Four around a U,
with an X in it.

One fold, drawn once and run everywhere: take an axis through the origin, invert it, and the space folds into four mirror regions around a basin, meeting at a crossing, with a phase change at the seam. It is self‑inverse — do it twice and you are home. That single property is the corpus keeper axis, and it shows up at four wildly different scales.

Reading the fold

4 inverse‑mirrored — two pairs of regions (I↔III, II↔IV) swapped by the map (u,v)→(−u,−v). The violet arrow is that inversion.
U basin — the hyperbolae u·v = const: the throat, the well, the invariant every mirror preserves.
X — the bifurcation crossing at the origin, where all four regions meet and the fold has its fixed point.
phase change — the dashed seams (u·v = 0): cross one and a coordinate flips role — the signature swap.

∞

One fold — run for all four

The same self‑inverse structure, instantiated at four scales that share nothing else. Each row is verified on the real i13 compiler.

Scale · spacetime

The wormhole

The maximally‑extended Schwarzschild (Kruskal) diagram: our exterior, a mirror exterior, and two interiors, joined by an Einstein‑Rosen bridge.

mirror(u,v)→(−u,−v) basinu·v preserved → 6 = 6 Xthe bifurcation point phasehorizon: r & t swap

Scale · the corpus

The five worlds

The ud0 palindrome [ W1 | W2 ‖ W3 ‖ W4 | W5 ]. Reverse it: W1↔W5, W2↔W4, and W3 holds the axis.

mirrori → 4−i basinW3 the hallway → fixed point 2 Xthe ternary “:” axis phasebinary worlds → ternary

Scale · the genome

The CRISPR site

A restriction/palindrome site like GAATTC reads the same reversed‑and‑complemented — the enzyme’s mirror.

mirrorreverse & complement (b^1) basinthe cut axis → site = itself Xthe palindrome centre phasestrand → anti‑strand

Scale · the machine

The NES memory

2 KB of RAM appears four times in the address space — drawer 5 and drawer 2053 are one drawer, two labels.

mirrora → a % 2048 basin4 windows → one basin (0) Xthe bus decode phaseregion change: 2048 → 8

i13.exe run mirror_fold.i13 · VALID · 7 regions · 922 steps · depth 7

the fold, run for all four scales on the real compiler:
crispr_is_palindrome          = 1   GAATTC == revcomp(GAATTC)
crispr_self_inverse           = 1   revcomp(revcomp(s)) == s
world_axis                    = 2   W3 the U-basin fixed point
world_p1a / world_p1b         = 4 / 0 W1 ↔ W5
world_self_inverse            = 1   4-(4-i) == i for all i
nes_four_windows_one_basin    = 1   0,2048,4096,6144 → 0
kruskal_regions               = 4   four around the X
kruskal_basin_invariant       = 1   u·v = 6 under (u,v)→(-u,-v)
FOLD_IS_SELF_INVERSE          = 1   ← the one property, all four scales

Every line computed by i13.exe — David Lee Wise’s compIle 13 — not asserted. The keeper axis is self‑inverse: the fold is its own undo.

Why one glyph carries all four

A mirror through the origin is the simplest map that is its own inverse: f(f(x)) = x. That is exactly the corpus’s first keeper (a palindrome is its own checksum; a time‑reversible law retraces its path). So the wormhole’s (U,V)→(−U,−V), the palindrome’s i→4−i, the enzyme’s reverse‑complement, and the memory’s fold‑to‑basin are not four analogies — they are one operator wearing four costumes. Four around a U, with an X in it.