SGA: Working Translation, Source-Repair, and Audit Drafts (SGA6 idx540 Source-Rescribe Checkpoint)

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 #537, scan idx540 / volume p527 / Expose X p9. The next unchecked page is idx541 / volume p528 / Expose X p10. Open first: the SGA5 French workpass PDF, 01_SGA6_French_SourceRescribe_Workpass_NotCertified_idx540_20260714.pdf, and the SGA6 English unsynchronized working-draft PDF. File 04_SGA6_TeX_SourceRescribe_Audit_NotCertified_idx540_20260714.zip contains editable French TeX, certification and errata ledgers, clean compile logs, a 98-page high-resolution source witness, boundary images, rendered output checks, PDF-text readback evidence, checksums, and a status README. What changed: since #439 / idx442, 98 directly checked source pages finish Expose VII, cover Exposes VIII and IX, and reach Expose X p9. The pagewise pass restores omitted authored text, proofs, displays, and notation; reverses paraphrase or condensation where encountered; and corrects source-level mathematical errors. The current frontier includes the source-backed filtration formula x*w in Filt_{j-i-1}(X). Material after idx540 remains inherited scaffold and is not certified merely because it appears in the compiled reader. 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. SGA5 remains incomplete and contains known errors. SGA7 remains partial and caveat-heavy. The 383-page French PDF has zero fatal errors, zero overfull boxes, zero underfull boxes, and no invalid math-mode accent warning. 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.