ATTRIBUTION AND COMPONENT TERMS

Analytic finiteness for preparation
Human author: Guillaume Valette.
Source: On subanalytic geometry, arXiv:2507.23622v1, 31 July 2025.
https://arxiv.org/abs/2507.23622v1
Sections: 1.3.2, 1.4–1.5, 1.6–1.8 (complete expression/global cell preparation and Puiseux), and 2.2 (choice, curves and Łojasiewicz inequalities).
Licence: Creative Commons Attribution 4.0 International.
https://creativecommons.org/licenses/by/4.0/
The author remains credited. Identified changes include transcription/notation, complete algebra and prescribed-jet arguments, signed compact normalization, convergence estimates, compact-domain/unit/translation/power details and full ordinary and two-coordinate reductions, joint dimension induction, projective-product witness/cell constructions, bounded local comparison, parameter convergence and even cleared exponents. Curve, supremum and gradient details and two solved teaching exercises are identified additions. No endorsement is implied.

Weierstrass preparation and division
Human author: Jean-Pierre Demailly.
Source: Complex Analytic and Differential Geometry, 21 June 2012.
https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/agbook.pdf
The author's publication page describes the book as OpenContent and permits printing, spreading and modifying it on the web, except claiming authorship:
https://www-fourier.univ-grenoble-alpes.fr/~demailly/documents.html
This is the author's custom grant. No Creative Commons licence is substituted for it. The selection includes preparation, Cauchy division, Noetherianity and one solved exercise. Demailly credits the Cauchy division method to C. L. Siegel.

Adaptation and checking
Adapted by GPT-6.1 Sol (OpenAI), Ultra, October 2026. AI additions and proof details are identified in the readings. Author self-check performed; independent review is not claimed. Both human components retain the terms above.

Reader implementation
The added reader build scripts, template, styling and reading-selection metadata are dedicated to the public domain under CC0 1.0:
https://creativecommons.org/publicdomain/zero/1.0/
This dedication does not apply to either human mathematical component or replace its terms.

Primary definition context
Jean-Marie Lion and Jean-Philippe Rolin, Théorème de préparation pour les fonctions logarithmico-exponentielles, Annales de l'Institut Fourier 47 (1997), 859–884, DOI10.5802/aif.1583. The projective product definition is cited; this article is not imported or relicensed. The elementary chart/witness proofs are supplied in the reading.

Additional adapted human scope: Valette §2.3, dimension, closure, frontier and parameter continuity. The expanded proofs and three identified solutions retain CC BY4.0. An injective bounded transform and relative closed-graph argument replace the original shortcut. No endorsement is implied.