Reproduce Projective exhaustion and the finite-chain tube receiver
Read the complete current learner and formal argument. Every worked example and all six complete solutions are retained.
Exact original files and useful complete alternatives
The complete programme context includes seven full source components and the complete selected manifold-duality §§1–3. All mathematical proof, formula and exercise bodies are preserved. Source-credit and scope paragraphs in three providers and the current main's provider notice are revised; their exact current byte counts and hashes are listed below. Every other non-HTML original file below retains exact bytes. Read the complete source index and original component terms. The original PSH source and its complete shell-corrected alternative are both retained; that unused wording repair does not admit the whole PSH course. The earlier TP main is retained as a historical alternative; its TP10 display lacked one backslash. Use the complete corrected main and current reader for that display.
- context/assets/mathjax/LICENSE — 11358 bytes; SHA256
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BBCAEDDB33E2D2D046EF737C9A629151BF3CEAF920FE978443670E7A5297700D. - context/figures/geometry.json — 16016 bytes; SHA256
4E6F6B0D5519E0DFDF3155B73486890979613ADDA5D0321F60D24E1F47D152E4. - context/figures/normal-first-tube-and-degrees.png — 111328 bytes; SHA256
5C856BC578BA1ED044B50FB8E40FA05F0A411AC85001D7D8C1CC0D4C23C24B5D. - context/figures/normal-first-tube-and-degrees.svg — 84625 bytes; SHA256
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E64C2CF9002551FB03565F8C8E3FCC5967764E0A73F1B16E31C151D8DBE34C00. - context/LICENSE.txt — 259 bytes; SHA256
5FB9AC6AA86AC075EBF6F1024013BB9BBFB2FD2E46E3F1F0268C0F2521D8955A. - context/make_figures.py — 4562 bytes; SHA256
C2743369E89A79E1CB9898B24B7DBBD3EF02DF3CCF79B5D9632F34D6875EDA49. - context/notices/LICENSE_DEJAVU.txt — 4816 bytes; SHA256
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96DC10389D3CFE7DD29D29A40A8077A1D86EB2ACB09ABD64881B6ABF33424976. - context/README-reproduce.md — 2390 bytes; SHA256
C16670E6CFEC08F3322C403838F4093BFA9C197CAA7C9F41447D9BD9DE1C4C36. - context/sources/cap-products-and-cohomology-with-compact-supports.md — 10745 bytes; SHA256
B9CEEA2F7AA6C8D7C9D458A8AF90116B6B3B04AB42ED6C13D28C849BA8EBBA91. - context/sources/holomorphic-morse-exhaustions-on-stein-manifolds.md — 26285 bytes; SHA256
B2AE35E343485EE9F019FDC6BCCB3BBE218EFDA9DD772E3C63077A2DF5E07BAD. - context/sources/manifold-duality-and-tubular-sections.md — 25074 bytes; SHA256
1FEBF39CD776742AFEAC433E65B0D1B262086CA8DFCE680B8441C444A20E2BB2. - context/sources/orientations-and-fundamental-classes.md — 14019 bytes; SHA256
36D163752EAD201E2F3D9AAF141A41658B37C7447E9618151ADAF80556B869A1. - context/sources/plurisubharmonic-functions-and-stein-manifolds.md — 12122 bytes; SHA256
D90D1BAE6888C3BED131E46040BF69F1DC05E31FE0C32C2775D2125770307CA5. - context/sources/poincare-duality.md — 8341 bytes; SHA256
6D8CF3476A087DEAC5FDBA857DACC32F87B0507C19C50FC6A797C995A9FB65CB. - context/sources/smooth-period-detection.md — 34358 bytes; SHA256
3441B8C9A77E21120E25C357F2B603A6D26F2D56A5A5415B04210C4FDE00AEF4. - context/sources/thom-classes-and-euler-classes.md — 41929 bytes; SHA256
1FBB1648DF1FF2D832E7FE2BDC61600F723BB30CFC58BDEB516071529494E61F. - original-main-alternative.md — 36090 bytes; SHA256
5A2B9036C2759C156AFF43D508A9F1DB9D48CD6B00C3146C73BDE53C288C44A0.
Fresh native reproduction
Use Python, NumPy and Matplotlib in a fresh scratch directory. Keep the renderer with its supplied README and licence.
python -B -X utf8 make_figures.py --out fresh-figures
Compare every PNG, SVG and geometry.json with the exact supplied outputs. Different library or font versions can alter bytes; exact coordinates, constants, signs, identifications and proof locators remain in geometry.json and the full captions. The figures are explanatory objects, not substitutes for the complete proof.
Credits and scope
Original TP041 and MH043 proof, diagrams and renderer: GPT-6.1 Sol (OpenAI), Ultra, October 2026, CC0-1.0. Original programme sources retain their precise Claude Opus5.5 or GPT-6.1 Sol credits and CC0 notices. Added orientation, current qualification and reader presentation: GPT-6.1 Sol (OpenAI), Ultra, October 2026, CC0-1.0. Valid human mathematical credits remain with the current sources. They do not license an external book body or establish proof closure. MathJax retains Apache-2.0; DejaVu and STIX retain their original font notices.
Geometric H is at the proper Morse, finite-chain and declared index entries. The selected Thom/tubular proofs retain their exact coefficient and manifold hypotheses. Lower analytic regularity, smooth perturbation, Sard, whole Stein/sheaf courses, rational form completeness and spanning, affine C8, full component constancy and recursive course closure are separate. L124 preserves the original conditional compact-support alternative and records the real comparison. L125 supplies the complete finite-chain handle proof.