Error Confinement — Bruhat–Tits Error Suppression Demo

How to use this demo (click to collapse)

Prime buttons — choose the branching factor p of the Bruhat–Tits tree (2, 3, or 5).
Depth slider — how many levels deep to build the tree (1–6).
Inject error — toggle error mode, then click any node to inject an error at that node.
Tree geometry tab — see the full tree; the error subtree is shown in red.
Confinement analysis tab — bar chart of subtree sizes by injection depth (proves confinement).
Reset — clear all selections and errors.

Effective prime p (branching factor)

Tree depth d

Current depth: 3

Controls

Key equation (strong triangle inequality)

d(x, z) ≤ max{ d(x, y), d(y, z) }
Ultrametric property: error cannot leak outside the infected subtree

Live metrics

Total nodes

Tree depth

Error at depth

—

Nodes affected

—

Nodes safe

—

Confinement %

—

Key insight — verify it yourself

In an Archimedean (Euclidean) space, an error at node v could potentially affect any other node — sibling, parent, or distant cousin — because triangle paths can connect everything. In an ultrametric space (Bruhat–Tits tree), the strong triangle inequality locks the error inside the subtree of v. Click nodes at different depths: the shallower the error, the larger the affected subtree. A leaf error affects only itself (perfect confinement). This property makes p-adic QEC codes exponentially more efficient at suppressing cascading errors.

Source: QWAV A1 · DOI 10.5281/zenodo.20134944

Root (L)

Selected node

Error source

Affected subtree

Safe (confined)