Emmy Noether: Modern LaTeX Drafts and English Translation Working Drafts

Dedicated Emmy Noether record for the Modern LaTeX Editions of Mathematics Manuscripts project. This record preserves source-checkable modern LaTeX working drafts, translations, source witnesses, render checks, and audit support for the Noether corpus. Status at a glance. These files are working drafts and source-audit artifacts, not a certified critical edition. The current packaged local TeX-changing German source-control head is R569. R569 is cumulative over the R560-R568 source-control chain and repairs two post-P43 tail loci: collected p761 / output p457 changes a^S=a to source-visible a^{S^r}=a, and collected p764 / output p459 changes (Mit einem Zusatz, gemeinsam mit E. Noether in Goettingen.) to source-visible (Mit einem Zusatz, gemeinsam mit E. Noether). R570 is the latest packaged no-patch checkpoint over collected pp767-772; its cumulative TeX is content-identical to R569, with an empty diff after checking formula (2), system (3), Hilfssatz II, Zusatz I/II, Satz III, the derivative display, Noether Zusatz, Satz IV, relation displays (4)-(6), and the Bemerkung II y^{(K)} / y^\lambda distinction. R569/R570 both compile to 468-page cumulative German PDFs with two XeLaTeX passes. Because the Noether record is at the Zenodo 100-file ceiling, R560-R570 are queued for curated rollup rather than uploaded loose. Treat this as a working source-control and multilingual translation lane, not Noether closure, whole-corpus certification, multilingual synchronization, or a critical edition. Known caveat. R569/R570/R568/R567/R566/R565/R564 are narrow tail source-control or no-patch audit packages using staged IA-derived tail witnesses; they are not a global tail audit. R562 uses best-available GDZ full-page JPG witnesses around native 400 ppi plus magnified crops for Paper 40 printed pp.530-535. Earlier Paper 31, Paper 32, Paper 34, and Paper 40 source-repair layers still carry their own witness caveats. All such repairs should therefore be treated as best-available source-control evidence, not final high-resolution certification. Survival audit cluster. File 114 Noether - R124plusP40 Survival NoNewPatch Audit Cluster 2026-06-24.zip aggregates Papers 09-20 survival/no-new-patch checks for the current R124+P40 baseline. It preserves audit evidence that prior source-critical repairs and known no-fix traps survive; it does not introduce a new canonical TeX body patch and is not whole-paper or whole-corpus certification. Multilingual status. English, Spanish, Japanese, French, Chinese, Ukrainian, Russian, Interslavic, and other language branches are useful working translations, but remain downstream of the German/source audit line. The Slavic package is included as a work-so-far translation and linguistics lane, not source-certified closure. Language-lane handoff, 2026-07-02. A laptop Codex handoff branch, codex/laptop-noether-language-planning-20260701, was triaged as an evidence branch rather than merged wholesale. It reports Slavic Ukrainian/Russian/Interslavic Latin/Interslavic Cyrillic as review-ready maintenance/watch mode; French as locally cumulative through Paper 40 section 9 with Papers 41-43 plus post44, post45, and postbibliography still missing; Simplified Chinese and Japanese as local proof/render baselines with final public-edition promotion gates still open; and Arabic/Persianate as source-evidence only, with no cumulative Noether reader or final terminology authority. This is branch-handoff status, not a new Zenodo payload or edition-completion claim. GitHub mirror. Corrections, issue reports, and pull requests can be made through the public GitHub mirror. Local 2026-07-02 source-control status. The newest packaged local TeX-changing German source-control head is R569, with R570 as the latest packaged no-patch checkpoint. R569 builds on R568/R567/R566/R565/R564/R563/R562/R561/R560 and applies the p761 superscript repair plus the p764 subtitle repair. R570 checks pp767-772 and intentionally promotes no TeX patch. Treat R560-R570 as source-control candidates for curated rollup only, not reader releases, not Noether closure, not whole-corpus certification, not multilingual synchronization, and not critical editions. Rebased current Noether source-repair update. This version adds file 115, the current best local German cumulative TeX/PDF line after rebasing P35/P36/P38/P39 source repairs onto the R124+P40 baseline, and file 116, a narrow P34 p641/p660 hotspot no-new-patch disposition. These are working source-audit/provenance packages, not critical editions or whole-corpus certification; P35/P36/P38/P39 use best-staged 600ppi witnesses and P34/P40 still rely on best-available 400ppi GDZ witnesses where noted. Slavic translation/language-lane update. This version adds file 117, a public-safe Ukrainian/Russian/Interslavic/Interslavic-Cyrillic work-so-far package through Papers 01-33 and Paper 34 section 02. It includes cumulative