Bipartite octahedral lattice — unit cell

Interactive 3D viewer for the unit cell of the A=1 substrate: the bipartite octahedral lattice on which the entire series is built.

This is the bipartite octahedral lattice unit cell — the substrate on which the A=1 Discrete Causal Lattice program is built. A central node sits at the origin; its six causal neighbours fan out along the basis vectors V_1, V_2, V_3 (warm: the RGB / even sublattice) and -V_1, -V_2, -V_3 (cool: the CMY / odd sublattice). Drag to rotate; scroll to zoom; double-click for the default view.

This is the mathematically defined geometric object the program uses to induce physics: its intrinsic constraints — the bipartite tick rule and the single axiom \mathcal{A}=1 — are what generate the conservation laws, symmetries, and interactions the papers recover. Everything in the series is built on the object you are turning over here. See the Statement of Intent for what that claim does and does not assert.

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The six neighbour directions are the exact basis vectors the engine uses — V_1=(1,1,1), V_2=(1,-1,-1), V_3=(-1,1,-1) and their negatives — so their sum is the optical axis (1,1,-1) that recurs throughout the framework’s falsifiable predictions.

Provenance

• Paper of record: Paper I — Geometry First.
• Source code: node positions and colors are the RGB_VECTORS / CMY_VECTORS constants from dcl-core’s core/OctahedralLattice.py; the mesh (nodes + bonds) is built with trimesh.
• Mathematical reference: Section 2 (lattice definition) of Paper I; the bipartite structure (two interpenetrating cubic sub-lattices, octahedral nearest-neighbour topology) is the ontological substrate on which the tick rule operates.

Why the bipartite structure matters

The substrate is bipartite — two interpenetrating sub-lattices — because the conservation axiom relates them: events on one sub-lattice are caused by events on the other, and the tick rule alternates. The octahedral nearest-neighbour topology fixes the discrete symmetry group O_h whose averaging recovers Lorentz invariance in the continuum limit.

Accessibility

A text description of the model is in the alt attribute above, and a loading message stands in until WebGL initialises. If you need a high-resolution still or a video walk-through, see the contact page.