{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NNQQ7P7FWG4JEA6PZDIWK7L7ZO","short_pith_number":"pith:NNQQ7P7F","canonical_record":{"source":{"id":"1812.07456","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-12-14T20:38:34Z","cross_cats_sorted":["math.NA","physics.comp-ph"],"title_canon_sha256":"3873e20720e9a8fe7e55eaf6e84837156a7e86ee131987cc1abc338571516cf3","abstract_canon_sha256":"e0f7e91342d60cd89c3d03a88374207ce2711b98531484757a69b940b2cfe521"},"schema_version":"1.0"},"canonical_sha256":"6b610fbfe5b1b89203cfc8d1657d7fcb8b0cd020ccaaf44600ce6f4d8037c817","source":{"kind":"arxiv","id":"1812.07456","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07456","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07456v3","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07456","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"NNQQ7P7FWG4J","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NNQQ7P7FWG4JEA6P","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NNQQ7P7F","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NNQQ7P7FWG4JEA6PZDIWK7L7ZO","target":"record","payload":{"canonical_record":{"source":{"id":"1812.07456","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-12-14T20:38:34Z","cross_cats_sorted":["math.NA","physics.comp-ph"],"title_canon_sha256":"3873e20720e9a8fe7e55eaf6e84837156a7e86ee131987cc1abc338571516cf3","abstract_canon_sha256":"e0f7e91342d60cd89c3d03a88374207ce2711b98531484757a69b940b2cfe521"},"schema_version":"1.0"},"canonical_sha256":"6b610fbfe5b1b89203cfc8d1657d7fcb8b0cd020ccaaf44600ce6f4d8037c817","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:57.849383Z","signature_b64":"0u3m2l1rA67ZutWhoerIP5CtjZsd7iIf3I5rbZJqjxYoGNVak32dk8em2rty6zWiD8zCV5wF/6Ii7jsuL2eAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b610fbfe5b1b89203cfc8d1657d7fcb8b0cd020ccaaf44600ce6f4d8037c817","last_reissued_at":"2026-05-17T23:45:57.848933Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:57.848933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.07456","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":"2026-05-17T23:45:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y7lYyu9+ou0RF75EeG32X7RXYrd0nqw5QU+a/cE6pqdjvrQbM/u1PLoB8rHB0UZth4TDjy58njM25gIMsi7hAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:57:50.648371Z"},"content_sha256":"5dfc174f33bb0a83462472982d9923ebfdf10f445c651e6c5db4a21f36ae5e5c","schema_version":"1.0","event_id":"sha256:5dfc174f33bb0a83462472982d9923ebfdf10f445c651e6c5db4a21f36ae5e5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NNQQ7P7FWG4JEA6PZDIWK7L7ZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Electromagnetic surface wave propagation in a metallic wire and the Lambert $W$ function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","physics.comp-ph"],"primary_cat":"physics.class-ph","authors_text":"J. Ricardo G. Mendon\\c{c}a","submitted_at":"2018-12-14T20:38:34Z","abstract_excerpt":"We revisit the solution due to Sommerfeld of a problem in classical electrodynamics, namely, that of the propagation of an electromagnetic axially symmetric surface wave (a low-attenuation single TM$_{01}$ mode) in a cylindrical metallic wire, and his iterative method to solve the transcendental equation that appears in the determination of the propagation wave number from the boundary conditions. We present an elementary analysis of the convergence of Sommerfeld's iterative solution of the approximate problem and compare it with both the numerical solution of the exact transcendental equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07456","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":"2026-05-17T23:45:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JzKL7shirEyjrROV6ddkiyv4TjPu13x2zCuNx4vp1FyTMmL2FDaGPKZXuedfF3cqTS4y4dgIKAaIl846srhhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:57:50.648717Z"},"content_sha256":"bcff9685dcb7dad73f74ae1ec65b6a126aebc9bf3ad1003aa95eccfbed9a17dc","schema_version":"1.0","event_id":"sha256:bcff9685dcb7dad73f74ae1ec65b6a126aebc9bf3ad1003aa95eccfbed9a17dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNQQ7P7FWG4JEA6PZDIWK7L7ZO/bundle.json","state_url":"https