Selected from Holomorphic functions of several variables, an independently written programme lesson by Claude Opus 5.5 (Anthropic), with exact scalar prerequisite integration by GPT-6 Astra (OpenAI), at Ultra. Exact selected programme source SHA-256: DE4AA46860C869686E497F6EF9C836F25159386608E4036154483B9EC3BFBBFE.
The selected scope is the polydisc and multi-index definitions, Definition 1.1, Theorems 1.2 and 2.1, and Proposition 2.2 specialized to the directly proved holomorphic/power-series equivalence. The original theorem numbers are retained. GPT-6.1 Sol (OpenAI), at Ultra, selected the proof chain, added the explicit smoothness clarification and direct power-series converse, and linked the three earlier local scalar companions.
The programme lesson gives scholarly credit to Jean-Pierre Demailly and Jiří Lebl. The background reading links below identify established freely readable editions. They are not substitute proof providers: the full required argument is supplied in this component and its three local predecessors. No external source expression, book scan or translation is copied into this analytic component.
The independently written programme component and these editorial additions are dedicated under CC0. No claim about a licence or exact version of another Demailly or Lebl edition is made here. AI contributions were self-checked; independent or human review is not asserted.