SGA 5 and SGA 6: Modern LaTeX Working Editions, English and Spanish Translations, French Source Repair, and Audit Materials

This is the reader-facing SGA working record for the Modern LaTeX Editions of Mathematics Manuscripts project. It contains modern LaTeX working editions, machine-assisted English and Spanish translations, French source-repair workpasses, high-resolution source witnesses, and audit material for SGA 5 and SGA 6. Open first: 00_SGA5_English_SourceChecked_WorkingTranslation_NotCritical_20260717.pdf, the current 309-page source-aware SGA 5 English working translation. The record now also directly exposes 02b_SGA5_Spanish_SourceReconciled_WorkingTranslation_Through_ExposeX_NotCritical_20260718.pdf, a 268-page Spanish source-reconciled working reader. For SGA 6 English, open 02_SGA6_English_FullRange_Layered_WorkingReader_CORRECTED_20260718.pdf. For the current French source-rescribe checkpoint, open 01_SGA6_French_SourceRescribe_Workpass_NotCertified_idx684_20260718.pdf. SGA 5 Spanish update: the released checkpoint contains 297 editable, unitized TeX bodies reconciled against the frozen French workpass and checked against the scan by the production lane. It integrates complete Exposes I, III A, III B, V, VI, VII, VIII, and X, including Expose X section 7, Corollary 7.12, Lemma 7.14, their proofs, and the references. The build is 268 pages with zero forbidden diagnostics; the five pages added beyond the preceding section-6 render gate were rendered and inspected. Expose XII is the next ordered cursor. Later drafts are excluded until they receive the same source reconciliation. SGA 6 French checkpoint: the linear pagewise pass remains frozen at source idx684 / volume p. 671 / Expose XIV p. 5, with idx685 next in this public version. The grouped ZIP contains editable TeX, the pagewise repair ledger, errata, source witnesses, render checks, compile evidence, and checksums. Explicit deferred issues remain; idx684 is a processing cursor, not whole-volume certification. SGA 6 English authority layers: source-PDF 001-525 uses an inherited English control that is partially source-synchronized but not globally source-checked; idx532-662 is source-checked against the directly checked French workpass available for that range; idx663-702 and terminal back matter are scan-checked English draft layers pending later French reconciliation. The bounded Spanish SGA 6 Expose X tranche for idx532-537 is retained. Status: these are substantive machine-assisted, source-aware working editions and translations, not OCR-only output. They are not independently human-certified critical editions, complete SGA translations, whole-volume source-faithfulness certifications, publication-grade proofread editions, or diagram-by-diagram certifications. SGA 5 retains known residual errors. Corrections can be proposed through the GitHub mirror.