Reproduce Compact supports, a closed submanifold and the normal circle
Read the complete lesson. The argument below uses the stated ordinary CD034 and selected tubular/Thom hypotheses. It proves the real compact closed–open sequence, its actual integration comparison and the annular normal-circle calculation. The complete earlier CO046 alternative is retained with its historical notation. L127 separately supplies normalized form duality and its unshifted right-cap identification. L128 separately constructs the rational coefficient comparison and rational connecting map.
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. This complete supplied source contains both its formal argument and all learner examples and solutions. The original downloads below remain exact.
- closed-open-forms-and-the-normal-circle.md — 37006 bytes; SHA256
6ACD5535541CE3B5366AC894790FEF875E09F7BC60D557CF9441A4D4C6A07CDA. - make_figures.py — 5715 bytes; SHA256
B5E83432AA048721D46CD391A397397C6883473CE23AF638D5ACD39396246932. - README.md — 848 bytes; SHA256
39F834D048710F2352E190E4D32AD4E3657EA7A4CB55835EEB24373C33E72CEB. - LICENSE-original.txt — 228 bytes; SHA256
1E3FE7B1326967B8D5F2B28ED3B049920E7E511EB5977CFB2D4CAEA599BA4A31. - figures/geometry.json — 1567 bytes; SHA256
F3306228C6A0C9F0797AEC52AC627443430CFB7EDE9099BA5D6EDE77DDF08293. - figures/kernel-complex-to-open-support.png — 145441 bytes; SHA256
39CE42439F3E5D11E8334EE26E2D80649333A41E33EC183BDDA746B5D36129B9. - figures/kernel-complex-to-open-support.svg — 55549 bytes; SHA256
E428B9C55452FECA2F0EB11B4FFA1E04B57B21C85D9697DE5B269B407F745C8D. - figures/radial-cutoff-and-normal-first-sign.png — 136314 bytes; SHA256
7156A01961E60CABF86164EE2CDCAE1C35EEF4F22F704C56F981ACAD9C24C9A2. - figures/radial-cutoff-and-normal-first-sign.svg — 61314 bytes; SHA256
D7CC121B14AD20EDB969E6F6C27C8431AC09A30EE73EB58FA174C31F57D437CD. - original-CO046-alternative/closed-open-forms-and-the-normal-circle.md — 37005 bytes; SHA256
9FCAF1A2859A17AB4918BCD925F6FF393E1B91E605039F775114B073664AED1B. - original-CO046-alternative/make_figures.py — 5715 bytes; SHA256
B5E83432AA048721D46CD391A397397C6883473CE23AF638D5ACD39396246932. - original-CO046-alternative/README.md — 848 bytes; SHA256
39F834D048710F2352E190E4D32AD4E3657EA7A4CB55835EEB24373C33E72CEB. - original-CO046-alternative/LICENSE-original.txt — 228 bytes; SHA256
1E3FE7B1326967B8D5F2B28ED3B049920E7E511EB5977CFB2D4CAEA599BA4A31. - original-CO046-alternative/figures/geometry.json — 1567 bytes; SHA256
F3306228C6A0C9F0797AEC52AC627443430CFB7EDE9099BA5D6EDE77DDF08293. - original-CO046-alternative/figures/kernel-complex-to-open-support.png — 145441 bytes; SHA256
39CE42439F3E5D11E8334EE26E2D80649333A41E33EC183BDDA746B5D36129B9. - original-CO046-alternative/figures/kernel-complex-to-open-support.svg — 55549 bytes; SHA256
E428B9C55452FECA2F0EB11B4FFA1E04B57B21C85D9697DE5B269B407F745C8D. - original-CO046-alternative/figures/radial-cutoff-and-normal-first-sign.png — 136314 bytes; SHA256
7156A01961E60CABF86164EE2CDCAE1C35EEF4F22F704C56F981ACAD9C24C9A2. - original-CO046-alternative/figures/radial-cutoff-and-normal-first-sign.svg — 61314 bytes; SHA256
D7CC121B14AD20EDB969E6F6C27C8431AC09A30EE73EB58FA174C31F57D437CD.
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.