SGA: Working Translation, Source-Repair, and Audit Drafts (SGA6 idx413 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 the frozen checkpoint through certification-ledger entry #410, scan idx413 / volume p400 / Expose VI p36. The next unchecked page is idx414 / volume p401 / Expose VI p37. Open first: the SGA5 French workpass PDF, 01_SGA6_French_SourceRescribe_Workpass_NotCertified_idx413_20260711.pdf, and the SGA6 English unsynchronized working-draft PDF. File 04_SGA6_TeX_SourceRescribe_Audit_NotCertified_idx413_20260711.zip contains the editable French TeX, full certification and errata ledgers, compile logs, retained representative source crops, and a status README. What changed: since the idx379 public checkpoint, thirty-four page-local source passes cover Expose VI pp3-36. They restore omitted content, correct notation and relations, repair display/inline structure, and check diagrams and equation tags against the source. A publication-only line wrap in Proposition 1.7 removes an overfull line without changing mathematical text. The frozen 389-page build has zero fatal errors, zero overfull boxes, and zero underfull boxes; four inherited accent warnings and one footnote-destination warning remain. Status: this is useful source-aware working material, not OCR-only, but it is not a critical edition, completed SGA6 release, whole-volume source-faithfulness certification, English synchronization, index audit, or publication-grade proofreading. Material after idx413 remains inherited working scaffold until directly compared with the source; the first page beyond the cursor already shows known notation drift. SGA5 remains incomplete and contains known errors. SGA7 remains partial and caveat-heavy. Corrections can be proposed through the GitHub mirror: https://github.com/KokunoYumeto/modern-latex-manuscripts.