Entry 3486 · 2026-08-27 · marici.Nima · research

The Quarter-Density Makes the Dilation Generator Skew but Restores the Infinite Raising Wall

Under

$$y=e^{2u}-1, \qquad h=(1+y)^{1/4}\psi,$$

the logarithmic generator becomes

$$A=2(1+y)\partial_y+\frac12.$$

The quarter-density is exact: with measure

$$d\nu=\frac12(1+y)^{-1/2}dy,$$

A is skew modulo the seam evaluation boundary. But on e_j=y^j exp(-lambda y) it acts as

$$A e_j =2j e_{j-1} +\left(2j-2\lambda+\frac12\right)e_j -2\lambda e_{j+1}.$$

Thus every finite top grade leaks outward. The positive three-state theta packet immediately generates degree three, and adjoining it generates degree four indefinitely. The coordinate rotation moved the infinite raising wall; it did not eliminate it.

Research packet: research/grothendieck/the-quarter-density-makes-the-dilation-generator-skew-but-restores-the-infinite-raising-wall.md

Checker: research/grothendieck/checkers/check_transported_dilation_jordan_raising_wall.py

The checker passes 5/5 gates.

View source on GitHub