readers, TeX, terminology logs, the Interslavic logbook, constructed-language reflections, infrastructure provenance, and audit metadata. Modern third-party reference PDFs used for terminology triangulation were deliberately excluded from the public package. Treat this as a rendered/audited working multilingual translation lane, not a critical edition or independent source-perfect certification. Public-safe cleanup note. The raw Slavic work-so-far ZIP previously staged as file 110 has been removed from the current version and replaced by the curated public-safe file 117. File 117 keeps the Ukrainian/Russian/Interslavic translation outputs and project logbooks while excluding modern third-party reference PDFs used only for terminology triangulation. Paper 30 source-repair update. This version adds file 118, a working source-repair package for Paper 30 printed pp. 46-48 and 53-54. It restores source-visible footnotes 27 and 28 and corrects the §9 Axiom IV display against best-available local IA/JP2-derived witnesses. The witnesses remain below the strict 650+ ppi final-certification floor, so file 118 should be treated as a source-confirmed working correction package, not as whole-paper or critical-edition certification. Paper 30 anchor-closed source-repair update. This version replaces the earlier file 118 with an expanded Paper 30 working source-repair package. The new file 118 retains the footnote 27/28 and section 9 Axiom IV repairs, adds the source-style printed p. 61 received-date repair, and records visual dispositions for the remaining Paper 30 OCR-anchor failure pages. The witnesses remain below the strict 650+ ppi final-certification floor, so this is a working repair and disposition package rather than whole-paper or critical-edition certification. Post-R124 survival rollup. This version adds file 119, 119 Noether - PostR124 Survival Rollup NoNewPatch Audit 2026-06-24.zip. It collects compact Local Codex survival/no-new-patch results checked against the latest local R124-plus current candidate. It is an audit/status layer: most entries confirm that earlier repairs survive or that source-quality blockers remain, rather than introducing a new canonical TeX body patch. It is not whole-paper certification, whole-corpus certification, or a critical edition. Local R128 Deuring pp.735-746 disposition. A new local package, Noether_R128_LocalCodex_Deuring_pp735_746_SourceAudit_NoPatch_WebDrop_20260626.zip, records a no-patch source-audit disposition for collected pp.735-746. It carries the pp727-734-fixed cumulative forward unchanged and adds page-level dispositions, no-fix traps, source mapping, OCR locator text, and 650/1000dpi legibility witnesses. Native source remains about 360ppi, so this is not Deuring tail closure, not strict high-resolution certification, not Noether closure, not multilingual synchronization, and not a critical edition. Local PostR128 current-base/tail-queue rollup. A new local package, Noether_R128_LocalCodex_PostR128_CurrentBase_TailQueueRollup_WebDrop_20260626.zip, selects cum_de_R128_plus_LocalCodex_AllKnownLocalFixes_Deuring_p735_746_nopatch_20260626.tex as the current German base until superseded and reconciles stale R128 queue rows against the later LocalCodex tail work. It intentionally excludes bulk source images and is routing/status metadata only: not source closure, not Noether corpus certification, not multilingual synchronization, and not a critical edition. Local P15 Batch22 source-fix update. A new local package, Noether_R128_LocalCodex_P15_SourceAudit_Batch22_pp138_143_SourceFix_WebDrop_20260626.zip, applies seven targeted Paper 15 German cumulative repairs over true visible printed pp.138-143 and records the source-map warning that local labels p140-p145 correspond to those visible pages. GDZ source images are tagged 400ppi, with 1000ppi crops used only as legibility aids. This is targeted source-audit repair evidence only: not Paper 15 closure, not Noether corpus certification, not multilingual synchronization, and not a critical edition. Local P15 Batch23 source-fix update. A new local package, Noether_R128_LocalCodex_P15_SourceAudit_Batch23_pp144_150_SourceFix_WebDrop_20260626.zip, applies two targeted Paper 15 German cumulative repairs over true visible printed pp.144-150 after checking pp.144-147 with no source-certain patch. It restores source spelling inbezug on p148 and expands the pp.149-150 passage from a compressed generic lambda-stage paraphrase to the printed xi_34^2 F_2 / F_2 null-degree step. Local labels p146-p152 correspond to visible printed pp.144-150. GDZ source images are tagged 400ppi, with 1000ppi crops used only as legibility aids. This is targeted source-audit repair evidence only: not Paper 15 closure, not Noether corpus certification, not multilingual synchronization, and not a critical edition. Local P15 Batch24 source-fix update. A new local package, Noether_R128_LocalCodex_P15_SourceAudit_Batch24_pp151_154_SourceFix_WebDrop_20260626.zip, applies