://pith.science/pith/NNQQ7P7FWG4JEA6PZDIWK7L7ZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNQQ7P7FWG4JEA6PZDIWK7L7ZO/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":"2026-06-27T12:57:50Z","links":{"resolver":"https://pith.science/pith/NNQQ7P7FWG4JEA6PZDIWK7L7ZO","bundle":"https://pith.science/pith/NNQQ7P7FWG4JEA6PZDIWK7L7ZO/bundle.json","state":"https://pith.science/pith/NNQQ7P7FWG4JEA6PZDIWK7L7ZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNQQ7P7FWG4JEA6PZDIWK7L7ZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NNQQ7P7FWG4JEA6PZDIWK7L7ZO","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":"e0f7e91342d60cd89c3d03a88374207ce2711b98531484757a69b940b2cfe521","cross_cats_sorted":["math.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-12-14T20:38:34Z","title_canon_sha256":"3873e20720e9a8fe7e55eaf6e84837156a7e86ee131987cc1abc338571516cf3"},"schema_version":"1.0","source":{"id":"1812.07456","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07456","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07456v3","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07456","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"NNQQ7P7FWG4J","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NNQQ7P7FWG4JEA6P","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NNQQ7P7F","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:bcff9685dcb7dad73f74ae1ec65b6a126aebc9bf3ad1003aa95eccfbed9a17dc","target":"graph","created_at":"2026-05-17T23:45:57Z","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":"We revisit the solution due to Sommerfeld of a problem in classical electrodynamics, namely, that of the propagation of an electromagnetic axially symmetric surface wave (a low-attenuation single TM$_{01}$ mode) in a cylindrical metallic wire, and his iterative method to solve the transcendental equation that appears in the determination of the propagation wave number from the boundary conditions. We present an elementary analysis of the convergence of Sommerfeld's iterative solution of the approximate problem and compare it with both the numerical solution of the exact transcendental equation","authors_text":"J. Ricardo G. Mendon\\c{c}a","cross_cats":["math.NA","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-12-14T20:38:34Z","title":"Electromagnetic surface wave propagation in a metallic wire and the Lambert $W$ function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07456","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":"sha256:5dfc174f33bb0a83462472982d9923ebfdf10f445c651e6c5db4a21f36ae5e5c","target":"record","created_at":"2026-05-17T23:45:57Z","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":"e0f7e91342d60cd89c3d03a88374207ce2711b98531484757a69b940b2cfe521","cross_cats_sorted":["math.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-12-14T20:38:34Z","title_canon_sha256":"3873e20720e9a8fe7e55eaf6e84837156a7e86ee131987cc1abc338571516cf3"},"schema_version":"1.0","source":{"id":"1812.07456","kind":"arxiv","version":3}},"canonical_sha256":"6b610fbfe5b1b89203cfc8d1657d7fcb8b0cd020ccaaf44600ce6f4d8037c817","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b610fbfe5b1b89203cfc8d1657d7fcb8b0cd020ccaaf44600ce6f4d8037c817","first_computed_at":"2026-05-17T23:45:57.848933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:57.848933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0u3m2l1rA67ZutWhoerIP5CtjZsd7iIf3I5rbZJqjxYoGNVak32dk8em2rty6zWiD8zCV5wF/6Ii7jsuL2eAAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:57.849383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.07456","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dfc174f33bb0a83462472982d9923ebfdf10f445c651e6c5db4a21f36ae5e5c","sha256:bcff9685dcb7dad73f74ae1ec65b6a126aebc9bf3ad1003aa95eccfbed9a17dc"],"state_sha256":"9a0d3f7a0f291697375289f3b8b4cdf517ffd61ecc256007f89169989cf3d412"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X53HT63vd5TkgrTr8b3B7/PNu4qLHbnfoCICSTKbxHORlWgkA1KJH3T5Ksb47hjkI5XYHzm+7iCtVKxVPw1KBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:57:50.650607Z","bundle_sha256":"0f76ec61e3fd9bd476046719e6c1129005ce263b1b66c5eebd95f980c92b1374"}}