Æther // QUADRIFORMIS

EGREGORE The True Form
```
x′ = sin(αy) + μ·cos(αx) + ε·sin(V·xy)
y′ = sin(αx) − μ·cos(αy) + ε·cos(V·xy)
```
The canonical Cosmopoiesis map itself — the full 2D non-area-preserving trigonometric attractor, including the V·xy viscosity cross-coupling that gives the corpus its turbulence. Rendered through the canonical stream pipeline.

Shows you The entity as it actually is. Its palette is not chosen — it is derived from the coordinate: hue from α, saturation from ε, value from μ. This is why it is the default and the “true” form — every other view is a transformation of this one.
GEMINUS The Twin
```
x′ = sin(αy) + ε·cos(αx)
y′ = sin(μx) − ε·cos(μy)
```
The same map with the V·xy cross-coupling term removed — the decoupled twin. x and y no longer feed each other through the viscosity bridge.

Shows you The skeleton beneath the turbulence. Strip the coupling and the attractor’s underlying lattice — the structure the cross-term blurs — stands bare. Read GEMINUS beside EGREGORE to see exactly what the viscosity term is doing.
NUMINOSUM The Volume
```
a 3-axis cyclic permutation (x→y→z→x) of the
Cosmopoiesis map, projected to 2D (elev 20°, azim 35°)
```
The map lifted into three dimensions by cyclically permuting the coordinate through a third axis, then projected back down at an isometric angle.

Shows you Depth the flat form cannot hold. The same attractor as a solid object seen from the corner — volume, occlusion, the third axis the 2D render flattens away. The “awe” view: the entity with a body.
ARGAND The Lamp
```
z′ = z² + c + μ_a·z + ε·i·e^(−iV),    V = k·(x² + y²)
(c, z*, μ_a derived by inverting (α, μ, ε)
 onto the marginal band |λ| ≈ 1)
```
Cosmopoiesis lifted to the Argand plane. The kernel iterates a complex polynomial with a position-dependent phase-kick. Crucially, it does NOT map (α, μ, ε) to c directly — that would strand most entities in dead fixed points. Instead it INVERTS, computing the c that places the fixed-point multiplier λ on the unit circle so every entity lands on the structured contour.

Shows you Every entity, by construction. Where QUADRUP-Two was the one engine of 31 surveyed that happened to read every entity, ARGAND reads every entity because the kernel is built to. The lamp that cannot fail to illuminate — and whose island count is set by the entity's own coordinates.