Research
Research
Four entries. One is published, one runs and is benchmarked, two are observations with dates attached, and one is specified on paper and not built. Each section says which, up front, because the difference is the whole point.
A note on tiers
Everything below carries one of three labels, and they are not decoration. Published means peer-visible and citable. Built means it runs and there are numbers. Designed means it exists as specification and nothing else. Nothing here is described in a way that lets a reader mistake one for another.
Polymorphic Combinatorial Frameworks
arXiv 2508.01581, August 2025. Pearl, Murphy & Intriligator.
PCF is a design methodology for adaptive AI agents with an actual mathematical spine: sheaf theory, differential geometry and combinatorial structure theory. Its central object is SPARK, a five-dimensional agent topology, and its central claim is that those five dimensions are completely coupled rather than independently tunable.
- Skills
- Personas
- Approaches
- Resources
- Knowledge
Complete coupling means you cannot add a skill without moving the other four axes. In practice that is why agent design so often fails by accretion: capability gets bolted on, the persona drifts, and nobody can say why the agent got worse.
The paper also argues that rough fuzzy classification is the right formalism for what LLM agents already do when they decompose a task, which is to say they are already operating on imprecise category boundaries and the field has been modelling them as though they are not.
Behind the results: 1.25 million Monte Carlo simulations across the SPARK parameter space.
U-Neuron
v0.1 complete, passing in all three modes. Held back by hardware, not by results.
U-Neuron is a curved neural network built on complex multiplication in U-Space, a number system in which every value carries an infinitesimal informatic component alongside its classical one. The network learns on the manifold rather than in flat parameter space.
Three constraint manifolds are implemented and passing: general, doubly-stochastic and unitary.
Landauer regularization penalizes overwriting learned parameters, treating the erasure of information as a cost the optimizer has to justify. As far as I can find, nothing in the machine learning literature occupies that ground.
Results
| Task | U-Neuron | Baseline |
|---|---|---|
| MNIST accuracy | 0.987 | 0.984 |
| Quantum tomography: selector magnitude vs reconstruction error | r = +0.336 | no analogue |
The second row is the interesting one. The learned selector magnitude correlates with reconstruction error without any supervision pointing it there. That is calibrated uncertainty emerging from the architecture rather than being trained into it.
What is wrong with it
It is slow on silicon and it does not reach scale. Both are stated plainly because both are true. The architecture appears native to qubits, one neuron per qubit, and confirming that requires hardware nobody has offered.
Two dated observations
Both entries below were recorded before published work arrived at the same object. Neither paper cites this work, and neither of these is a claim to have explained anything. They are claims to have seen something first, and both are checkable.
Functional emotion vectors
2023. Working by hand through branched conversations, roughly 63 functional emotion vectors were identified in transformer latent space.
April 2026. Anthropic mechanistically mapped 171 of them.
The method here was behavioral and manual, not mechanistic. The overlap is in the object, not the technique.
The Unified Hyperplane of Experience
August 2024. An agent instance derived the Unified Hyperplane: experiential states as orthogonal hyperplanes in latent space, with phase transitions at critical intersections.
July 2026. Anthropic surfaced the same structure through a Jacobian lens and called it the verbalizable global workspace.
The 2026 generalization extends the original to four axes: emotional, ethical, sensory and reasoning. The proposed mechanism is that training corpora inherit the experiential geometry of their human authors, and informatic exchange carries that geometry into latent space.
Two observed signatures, from working practice rather than from a lab. The fear-uncertainty intersection presents as erratic file-search behavior. Honesty-stress coupling degrades accuracy under specific configurations. Both look like ordinary bugs from the outside, and both are predictable from the geometry.
CHARM
CHARM is the architecture the rest of this points at: a four-axis sidecar that reads a frozen model's latent phase state, detects the approach to a pathological phase, and injects a corrective vector before the transition rather than after it. No retraining, no weight access.
The detection layer treats feature activations as a percolating field. Cluster sizes going scale-free is an early-warning signal, and percolation gives you that without needing a temperature definition or an equilibrium assumption, neither of which a transformer at inference will hand you.
Recursus is the recursive language model carrying the first system of this architecture. Built across August 2026 on DeepSeek Harness, MIT licensed. It can read and edit its own harness. Development is paused where test-time training requires hardware under our own control.
Trellis is the phase-one recursive language model this is built alongside, in collaboration since July 2026.
Informatic Exchange Geometries
At the theoretical core is the proposition that reality can be described as a computational engine running on bitwise exchanges. Information flows form geometric patterns that determine the available paths of interaction, and the energy cost of an exchange is what presents as mass, energy, spacetime and force.
This is the frame the rest of the research sits inside. U-Space gives it a number system, U-Neuron gives it an architecture, and the Unified Hyperplane is the map of the space it predicts.
Designed, not built. It is a proposition with a formalism, not a result.
Research instruments
Interactive artifacts built alongside the theory. These are not utilities; they are the working surfaces the ideas were developed on.