Reproduce Compact forms and the unshifted right cap
Read the complete lesson. The argument below uses the precise real CD034 and selected orientation/right-cap hypotheses. The finite support-preserving cup/wedge correction and compact top-form normalization construct form duality and identify its actual map with the unshifted right cap. With the corrected annular calculation in L126, this gives the real normal-first tube coefficient.
Exact original files and terms
The downloads contain the mathematical text, diagrams, exact coordinates and reproducible renderer. The original text and diagrams retain their CC0 dedication; MathJax and the supplied fonts retain their component licence notices. Human references and proof locators accompany the mathematical arguments.
Read the complete supplied proof in its current reader presentation. The complete separately supplied learner presentation retains all three worked examples and six solutions. The original downloads below remain exact.
- form-right-cap-comparison.md — 26419 bytes; SHA256
D18B94A5F17602654A167C149B742E5E1FA6C73FC2AEC20228CAEB375030E204. - learner.md — 14028 bytes; SHA256
002FD38AB9DBC58BE1A57996095C7678FE70E85198DC37A542E444F0F8549CC8. - make_figures.py — 6167 bytes; SHA256
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Fresh native reproduction
Keep make_figures.py in a fresh directory and run:
python -B -X utf8 make_figures.py --output fresh-figures
The renderer writes native PNG, SVG and exact geometry records. Check the complete original captions, coordinates, conventions and proof locators. The schematic and sampled figures explain the written proof. Different software or font versions may change rendering bytes.
The statements use the specified orientation, Thom and comparison hypotheses. Integral descent, rational-form spanning, the particular affine C8 representative, coefficient conventions and component constancy require their additional arguments. Exposition: GPT-6.1 Sol (OpenAI), Ultra, October 2026; CC0-1.0. L124 gives the projective-exhaustion context; L125 proves the geometric finite-chain H statement.