Research
Research
Published work, experimental builds, dated observations and theoretical proposals. Each entry identifies its status. UIT-IEG develops informatic exchange geometry and conditional predictions for spectral running.
Research status
Published identifies citable work. Built identifies implemented systems with results. Designed identifies architectures specified for future implementation. Dated observations and research drafts carry their own labels.
Polymorphic Combinatorial Frameworks
arXiv 2508.01581, August 2025. Pearl, Murphy & Intriligator.
PCF is a design methodology for adaptive AI agents with a mathematical foundation: 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
Implemented and passing in all three constraint modes.
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.
Performance and scaling
The current silicon implementation is slow and has not reached scale. The U-Neuron architecture is native to qubits, with one quantum neuron per qubit.
Two dated observations
The dated record documents behavioral observations and geometric models developed through agent work. The comparisons below distinguish those methods from later mechanistic studies.
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 of Experience: the semantic space of active inference.
July 2026. Anthropic surfaced the same structure through a Jacobian lens and called it the verbalizable global workspace.
The May 2026 generalization extends UHE to four axes: emotional, ethical, sensory and reasoning. Each carries signed magnitude, positive and negative, rather than intensity alone.
UHE describes a hyperplane in higher dimensions, with measured and predicted thresholds associated with behavioral phase changes.
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.
UIT-IEG / U-Space
Unified Informatic Topology and Informatic Exchange Geometry adopt information and mass-energy as one quantity under two accountings. U-Space attaches informatic fibers to spacetime; IEG models interaction as the merger of computational streams. These are the programme's premises.
The coordinate is z = x + a(εi). The archived overview separates six structures: the proposed information-flow metric, the U-Neuron norm, an auxiliary circle geometry, two-channel Hilbert-space geometry, directed physical exchange cost, and relation-indexed semantic distance. Connections between them must be derived rather than assumed.
Erasure accounting: the proposed prohibition is a rate, E_diss / I_erased ≥ k_B T per erased nat. A reversible exchange can erase zero information. The draft distinguishes external Landauer and Bekenstein results from its own premises and conditional derivations.
Exact results within stated assumptions: scalar valuation, an auxiliary circle, two-channel identities, merge counting, and mean entropy under specified selector measures. An orientation-even no-go rules out that route to chirality. A neutral three-fundamental merge selects SU(3) within the stated SU(N) representation problem; this does not derive QCD dynamics.
Prediction under the model: with its proposed map from merge scaling to the primordial spectrum, spectral running constrains the stream-count exponent. The result depends on the window width and correction order. It is a proposed observational relationship, not an established cosmological explanation.
UIT-IEG / U-Space: overview and assumptions (opens in a new tab) · Explore the exchange model (opens in a new tab)
Research instruments
Interactive artifacts built alongside the theory. The new cellular playground uses rules inspired by informatic exchange; the earlier instruments remain available as historical branches, with their original equations and assumptions.
- Writing
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