{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:S2JKI5P5FJGJL7HC46O6T4UYUG","short_pith_number":"pith:S2JKI5P5","canonical_record":{"source":{"id":"1304.5397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-19T12:45:24Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"01595d3034046ce481d1c4e65b7cabcf8464578ffa3a0cc0d5b395cbd0a1fbc3","abstract_canon_sha256":"c30cb5b7bf943d631d67950a15c06c81c0f685920cbe09149b3c51e85b7758b9"},"schema_version":"1.0"},"canonical_sha256":"9692a475fd2a4c95fce2e79de9f298a1b2e91b7819b6ba0af4e5a3673ab9d041","source":{"kind":"arxiv","id":"1304.5397","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:S2JKI5P5FJGJL7HC46O6T4UYUG","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-19T12:45:24Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"01595d3034046ce481d1c4e65b7cabcf8464578ffa3a0cc0d5b395cbd0a1fbc3","abstract_canon_sha256":"c30cb5b7bf943d631d67950a15c06c81c0f685920cbe09149b3c51e85b7758b9"},"schema_version":"1.0"},"canonical_sha256":"9692a475fd2a4c95fce2e79de9f298a1b2e91b7819b6ba0af4e5a3673ab9d041","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:24.547519Z","signature_b64":"nvcWaJV3WvI+zOtLKA4Y4MFlugXzj2v2VQk6h6HJ26YBMoUn5W1RKDNae0jNXynDKwn4lexJLvfTChWsHinQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9692a475fd2a4c95fce2e79de9f298a1b2e91b7819b6ba0af4e5a3673ab9d041","last_reissued_at":"2026-05-18T01:50:24.546890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:24.546890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5397","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MviHg5qiZjwCtasfu9cvrvy5DB0Z9hm2XdNVMcBFuSKs619lwTRhhtodaN+XmZYE5ygwVokwddAgRcwATL9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:39:31.852403Z"},"content_sha256":"e7b2d9c6a91deb26f2abffd91dfa218b340de13f5480e8685ff7f29bece6767e","schema_version":"1.0","event_id":"sha256:e7b2d9c6a91deb26f2abffd91dfa218b340de13f5480e8685ff7f29bece6767e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:S2JKI5P5FJGJL7HC46O6T4UYUG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-transmission-line-beam interactive system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Figotin, Guillermo Reyes","submitted_at":"2013-04-19T12:45:24Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5397","kind":"arxiv","version":2},"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":"2026-05-18T01:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9UeDztOFpOOaATSDlzMU5rZnnQ4fHy9uqKRY4Vy6JkPZoLto1ogb5jiEIljHURtwQa1xFVebVqkBNxoCFPvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:39:31.852995Z"},"content_sha256":"3884011da8c5ceeaaea3f72b489ae2ced804289c6ad1be384084108d98cbf790","schema_version":"1.0","event_id":"sha256:3884011da8c5ceeaaea3f72b489ae2ced804289c6ad1be384084108d98cbf790"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2JKI5P5FJGJL7HC46O6T4UYUG/bundle.json","state_url":"https://pith.science/pith/S2JKI5P5FJGJL7HC46O6T4UYUG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2JKI5P5FJGJL7HC46O6T4UYUG/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":"2026-05-26T05:39:31Z","links":{"resolver":"https://pith.science/pith/S2JKI5P5FJGJL7HC46O6T4UYUG","bundle":"https://pith.science/pith/S2JKI5P5FJGJL7HC46O6T4UYUG/bundle.json","state":"https://pith.science/pith/S2JKI5P5FJGJL7HC46O6T4UYUG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2JKI5P5FJGJL7HC46O6T4UYUG/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vPndWMjb6uGAJQbzpn89wSmv0fnrSEzQ0DG1BZOuQUq/ScOe7qZy+QavXixoGrABw50CBh01+YBWtzLRWzEMCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T05:39:31.856007Z","bundle_sha256":"89cef155d4b7375ee21372dc9b6f483d04e26875a53bdba1e384c086c325fb08"}}