SGA: Working Translation, Source-Repair, and Audit Drafts (SGA6 idx662 Source-Rescribe Checkpoint)

Superseded build note: This version is superseded by 10.5281/zenodo.21419947. Independent validation found one inherited Proposition 1.7 display with a 129 pt overfull-box warning in this version. The successor restores the prior continuation-row layout without changing words or formulas and rebuilds with zero overfull warnings. This is the reader-facing SGA working record for the Modern LaTeX Editions of Mathematics Manuscripts project. It retains the compact SGA5 and SGA6 reader-first surface and updates the front SGA6 French source-rescribe workpass to certification-ledger entry #679, scan idx662 / volume p649 / Expose XIII p34. The next unchecked page is idx663 / volume p650 / Expose XIII p35. Open first: the SGA5 French workpass PDF, 01_SGA6_French_SourceRescribe_Workpass_NotCertified_idx662_20260717.pdf, and the SGA6 English unsynchronized working-draft PDF. File 04_SGA6_TeX_SourceRescribe_Audit_NotCertified_idx662_20260717.zip contains editable French TeX, certification and errata ledgers, clean compile logs, the sixteen-page high-resolution idx647-662 source delta, boundary images, rendered output checks, PDF-text readback evidence, checksums, and the retained source-checked English Expose X tranche through printed p524. What changed: the sixteen-page direct-source delta continues Expose XIII from p19 through p34. It restores source-visible theorem and proof structure, parenthetical clauses, Picard-functor versus representing-scheme notation, inline mathematical arrangements, cross-references, punctuation, and typography. Material after idx662 remains inherited scaffold and is not certified merely because it appears in the compiled reader; output page 346 crosses the checked frontier. Status: this is substantive source-aware working material, not OCR-only, but it is not a critical edition, completed SGA6 release, whole-volume source-faithfulness certification, synchronized English edition, publication-grade proofread edition, or diagram-by-diagram certification. The 377-page French PDF has zero fatal errors, zero overfull boxes, zero underfull boxes, no missing characters, and no unresolved references. SGA5 remains incomplete and contains known errors. SGA7 remains partial and caveat-heavy. Output page count is not a completion metric because source restoration and layout reflow can add or remove pages. Corrections can be proposed through the GitHub mirror: https://github.com/KokunoYumeto/modern-latex-manuscripts.