{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MFPHEE64MPYFU4QWFYCJEMWMKR","short_pith_number":"pith:MFPHEE64","schema_version":"1.0","canonical_sha256":"615e7213dc63f05a72162e049232cc546bcb2cfb1911cded7ddd0689019624fb","source":{"kind":"arxiv","id":"1809.10233","version":2},"attestation_state":"computed","paper":{"title":"Direct construction of optimized stellarator shapes. I. Theory in cylindrical coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.plasm-ph","authors_text":"Matt Landreman, Wrick Sengupta","submitted_at":"2018-09-26T21:13:01Z","abstract_excerpt":"The confinement of guiding center trajectories in a stellarator is determined by the variation of the magnetic field strength $B$ in Boozer coordinates $(r, \\theta, \\varphi)$, but $B(r,\\theta,\\varphi)$ depends on the flux surface shape in a complicated way. Here we derive equations relating $B(r,\\theta,\\varphi)$ in Boozer coordinates and the rotational transform to the shape of flux surfaces in cylindrical coordinates, using an expansion in distance from the magnetic axis. A related expansion was done by Garren and Boozer [Phys. Fluids B 3, 2805 (1991)] based on the Frenet-Serret frame, which "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1809.10233","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.plasm-ph","submitted_at":"2018-09-26T21:13:01Z","cross_cats_sorted":[],"title_canon_sha256":"2b659de2ee8c0fe6e3d37ba462a577b8f557415974c0926cf3e883b2198afabf","abstract_canon_sha256":"358e3c082512a48ca36582b218eba0a0c5bd0baad97ade1d56b6e56e76ce439c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:17.736996Z","signature_b64":"d9Y8/tJhdDYfJMNiVtB5aI1ibLGKyI2FN5BpsOiA4eUKUVlfCfgEfZTpFK7KRELXP7KPt7i+1VbOvRfI2sMrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"615e7213dc63f05a72162e049232cc546bcb2cfb1911cded7ddd0689019624fb","last_reissued_at":"2026-05-17T23:56:17.736380Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:17.736380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Direct construction of optimized stellarator shapes. I. Theory in cylindrical coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.plasm-ph","authors_text":"Matt Landreman, Wrick Sengupta","submitted_at":"2018-09-26T21:13:01Z","abstract_excerpt":"The confinement of guiding center trajectories in a stellarator is determined by the variation of the magnetic field strength $B$ in Boozer coordinates $(r, \\theta, \\varphi)$, but $B(r,\\theta,\\varphi)$ depends on the flux surface shape in a complicated way. Here we derive equations relating $B(r,\\theta,\\varphi)$ in Boozer coordinates and the rotational transform to the shape of flux surfaces in cylindrical coordinates, using an expansion in distance from the magnetic axis. A related expansion was done by Garren and Boozer [Phys. Fluids B 3, 2805 (1991)] based on the Frenet-Serret frame, which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10233","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1809.10233","created_at":"2026-05-17T23:56:17.736482+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.10233v2","created_at":"2026-05-17T23:56:17.736482+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10233","created_at":"2026-05-17T23:56:17.736482+00:00"},{"alias_kind":"pith_short_12","alias_value":"MFPHEE64MPYF","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"MFPHEE64MPYFU4QW","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"MFPHEE64","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MFPHEE64MPYFU4QWFYCJEMWMKR","json":"https://pith.science/pith/MFPHEE64MPYFU4QWFYCJEMWMKR.json","graph_json":"https://pith.science/api/pith-number/MFPHEE64MPYFU4QWFYCJEMWMKR/graph.json","events_json":"https://pith.science/api/pith-number/MFPHEE64MPYFU4QWFYCJEMWMKR/events.json","paper":"https://pith.science/paper/MFPHEE64"},"agent_actions":{"view_html":"https://pith.science/pith/MFPHEE64MPYFU4QWFYCJEMWMKR","download_json":"https://pith.science/pith/MFPHEE64MPYFU4QWFYCJEMWMKR.json","view_paper":"https://pith.science/paper/MFPHEE64","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.10233&json=true","fetch_graph":"https://pith.science/api/pith-number/MFPHEE64MPYFU4QWFYCJEMWMKR/graph.json","fetch_events":"https://pith.science/api/pith-number/MFPHEE64MPYFU4QWFYCJEMWMKR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MFPHEE64MPYFU4QWFYCJEMWMKR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MFPHEE64MPYFU4QWFYCJEMWMKR/action/storage_attestation","attest_author":"https://pith.science/pith/MFPHEE64MPYFU4QWFYCJEMWMKR/action/author_attestation","sign_citation":"https://pith.science/pith/MFPHEE64MPYFU4QWFYCJEMWMKR/action/citation_signature","submit_replication":"https://pith.science/pith/MFPHEE64MPYFU4QWFYCJEMWMKR/action/replication_record"}},"created_at":"2026-05-17T23:56:17.736482+00:00","updated_at":"2026-05-17T23:56:17.736482+00:00"}