# Rung 1 Interpretation: What the Numbers Mean

**Date:** 2026-03-04
**Context:** First empirical results from the Continental Computation experiment.
Benchmark code at `rhombic/benchmark.py`. Raw data at `rhombic/RESULTS.md`.

---

## What We Set Out to Prove

That for isotropic workloads, the cube is not the optimal fundamental cell
for computation, and that replacing it with the rhombic dodecahedron produces
measurable, reproducible advantages.

## What We Proved

Exactly that, across four independent metrics, at three scales, with consistent
ratios. The FCC lattice is 30% more efficient at routing, 40% more resilient at
worst-case, and 2.4× harder to fragment — all from topology alone. No algorithm.
No optimization. Just the shape of the cell.

## Why the Consistency Matters

The ratios don't drift. 30% shorter paths at 125 nodes, 30% at 1000, 29% at
4000. This is not an empirical correlation that might break at scale — it's a
structural property of the tessellation. It will hold at a million nodes because
it derives from the geometry, not the sample. The experiment doesn't discover
the advantage; it makes the advantage *legible* to people who need numbers
before they'll consider changing a foundation.

## The Cost and Its Gradient

2× more edges sounds expensive until you ask what an edge actually *is* in
different domains.

In a physical network, an edge is a wire — real cost, real space, real power.
In a software data structure, an edge is a pointer — 8 bytes. In a memory
hierarchy, an edge is an adjacency relationship — it costs nothing until you
traverse it, and when you do, you arrive 30% sooner.

The domains where the cost is prohibitive (physical chip interconnect at the
smallest scales) are exactly the domains where the advantage matters most
(latency, bandwidth, fault tolerance). The domains where the cost is trivial
(software, data structures, logical topology) are exactly the domains where
adoption is easiest. This is a favorable gradient.

## What This Means for the Cybernetica Argument

The cultural genealogy — Descartes → von Neumann → cubic compute, parallel
to Mathers → GD → rectilinear esotericism — now has an empirical anchor.
We're not saying "the cube is a cultural artifact" as philosophy. We're
saying: here are the numbers, the cube costs you 30% of your routing efficiency
and 60% of your structural robustness, and the reason nobody noticed is that
nobody tested the alternative because the cube was the default assumption.

That's the Anglophone Bias chapter of Cybernetica, except now it has a
benchmark suite attached.

## What This Means for the Build

Every rung from here uses this library as substrate. Rung 2 (spatial
operations) will benchmark practical tasks — nearest neighbor, range queries,
flood fill — on both topologies. If the 30% routing advantage translates to
30% faster spatial queries, that's a drop-in replacement for cubic grids in
game engines, physics simulations, molecular dynamics, medical imaging. Not a
research prototype — a library someone pip-installs and uses because it's
faster.

Rung 3 (signal processing) will directly measure FCC vs cubic spatial sampling
with a topology-agnostic reconstructor — empirical evidence for whether the
geometric advantage translates to signal fidelity.

Rung 4 (context architecture) is the ambitious one — but by then we'll have
three rungs of proven code underneath it.

## What This Means for Promptcrafted and TASUMER MAF

This is a publishable result. Not in a top-tier venue yet — the graph theory
is elementary and the advantages are mathematically inevitable — but as a
technical report, a blog post, a demonstration, it establishes Promptcrafted's
credibility in a space where nobody else is asking this question.

The Cybernetica framing (Ashby, Beer, Bateson) elevates it from "obvious
graph theory" to "here's why this matters and here's why the default
assumption persists." That's the consulting thesis: the systems you built
aren't optimal, and the reason they aren't optimal is a cultural inheritance
you've never examined. We can show you the numbers. We can show you the
alternative. We can build it for you.

## The Sleeper: Algebraic Connectivity

Average path length and diameter are intuitive — more connections, shorter
routes, everyone gets that. But the Fiedler value measures something deeper:
**how much variety the topology can absorb before it fractures.**

This is Ashby's Law of Requisite Variety made geometric. The cube can absorb
perturbation along 6 axes. The rhombic dodecahedron can absorb it along 12.
The ratio isn't 2× (12/6) — it's 2.4×, because the isotropy of the FCC
lattice compounds the per-node advantage. The system is more than the sum of
its connections.

That's the cybernetic insight: it's not just more wires, it's a qualitatively
different kind of robustness. Beer would recognize it immediately as the
difference between a fragile hierarchy and a viable system.

---

*Interpretation written 2026-03-04. First empirical record of the Continental
Computation experiment.*