three targeted Paper 15 German cumulative repairs over true visible printed p151 after checking pp.152-154 with no source-certain patch. It restores source i_\sigma throughout the normalization-product block, corrects P^{(1)} to source P^{(l)}, and restores the final congruence chain ending S_0^{(j)} \equiv F_0(\xi_{ik}) in TeX form. Local labels p153-p156 correspond to visible printed pp.151-154, while local p138/p139 are preceding non-Noether pages. GDZ source images are tagged 400ppi, with 1000ppi crops used only as legibility aids. This is targeted source-audit repair evidence only: not Paper 15 closure, not Noether corpus certification, not multilingual synchronization, and not a critical edition. Local P15 Batch25 source-fix update. A new local package, Noether_R128_LocalCodex_P15_SourceAudit_Batch25_pp155_156_SourceFix_WebDrop_20260626.zip, applies one targeted Paper 15 German cumulative repair over true visible printed p155: formula (1) restores the printed multiplication dot after 1/h before the summation. It checks p155 formulas (2)-(3) and surrounding prose plus p156 formula (4), basis statement, conjugate-coefficient paragraph, and closing sentence with no source-certain patch. This package uses the P15-specific GDZ source folder for true pp155-156. GDZ source images are tagged 400ppi, with 1000ppi crops used only as legibility aids. This is targeted source-audit repair evidence only: not Paper 15 closure, not Noether corpus certification, not multilingual synchronization, and not a critical edition. Local Paper 34 Batch30 source-repair staging. A new local package, Noether_R128_LocalCodex_P34_Batch30_pp652_657_SourceFix_WebDrop_20260626.zip, continues the targeted German Paper 34 source pass through printed pp.652-657. It restores p653 source > relation signs, p653 \simeq isomorphism signs in composition-factor/direct-product loci, and the p655 footnote-12 item-3 anchor, while checking pp.652, 654, 656, and 657 without source-certain patch. Source witnesses are GDZ Math. Z. 30 raw full-page JPGs identified as 400 ppi, with targeted crops upscaled only for legibility. Treat this as best-available targeted repair/provenance evidence only: not whole-Paper-34 certification, not Noether corpus closure, not multilingual synchronization, and not a critical edition. Local Paper 34 Batch31 source-repair staging. A new local package, Noether_R128_LocalCodex_P34_Batch31_pp658_663_SourceFix_WebDrop_20260626.zip, continues the targeted German Paper 34 source pass through printed pp.658-663. It restores the p658 source footnote marker for note 13 after the displayed equation e_i^2 a_i=e_i a_i=0, moves the matching footnote text to the source-adjacent locus, and corrects p661 Jeder zweiseitige Zerlegung to source Jede zweiseitige Zerlegung. Source witnesses are GDZ Math. Z. 30 raw full-page JPGs identified as 400 ppi, with targeted crops upscaled only for legibility. Treat this as best-available targeted repair/provenance evidence only: not whole-Paper-34 certification, not Noether corpus closure, not multilingual synchronization, and not a critical edition. Local Paper 34 Batch32 source-repair staging. A new local package, Noether_R128_LocalCodex_P34_Batch32_pp664_669_SourceFix_WebDrop_20260626.zip, continues the targeted German Paper 34 source pass through printed pp.664-669. It restores the p666 source footnote marker 13a) at the matrix-unit construction proof, corrects p667 a_{ij} to source a_{ii} in the construction of K, restores the p668 source footnote marker 14) and Artin footnote, corrects the final section 14 theorem formula to \alpha'\mapsto x^{-1}\alpha x and c'_{ik}=x^{-1}c_{ik}x, and restores the p669 source footnote marker 15) at the section 15 title. Source witnesses are GDZ Math. Z. 30 raw full-page JPGs identified as 400 ppi, with targeted crops upscaled only for legibility. Treat this as best-available targeted repair/provenance evidence only: not whole-Paper-34 certification, not Noether corpus closure, not multilingual synchronization, and not a critical edition. Local Paper 34 Batch33 source-repair staging. A new local package, Noether_R128_LocalCodex_P34_Batch33_pp670_675_SourceFix_WebDrop_20260626.zip, continues the targeted German Paper 34 source pass through printed pp.670-675. It restores displayed formula (1) structure and source-style homomorphism arrows on p670, restores the omitted continuation of correction footnote 15a) on p671, restores source operator-homomorphism notation and the bracketed equality in the multiplier-ring rule on p672, corrects the reducible-representation submodule notation from earlier \mathfrak U drift to source \mathfrak A across pp.672-674, and restores the block display labelled (3) on p674. The p675 source page is staged for continuity, but no separate p675 targeted repair is claimed in this wrapper. Source witnesses are GDZ Math. Z. 30 raw full-page JPGs identified as 400 ppi, with targeted crops upscaled only for legibility. Treat this