Topological Fan-Out

A CAELIX 3D thin-slab experiment in Sine-Gordon kink splitting through a symmetrical T-junction

Run Experiment

Open the live browser experiment as a single-run view.

What Is It?

This experiment runs a CAELIX Sine-Gordon wire system through a 3D thin-slab T-junction. The visible image is a mid-plane cross-section, but the field itself is evolved as a masked 3D lattice.

A planar +2π kink wall fills the trunk cross-section and travels along the wire. When it reaches the junction, the wall pours into both branches and produces matched outputs. The result is a topological fan-out event rather than a painted split.

Why 3D Matters

In 3D, the kink wall is a two-dimensional plane filling the wire cross-section. At the T-junction, the two branches extend co-planar with that wall, so the wall can divide into both branches at once.

This is not a decorative distinction. In a true 2D reduction, the kink is a one-dimensional line orthogonal to the branch openings. That geometry reflects instead of splitting. The fan-out therefore depends on the third dimension even when the browser renders only the middle slice.

How It Works

The domain is a masked 3D slab with a carved wire geometry: a horizontal trunk, a diamond launcher and two vertical branch outputs. The current browser version renders the central z slice while preserving the 3D kernel contract.

Inside the wire, the Sine-Gordon stiffness is low enough to permit propagation. Outside the wire, the stiffness is high, so the exterior behaves like an acoustic mirror. Masked cells are clamped dead, while unmasked neighbours evolve through a local six-neighbour Sine-Gordon update.

The kink is initialised as a moving planar wall using a finite-shift velocity approximation. Detectors near the input and two branch outputs measure arrival strength and symmetry, giving the experiment a basic split diagnostic rather than just a visual result.

What It Tests

The experiment tests whether a topological field object can pass through a branching geometry and divide into matched outputs without explicit routing logic. The geometry supplies the junction. The local field update supplies the propagation. The split is allowed to succeed or fail.

The A/B detector traces and peak bars measure branch symmetry. If one branch dominates, if both fail, or if the incoming wall reflects, the geometry and parameters are wrong. The useful result is a balanced fan-out with a measurable branch pair.

What Is Not Hard-Coded

No branch routing rule chooses the outputs.
No 2D shortcut is used for the junction mechanism.
No final branch pattern is painted into the renderer.
No eigenmode or path solver directs the kink.
No manual clone of the pulse is placed in the branches.

The split must be produced by the 3D masked geometry, the Sine-Gordon kernel and the incoming topological wall.

Why It Matters

Topological fan-out is a useful stress test because it exposes a failure that flat 2D intuition can hide. Some structures only behave correctly when the object and the junction share the right dimensional geometry.

For CAELIX, this makes the experiment a bridge between browser-visible field dynamics and later 3D substrate work. It shows why thin-slab experiments can be valuable when they preserve the correct stencil and geometry, and why a simple 2D replacement would be the wrong experiment.