Final Euler visual companion
The guide is an article-format companion to the main paper and Lean guide. Its 17 pages consist of the title page, contents, and 15 focused mathematical pages. The 12 figures are vector PDFs. PNG versions are supplied for layout QA.
From the release root, regenerate the exact illustration data and figures:
python3 sources/generate_figures.py
This executes 5,490 bounded exact assertions. Coefficients are formed by
factorial-series reciprocal convolution modulo 2^256 through row 255, with
independent rational ordinary-series inversion through row 12. Every plotted
residue is exact. The universal exponent curves and scale arrays come from the
separately proved theorems; their coordinates are theorem-derived integer
data, not a numerical proof.
The tested domains and all figure/data hashes appear in
figures/figure_manifest.json. Its schema-version-1 provenance limits are
explicit: it records the script hash but does not impose machine-readable
resource caps. No randomness is used. Matplotlib and NumPy are used only for
rendering, matrix storage, and page coordinates; the arithmetic assertions use
Python integers and fractions.Fraction.
Compile from the sources directory, repeating the second command until the
references and contents are stable:
pdflatex -interaction=nonstopmode -halt-on-error \
-jobname=Paper_IX_Euler_Visual_Guide_Final visual.tex
pdflatex -interaction=nonstopmode -halt-on-error \
-jobname=Paper_IX_Euler_Visual_Guide_Final visual.tex
The wrapper uses standard TeX Live packages and Latin Modern fonts. Figure
paths in the wrapper body are relative to the sources working directory.
The final PDF is delivered at
output/pdf/Paper_IX_Euler_Visual_Guide_Final.pdf.
The final layout review is recorded in audits/VISUAL_GUIDE_QA.json, with
rendered pages in audits/visual_pages/ and the contact sheet in
audits/visual_contact_sheet.png. The clean final compilation has no
overfull/underfull boxes, duplicate anchors, or undefined references.
The guide explicitly separates inherited Lean coverage of the original completion and rank-four ordinary-step/metric results from the new generic prime-power transfer, mixed-step, factorial, and analytic extension. It does not describe the latter as newly formalized in Lean.