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

This is the reader-facing SGA working record for the Modern LaTeX Editions of Mathematics Manuscripts project. This version adds a 309-page cumulative English SGA 5 working translation synchronized against the current French workpass, with direct scan adjudication at source-critical formula, index, arrow, diagram, statement, footnote, and omission loci. Open first: 00_SGA5_English_SourceChecked_WorkingTranslation_NotCritical_20260717.pdf. The following two reader PDFs provide the current SGA 5 French workpass and the SGA 6 French source-rescribe checkpoint. Editable English TeX, the complete LNM 589 source scan, French and inherited-English controls, correction and structural ledgers, build logs, and complete rendered QA are grouped in 03_SGA5_English_TeX_Audit_and_SourceSupport_NotCritical_20260717.zip. SGA 5 English status: the cumulative covers the ten exposes represented in the current volume-level workpass (I, III, III B, V, VI, VII, VIII, X, XII, and XV) and the index through printed page 484. The final-resolution ledger closes 432 scan-derived candidates; additional residual and adversarial passes restore omitted sections and repair further prose, formula, and diagram-topology defects. The 309-page PDF renders completely. One source glyph ambiguity is retained explicitly rather than guessed. SGA 6 status: the French source-rescribe frontier remains ledger entry #679 / scan idx662 / volume p649 / Expose XIII p34, with idx663 next. The separate English SGA 6 synchronization lane is active, but no newer whole-lane English claim is made here: its TeX, PDF, ledgers, and status must agree on one frozen endpoint before promotion. Scope: these are substantive machine-assisted, source-aware working translations and repair materials, not OCR-only output. They are not independently human-certified critical editions, whole-SGA completion claims, or guarantees that every remaining source ambiguity has been resolved. Corrections can be proposed through the GitHub mirror: https://github.com/KokunoYumeto/modern-latex-manuscripts.