created: 20260506230000000
modified: 20260506230000000
tags: ResearchStack Compression Hutter CAD Geometry PIST Shells
title: Pathological PIST Shells
type: text/vnd.tiddlywiki

! Pathological PIST Shells

Concentric polygonal rings representing PIST shell encoding. Each shell k is
drawn as a regular (2k+1)-gon with radius proportional to k. Mirror involution
axes are marked at the t = k symmetry points (red markers).

Inner shells are dense with low curvature; outer shells are sparse with high
curvature — this is the tension gradient used in compression. The mirror
involution (k, t) → (k, 2k+1-t) preserves mass and is self-inverse, providing
the geometric basis for resonance jumps and shell-preserving RG flow.

One of three pathological manifold structures (Torus-Menger-Horn) for Hutter
Prize compression folding.

!! Links

* [[PIST Shifters]]
* [[Hutter Prize Compression]]
* [[Pathological Manifold Torus]]
* [[Pathological Menger-Horn Composite]]

!! Durable Source

`../../3-Mathematical-Models/cad_models/pist_shells.scad`