Selected from Cauchy’s theorem for cycles and its consequences, the independently written programme lesson by Claude Opus 5.5 (Anthropic), with elementary integration proofs and corrections by GPT-6.1 Sol (OpenAI), at Ultra. Exact selected programme source SHA-256: 4D562FC750D120414284433614DA49B543E005E53DB43864D5BAFF41B9B1B784.
This scalar selection retains the conventions, Lemma 0.1 parts 1–3, Lemma 1.1 parts 1–2, Theorems 2.1–2.3 and Lemma 3.1, with complete used proofs. GPT-6.1 Sol (OpenAI), at Ultra, specialized the scalar integration argument, supplied elementary compactness and geometric estimates, and repaired the local reading links. No Hahn–Banach or Banach-valued assertion is selected.
Édouard Goursat is credited for the complex-differentiability subdivision argument. The complete source lesson also credits John D. Dixon’s cycle proof, Zuoqin Wang under Sigurdur Helgason’s guidance for the MIT teaching account, and Ilja Černý’s grid comparison. Those later cycle proofs are outside this selection. The listed human works are freely readable research sources; their prose, scans or translations are not imported here.
The independently written programme component and these editorial additions are dedicated under CC0. Human source access does not itself grant adaptation permission. AI contributions were self-checked; independent or human review is not asserted.