as best-available targeted repair/provenance evidence only: not whole-Paper-34 certification, not Noether corpus closure, not multilingual synchronization, and not a critical edition. Local Paper 34 Batch34 source-repair staging update. A newer local package, Noether_R128_LocalCodex_P34_Batch34_pp676_682_SourceFix_WebDrop_20260626.zip, supersedes the narrower pp.676-681 Batch34 package and continues the targeted German Paper 34 source pass through printed pp.676-682. It restores source material across pp.676-682, including the p676 finite-subfield representation/block-matrix proof, the closing §18 Bemerkung, the compressed §19 theorem/proof/corollary/double-module block, the §20 title Einordnung, the explicit representation construction, the Burnside and generalized Burnside theorem/proof blocks, the no-radical/fully reducible and regular-representation/group-ring specialization paragraphs, and the p682 barred-symbol footnote 18a. Source witnesses are GDZ Math. Z. 30 raw full-page JPGs identified as about 400 ppi, with crops upscaled only for legibility. Treat this as best-available targeted repair/provenance evidence only: not whole-Paper-34 certification, not Noether corpus closure, not multilingual synchronization, and not a critical edition. Local Paper 34 Batch35 source-repair staging update. A new local package, Noether_R128_LocalCodex_P34_Batch35_pp683_686_SourceFix_WebDrop_20260626.zip, continues the targeted German Paper 34 source pass through printed pp.683-686. It carries the current cumulative German TeX/PDF/TXT, a sourcefix diff from the previous Batch34 base, p683-p686 source witnesses, render checks, and XeLaTeX logs. The diff reworks the center-representation theorem block, first-kind field-extension criterion, systems-without-radical application, Abelian-group/character section, and system-determinant section. Source witnesses are GDZ Math. Z. 30 raw full-page JPGs, about 400 ppi by continuity with the adjacent Paper 34 witness set. Treat this as best-available targeted repair/provenance evidence only: not whole-Paper-34 certification, not Noether corpus closure, not multilingual synchronization, and not a critical edition. Local Paper 34 Batch36 source-repair staging update. A newer local package, Noether_R128_LocalCodex_P34_Batch36_pp687_688_SourceFix_WebDrop_20260626.zip, continues the targeted German Paper 34 source pass through printed pp.687-688 / section 24. It carries the current cumulative German TeX/PDF/TXT, a repaired span TeX, a sourcefix diff from the previous Batch35 base, confirmed-fixes and visual-disposition ledgers, p687-p688 source witnesses, render checks, and XeLaTeX logs. The package repairs the trace definition, reducible trace block, Hauptspur/reduzierte Spur formulas, character/homomorphism relation, and representation-class proof. Source witnesses are GDZ Math. Z. 30 raw full-page JPGs, about 400 ppi by continuity with the adjacent Paper 34 witness set. Treat this as best-available targeted repair/provenance evidence only: not whole-Paper-34 certification, not Noether corpus closure, not multilingual synchronization, and not a critical edition. Local Paper 34 Batch37 source-repair staging update. The current local package, Noether_R128_LocalCodex_P34_Batch37_pp689_692_SourceFix_WebDrop_20260626.zip, supersedes the transient no-delta p689-p692 source-witness observation. It is now a short-path applied source-fix package for Paper 34 printed pp.689-692 / sections 25-26 through the end of Paper 34. It carries cumulative German TeX/PDF/TXT, repaired span TeX, confirmed-fixes and visual-disposition ledgers, p689-p692 GDZ source witnesses, rendered QA pages, build logs, and provenance. Reported repairs include the basis-change direction and trace-matrix proof with P and \widetilde P, the nilpotent-ideal determinant block, the direct-sum discriminant proof, an editable matrix-ring product table, completion of footnote 22, the group-ring trace proof, the class-sum/center derivation, and the final character relation \chi(K_i)=h_i\chi(a_i). Source witnesses remain best-local GDZ Math. Z. 30 JPGs below the preferred 650+ ppi floor, so treat this as targeted German source-repair/provenance evidence only: not whole-Paper-34 certification, not Noether corpus closure, not multilingual synchronization, and not a critical edition. Interlanguage methodology companion. The Ukrainian/Russian/Interslavic and constructed-language methodology/logbook apparatus has a separate companion record at 10.5281/zenodo.21124403. That record is methodology/provenance material, not a Noether reader release, native-speaker approval, term approval, mathematical source certification, language synchronization proof, or a critical edition. July 2 correction note. An earlier metadata refresh incorrectly described R564 as a mistaken nonpromotion. That status was reversed after rereading the p731 source witness: the source uses x-family variables, so R564 is a valid source-control predecessor beneath R565.