{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:S2JKI5P5FJGJL7HC46O6T4UYUG","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":"c30cb5b7bf943d631d67950a15c06c81c0f685920cbe09149b3c51e85b7758b9","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-19T12:45:24Z","title_canon_sha256":"01595d3034046ce481d1c4e65b7cabcf8464578ffa3a0cc0d5b395cbd0a1fbc3"},"schema_version":"1.0","source":{"id":"1304.5397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5397","created_at":"2026-05-18T01:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5397v2","created_at":"2026-05-18T01:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5397","created_at":"2026-05-18T01:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"S2JKI5P5FJGJ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S2JKI5P5FJGJL7HC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S2JKI5P5","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:3884011da8c5ceeaaea3f72b489ae2ced804289c6ad1be384084108d98cbf790","target":"graph","created_at":"2026-05-18T01:50:24Z","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 construct here a Lagrangian field formulation for a system consisting of an electron beam interacting with a slow-wave structure modeled by a possibly non-uniform multiple transmission line (MTL). In the case of a single line we recover the linear model of a traveling wave tube (TWT) due to J.R. Pierce. Since a properly chosen MTL can approximate a real waveguide structure with any desired accuracy, the proposed model can be used in particular for design optimization. Furthermore, the Lagrangian formulation provides for: (i) a clear identification of the mathematical source of amplification","authors_text":"Alexander Figotin, Guillermo Reyes","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-19T12:45:24Z","title":"Multi-transmission-line-beam interactive system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5397","kind":"arxiv","version":2},"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:e7b2d9c6a91deb26f2abffd91dfa218b340de13f5480e8685ff7f29bece6767e","target":"record","created_at":"2026-05-18T01:50:24Z","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":"c30cb5b7bf943d631d67950a15c06c81c0f685920cbe09149b3c51e85b7758b9","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-19T12:45:24Z","title_canon_sha256":"01595d3034046ce481d1c4e65b7cabcf8464578ffa3a0cc0d5b395cbd0a1fbc3"},"schema_version":"1.0","source":{"id":"1304.5397","kind":"arxiv","version":2}},"canonical_sha256":"9692a475fd2a4c95fce2e79de9f298a1b2e91b7819b6ba0af4e5a3673ab9d041","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9692a475fd2a4c95fce2e79de9f298a1b2e91b7819b6ba0af4e5a3673ab9d041","first_computed_at":"2026-05-18T01:50:24.546890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:24.546890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nvcWaJV3WvI+zOtLKA4Y4MFlugXzj2v2VQk6h6HJ26YBMoUn5W1RKDNae0jNXynDKwn4lexJLvfTChWsHinQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:24.547519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7b2d9c6a91deb26f2abffd91dfa218b340de13f5480e8685ff7f29bece6767e","sha256:3884011da8c5ceeaaea3f72b489ae2ced804289c6ad1be384084108d98cbf790"],"state_sha256":"60964a985be8e30f3d91e5271c9ca8d629df4bfe69f1f1d37cf3b552df1c278b"}