{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H23CBF3W4PDCDNQXHSCJYWJPO4","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":"ab726d5098f2c393de1ff1b1c1fb3b154d3d93d06494e4911dac58e3d8e53144","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2016-03-20T13:39:38Z","title_canon_sha256":"5b8e8440204af2f0b3004d0bbdf026c9a7418e76af8cd59657c5d5f2590b2a8e"},"schema_version":"1.0","source":{"id":"1603.06213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06213","created_at":"2026-05-18T01:18:50Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06213v1","created_at":"2026-05-18T01:18:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06213","created_at":"2026-05-18T01:18:50Z"},{"alias_kind":"pith_short_12","alias_value":"H23CBF3W4PDC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H23CBF3W4PDCDNQX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H23CBF3W","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:0e8c64c3ff658083cf46e74ed31e21e6f3b5e0403763da855d60fa802fb9cda5","target":"graph","created_at":"2026-05-18T01:18:50Z","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"},"paper":{"abstract_excerpt":"This note describes the solution of the Helmholtz equation inside a nanotorus with uniform Dirichlet boundary conditions. The eigenfunction symmetry is discussed and the lower-order eigenvalues and eigenfunctions are shown. The similarity with the case of a long cylinder and with that of the vibrations of a circular elastic membrane is discussed. This similarity is used to propose a classification scheme of the eigenfunctions based on three indices.","authors_text":"(2) Department of Electrical, B-4000 Li\\`ege, Belgium, Chicago, Computer Engineering, IL 60607, Michael A. Stroscio (2) ((1) D\\'epartement de Physique B5, N.D. Nguyen (1), R. Evrard (1), Universit\\'e de Li\\`ege, University of Illinois at Chicago, USA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2016-03-20T13:39:38Z","title":"Note on the numerical solution of the scalar Helmholtz equation in a nanotorus with uniform Dirichlet boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06213","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":"sha256:6faf0da658edd517fc2274f2b2327d4da1bcc9f64fe2bc33a57164abd9771653","target":"record","created_at":"2026-05-18T01:18:50Z","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":"ab726d5098f2c393de1ff1b1c1fb3b154d3d93d06494e4911dac58e3d8e53144","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2016-03-20T13:39:38Z","title_canon_sha256":"5b8e8440204af2f0b3004d0bbdf026c9a7418e76af8cd59657c5d5f2590b2a8e"},"schema_version":"1.0","source":{"id":"1603.06213","kind":"arxiv","version":1}},"canonical_sha256":"3eb6209776e3c621b6173c849c592f77026cc8f1b29e68192b63214cbb31ca7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3eb6209776e3c621b6173c849c592f77026cc8f1b29e68192b63214cbb31ca7f","first_computed_at":"2026-05-18T01:18:50.012711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:50.012711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9OojFX8kIJ5yWwoWRh+6Avc27JPe7fmb0usErQIdsJUNGLGOTKXPtB3y0Dx6EzzvpuIsq+eC3i9E0U08QBYsCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:50.013210Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6faf0da658edd517fc2274f2b2327d4da1bcc9f64fe2bc33a57164abd9771653","sha256:0e8c64c3ff658083cf46e74ed31e21e6f3b5e0403763da855d60fa802fb9cda5"],"state_sha256":"6f59d02eacfdc2c2f61b0b00b554750bed2788f73c14284306f21aae77674aaf"}