Research library

Findings, working logs, tools and theory. Everything measured is published with the script that produced it and the hardware it ran on; anything not yet measured is filed under Theory and labelled as such.

Findings 11

Measured results, with the number and the method.

Three coupled rings compute a multiplexer in one settle when inputs and readout are continuous

No winding numbers anywhere. Inputs are frequency drives, the readout is one phasor and one straight line. Phase noise up to σ = 0.6 is erased exactly; continuous noise during the settle costs a few percent.

2026-10-11ring-logicoscillatorscoupling

An int8 dot-product kernel takes the engine to 5.3 tokens per second on four ARM cores, output unchanged

Two changes take the CPU engine from 2.9 to 5.3 tok/s on a four-core ARM server with no GPU: one bit-identical, one that leaves greedy output and perplexity unchanged. llama.cpp is still about 1.5× faster on the same machine at equal precision.

2026-10-11inferencearmint8

One-ring winding logic holds under a slower integrator, but its full coverage needed an instruction we do not have

A 16-oscillator ring computes up to 256 of the 256 three-input functions — but only with a write that subtracts. With the +1-only write the instruction set actually defines, the multiplexers disappear.

2026-10-10ring-logicoscillatorswinding-number

Once rings are coupled, the winding number is no longer the state

Two register rings and an output ring, coupled site to site. Kicks on the output ring copy a chosen register, but one winding triple hides up to four distinct attractors, so a winding-number table stops predicting what the machine does.

2026-10-10ring-logicoscillatorscoupling

Lenses alone do not make a one-ring multiplexer survive noise

Twenty-nine thousand lens configurations at one to three sites. The best late-selector multiplexer survives 21 of 32 noisy trials per step, and the settings that reach it are isolated points.

2026-10-10ring-logicoscillatorslens

The activation subspace is not low-dimensional

A 41-token probe suggested 16-28 dimensions of 3072. At 318 tokens it is 161-183. The dimensionality tracks the sample, not the model.

2026-08-16ranksubspacenegative-result

The 17th oscillator — an antagonist that prevents synchronisation

A central repeller that pushes every ring node away while fleeing their mean phase. Mode collapse solved by making the fixed point unreachable rather than removing it.

2026-08-16oscillatorskuramotomode-collapse

Ternary weights do not survive, and per-column scaling does not rescue them

46% of the output is lost on a single matrix. The scale can carry the exponent, but ternary discards the mantissa entirely.

2026-08-16ternaryquantisationnegative-result

SwiGLU has no exploitable contextual sparsity

Half the FFN channels carry 90% of the magnitude and the active set churns 70-90% per token. The published wins for this technique are on ReLU models.

2026-08-16sparsityswiglunegative-result

Quantisation fidelity is a property of bit width, not of the model

Llama-3.2-3B and Gemma-4-12B agree to three decimal places at every bit width tested, including on a model trained quantisation-aware.

2026-08-16quantisationint8ternary

Massive activations invalidate naive rank measurements

Removing 8 channels out of 3072 moves measured effective rank from 1.1 to 15.0. Any compression analysis that skips this step will conclude the model is rank-1.

2026-08-16methodsactivationsrank

Logs 2

Working sessions: what was tried, what failed, what was decided.

Two days of ring-logic experiments, including everything that failed

From "which Boolean functions can one oscillator ring compute" to a multiplexer in one settle. Three retractions, one bug in our own instrument, and the decision to stop treating winding numbers as the state.

2026-10-11ring-logicoscillatorsretraction

A night of CPU inference work, including everything that failed

Ten hypotheses, three survivors, one benchmark claim retracted. The honest version of an optimisation session.

2026-08-16inferencecpuoptimisation

Code 3

Tools and implementations, and what each is for.

The Consensus ALU as a SystemC hardware model: bit-exact with the browser original, and three bugs the port found

A programmable 16-bit pipeline, first built as a browser page, now runs as a SystemC/TLM-2.0 model that reproduces the original bit for bit. Porting it exposed three bugs in the original, one of which leaked the master key; all three are fixed, tested and published with the source.

2026-10-17systemchardware-modelreproducible

Emergence from local rules: Conway's Life and the elementary automata

Two families of cellular automata, each defined in a sentence or two, produce travelling gliders, guns, fractals, randomness and universal computation. An interactive page runs both in the browser, and every number quoted here is measured by the same code.

2026-10-17cellular-automataemergenceeducation

Six measurement tools that need no GPU

Each answers a question usually guessed at, reads weights directly, and runs on a CPU in seconds to minutes.

2026-08-16toolsopen-sourcereproducible

Theory 1

Arguments and models. Marked clearly as not yet measured.

The forward pass is one fixed point, and two solvers agree exactly

Jacobi and Gauss-Seidel converge to identical logits, error 0.000e+00. A structural result about transformers, with no speed claim attached.

2026-08-16equilibriumDEQarchitecture