Reproduce the rational-period diagrams
The complete lesson contains the full learner and full PR1–PR31 formal proof, including all twelve sections, three examples and six complete solutions in each original. It preserves ordinary/integral/field conventions, dimensional endpoints and the conditional general receiver.
Download the unchanged original files
The eleven original files below are byte-identical to the PR036 inputs. LICENSE.txt identifies the original-work dedication and retained component terms. The proof and learner downloads are full Markdown documents.
- geometry.json — 2481 bytes; SHA-256
0DE6E8D9A59DAE9470B5DD648E6217907FBEC6CA3E39BCDF8AABBA5A495E21FE. - normal-tube-phase-map.png — 79655 bytes; SHA-256
D1A96575118FAEBAA542ED1CBE7D26AD143A5F123B3E57868F0D7B1B3641B72D. - normal-tube-phase-map.svg — 55365 bytes; SHA-256
278EB3E172E1419FFEA4000D3C9ECB806BCDC27B8031E7ADFA477494C7F373AD. - period-basis-and-tube.png — 87673 bytes; SHA-256
A9A57AD43E236F837CC3FE6F68155E826D7EBF261449C5B27D4A48101B411B1F. - period-basis-and-tube.svg — 67642 bytes; SHA-256
4C2111D54A34FC4F2CACA3BDE96E91860B9D56F9615348999A09789BC8B1C542. - punctured-plane-cover.png — 104910 bytes; SHA-256
F61781F8E37EAAE7BCC8568E3922F2E522836EBE52B409DA60611590C9316524. - punctured-plane-cover.svg — 70997 bytes; SHA-256
CCF13AC430ECA29D7DD273E3C6E36334ADC0ACACC844176DF308E45BEEB7A450. - make_figures.py — 8984 bytes; SHA-256
36E8159FFCDB54ED6B021345E73069E0CFA3FC546889AFA15D2C559E3ECC4771. - projective-rational-periods-learner.md — 43141 bytes; SHA-256
D70634480BC947E33D5DD7F9E1B63C9AD68F9BAF760CDDE078BA27FD493EB7CF. - projective-rational-periods-working-proof.md — 38481 bytes; SHA-256
6D5AF96EE82B097A8BDF1A1A167BAE39C1C9A023096BAC4CE0778794254E4B06. - README-reproduce.md — 1298 bytes; SHA-256
7ADA00D0AB96319F3D895868E626EAB182CFD8225C65B7BADDC0E52D226A7B52. - LICENSE.txt — 390 bytes; SHA-256
747209EC407251B30C50DA5809DBF1C3CB25E50774FFEAEA98D575D4F3FC8FFA. - CURRENT-SCOPE.txt — 1083 bytes; SHA-256
52199F3D8AF3B2078D54CD6DC03209AB8914D28709D214C86B580F843216937B.
Run the portable renderer
Keep make_figures.py at the root of a fresh scratch directory and run:
python -X utf8 make_figures.py
The unchanged program creates figures/ and writes three PNG diagrams, three SVG files and geometry.json. Alternatively use --output-dir replay. A current fresh run with Python 3.13.9, NumPy 2.4.4 and Matplotlib 3.10.9, using its bundled DejaVu Sans font, matched all seven supplied files byte for byte and every decoded PNG RGBA pixel. No SVG date or identifier normalization was performed. Byte identity is qualified by that observed software/font environment; other versions may change rendering bytes. The geometry JSON records the mathematical objects independently.
Exact figures, proof locators and credits
Figure 1 is a window of the exact slit-plane cover for S={-1,1}, delta=0.65 and circle radius 0.45. It includes the actual integral intersection map of PR12, with left/right components and the positive-circle kernel vectors; PR2–PR3 and PR11–PR15 prove the chain statements. Figure 2 is the d=2 unwrapped phase map modulo 2pi, with actual columns (-1,-1) and (1,0), determinant +1, and normal circle first; PR21–PR24 specify every coordinate. Figure 3 is the complete normalized diagonal period matrix and separate primitive tube vector for Example 2; PR6, PR17, PR25–PR26 establish its entries. Full original captions remain in the learner and assembled reader. Each native PNG has an explicit full-size route.
The diagrams, geometry and renderer are original GPT-6.1 Sol (OpenAI), Ultra work, October 2026, CC0. Historical mathematical credits are Atiyah, Bott, Gårding, Grothendieck and Hatcher, with free primary source links and precise comparison limits retained in the full learner. The smooth comparison used is CD034. The general algebraic/Stein/duality route remains an explicit prerequisite, not a claimed new proof. Existing MathJax, Matplotlib and font/software terms remain included and unchanged. No book scans or source media are distributed.