Research

Coalition intelligence theory

What determines the collective capability of a system composed of diverse agents? When does diversity become value, and when does its loss become catastrophic? Is the boundary between a functioning coalition and a collapsed one gradual or sharp? And what properties of a coalition are structural — invariant under any rearrangement of the system's economic or institutional surface?

These questions arise in every domain the Institute studies — in economies, in neural systems, in biological tissue, in artificial intelligence — but they are not themselves questions about any of those domains. They are mathematical questions about the structure of coalitions as such, independent of the substrate.

The Institute develops the mathematical foundations of coalition intelligence theory as a self-contained discipline: the structural layer on which every application to a specific substrate is built. This is the core of the Institute's research program.

Distributed artificial intelligence

Every artificial intelligence system runs on physical hardware, and every physical system is subject to energy constraints. Yet the dominant architectures in AI research — including the large-scale models now deployed across industry — have been designed without systematic reference to the energy bounds that any physical computing system imposes on intelligence.

The Institute studies what happens when those constraints are taken seriously. The research asks whether the architecture of a scalable general intelligence is a design choice among many, or a mathematical necessity — whether the physics of energy-efficient computation admits more than one path, or forces a specific organizational structure on any system that must be both capable and sustainable.

This work draws on statistical physics, non-equilibrium thermodynamics, information theory, and spectral theory. It connects to the Institute's research on the mathematical structure of coalitions, and it produces predictions about existing and proposed hardware that observation can confirm or refute.

Economics and institutions

Firms, economies, and political institutions are coalitions of agents with different capabilities. Classical economics has studied how these coalitions create value, how markets coordinate them, and how institutions shape their behavior — but it has done so without a mathematical framework that connects the heterogeneity of individual agents to the collective performance of the coalition they form.

The Institute studies that connection. The research asks how diversity of capability becomes collective economic value, what forces in a system preserve or destroy that diversity, whether institutional failure is gradual or abrupt, and what distinguishes an institution that maintains its collective capability over time from one that loses it.

This work draws on spectral theory, dynamical systems, game theory, and the mathematics of stochastic processes. It engages classical questions in growth theory, international trade, organizational design, and political economy — and asks whether they share a common mathematical structure that existing approaches have studied only in pieces.

Verification theory

Every field that depends on the integrity of complex claims — law, medicine, finance, pharmaceutical regulation, AI safety — faces the same unsolved problem: how do you verify, reliably and at scale, that a document or system satisfies the standards it is claimed to satisfy?

Current verification practice is informal, inconsistent, and labor-intensive. It cannot state what it guarantees, it cannot quantify what it misses, and it cannot be audited or reproduced. Despite the universality of the problem, the mathematical foundations of verification — what it can achieve, what it provably cannot, and what determines the difference — have not been established.

The Institute studies those foundations. The research asks what a rigorous theory of verification looks like: what guarantees are possible in principle, what limits no procedure can overcome, and what structural properties a verification system must have for its guarantees to be stated as theorems rather than aspirations.

This work draws on information theory, game theory, and the mathematics of stochastic processes. Its results have practical implications for any domain where society depends on the integrity of complex claims.

AI governance

The question of how to govern artificial intelligence systems — and in particular, how to govern systems that modify themselves — is now urgent. Most existing proposals are policy frameworks grounded in intuition, analogy, and precedent. Very few ask whether the governance structures they recommend are mathematically required, and none establishes what happens, precisely, when a specific governance condition is removed.

The Institute studies the mathematical structure of AI governance. The research asks what architectural constraints are necessary — not recommended, not prudent, but provably required — for a multi-agent AI system to remain aligned with its intended purpose. It asks whether a system can verify its own output, whether a governance layer can audit itself, and what the formal limits of self-certification are. It asks what happens to a governed system when each governance condition is individually removed, and whether the resulting failures are gradual or abrupt.

This work draws on mathematical logic, proof theory, game theory, information theory, and spectral theory. It engages the AI safety literature and the emerging regulatory landscape, and asks what a governance framework looks like when its provisions are theorems rather than recommendations.

Biological intelligence

Living systems are composed of populations of cells that interact, specialize, coordinate, compete, and sometimes fail catastrophically. Cancer biology, developmental biology, and systems biology each study aspects of this behavior — but each has built its own mathematical tools for its own domain, without a shared framework connecting the collective behavior of a tumor, a developing tissue, and a healthy organ.

The Institute studies that shared framework. The research asks what determines whether a population of cells maintains its collective capability or loses it, what distinguishes a differentiating tissue from one that collapses into uniformity, when and why a population that has been stable becomes fragile, and what the mathematical conditions are for a therapeutic intervention to produce a durable response rather than a transient one.

This work draws on spectral theory, dynamical systems, stochastic processes, and the mathematics of interacting particle systems. It treats cells as agents with capabilities, and asks what the collective behavior of the population can and cannot do — as a mathematical question, independent of the molecular details that vary from system to system.

Neuroscience and memory

Why is biological memory organized the way it is? Why does it use two stores — one fast, one slow — rather than one? Why does consolidation take time? Why is retrieval reconstructive rather than reproductive? Why does reconsolidation exist? And why do specific diseases destroy specific kinds of memory in a specific order?

These questions have been studied experimentally for over a century, producing detailed knowledge of the molecular, cellular, and systems-level mechanisms involved. What has been missing is a mathematical account of why memory must be organized this way — an account that derives the architecture from first principles rather than fitting it to observations, and that predicts the patterns of pathology as consequences of the theory rather than as separate phenomena requiring separate explanations.

The Institute studies that account. The research asks what constraints energy and fidelity impose on any memory system embedded in a physical intelligent system, and whether those constraints are sufficient to force the organizational features that neuroscience has observed — the two-store architecture, the gradient of retrograde amnesia, the reconstructive nature of retrieval, and the specific vulnerability profiles of neurodegenerative disease.

This work draws on spectral theory, differential geometry, dynamical systems, and non-equilibrium thermodynamics.

Self-improving machines

A system that rewrites itself — editing its own rules, structure, or capabilities against a criterion for improvement — is not a hypothetical. Biological evolution does it. Neural development does it. Agentic AI systems are beginning to do it. The question is not whether such systems exist, but what the mathematical limits on self-improvement are.

Can a self-improving system verify that a proposed change is actually an improvement? What does that verification cost? Can any stage of the process certify the safety of a later stage — or of itself? Is unbounded self-improvement achievable within computation, or does it require resources no physical system can provide? And what must a self-improving system know about itself in order to improve at all?

The Institute studies these questions as problems in mathematical logic, proof theory, and the theory of computation. The results apply to any system that modifies itself — biological, computational, or institutional — and they establish what self-improvement can and cannot achieve as a matter of mathematics, not engineering.