L/1bwnVCyiXdEkuML35B40iDA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:51:26.599019Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.14922","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdfd4c0cd95ab2fa7b492b9b37b7e185e3e4da309f50ecfdc41b912a85ddce7a","sha256:8cea7c1a9548e453d119cc2390b7c70e8130b635f1bf33cf5a27e7c0b71a714a"],"state_sha256":"acfed561e141e9afd43e8f4875a43020c1a7c0d239cd2d9733c3f68be6f3994a"}