Emmy Noether: Modern LaTeX Working Corpus and Multilingual Translation Drafts (v26/R821 Paper 20 Source Integration)

This is the reader-facing Emmy Noether working record for the Modern LaTeX Editions of Mathematics Manuscripts project. This version fronts 00_Noether_German_Cumulative_Working_SourceControl_v26_R821integrated_20260716.pdf, a 466-page German working reader. The matching TeX, source witnesses, integration diff, render checks, build logs, and original R820/R821 audit packages are grouped in the size-controlled 07_Noether_Current_German_SourceControl_v26_R821integrated_20260716.zip. What changed: the published v26/R819 German head now incorporates two further direct source passes on Paper 20, Absolute Irreduzibilitaet in einem beliebigen Grundkoerper. R820 records eight emphasis refinements across printed pages 27-32. R821 records four further whole-paper refinements across printed pages 26-33, including restored emphasis, source quotation marks, and theorem-transition typography. No OCR text was promoted. Guarded integration checks confirm that every byte outside Paper 20 is preserved from R819 and that the integrated Paper 20 exactly matches the sealed R821 text. Status caveat: this is a serious source-repair and translation working corpus, not a critical edition, author-wide source-faithfulness certification, paper-by-paper certification, complete multilingual synchronization, or publication-grade proofreading. Source-audit depth varies by paper, and the retained English and multilingual readers predate some German repairs. Inherited terms such as COMPLETE, closure, or closed refer only to bounded local tasks. GitHub: corrections, source comparisons, LaTeX fixes, and translation improvements can be suggested via issues or pull requests at https://github.com/KokunoYumeto/modern-latex-manuscripts.