# Joint Dirac and actual graph phase

Original mathematical figure and generator expression: CC0 1.0. No external image, text, font bytes or glyph outlines are incorporated. Installed renderer and viewer fonts retain their terms.

Run `python -B generate.py --output-dir generated`, then `node render.cjs generated` using existing Playwright and Chromium installations. Optional PLAYWRIGHT_MODULE and CHROME_EXECUTABLE select those installations. No runtime is bundled.

Exact proof: Theorem 11BO.1, DJ.7–DJ.33, Exercises 297–299. The auxiliary and normal terms share one positive speed. Actual multiplication and completed domain correction return to the original transversal. The full graph carrier has the concrete bounded phase P(1 tensor F_A0)P, compact creation errors and the inverse normal Clifford packet limit. The original positive disk pairing is +1. In the two-copy counterexample, x_n=lambda_n^(-1/3), bump width is comparable to x_n and coefficient is x_n^2; the two auxiliary contribution norms are comparable to x_n and 1. These are estimates, not equality claims or an unbounded compression theorem. Human source: Connes's graph-normal question, credited in the lesson.