Trace Institute
Research

A research program on the nature of reality

The Trace Institute is pursuing a single question: what is the nature of reality? The research is developing a mathematical theory in which conscious observers are primary, and the spacetime structures of physics emerge from their interactions. The core mathematical and philosophical frameworks include the Interface Theory of Perception, Conscious Agent Theory, Trace Logic, and Recursive Trace Logic.

The problem

Science has not formalized the observer

Quantum theory remains silent on the nature of the observer and fails to reconcile with General Relativity. Some pioneers saw this gap decades ago. John Wheeler called the observer a "participator" and proposed "it from bit" where the physical world is derived from information, and this information is what an observer elicits. The Trace Institute is building the scientific formalism that proposal was waiting for.

Trace does not abandon physics. Instead, it formalizes the observer that physics has long treated as an unanalyzed primitive, and proposes recovering all known laws of physics as limiting cases of this deeper theory.

Lacking a theory of observation has consequences. Cognitive science has mapped vast territories of perception and cognition without explaining how they form experience. The hard problem of consciousness has no solution inside the assumption of materialist reductionism. But a theory centered on the observer might be the remedy.

The theory

Four steps, one chain of reasoning

The Institute's research is one connected argument that arrives at the Recursive Trace Logic. Each step is peer-reviewed or under active development, earning the next step.

01 / 04

Interface Theory of Perception

The empirical entry point. The Fitness-Beats-Truth theorem proves that natural selection drives veridical perception to extinction: organisms see evolutionary fitness payoffs, not observer-independent structures. Spacetime and physical objects are best viewed as species-specific user interfaces or "headsets".

Hoffman, Singh & Prakash, 2015. Prakash et al., 2020, with the FBT proof.

02 / 04

Conscious Agent Theory

A minimal mathematical model of an observer: a measurable space of potential experiences and a Markov kernel governing their transitions. The kernel is the agent's dynamics; the state space is its phenomenology. The model is streamlined so networks of agents compose without privileged scale.

Hoffman & Prakash, 2014. Hoffman, Prakash & Prentner, 2023 (Fusions of Consciousness).

03 / 04

Trace Logic

The Trace Chain Theorem (2025): for any subset of a Markov kernel's state space, there is a unique trace chain that describes the effective dynamics seen by an observer restricted to that subset. This induces a partial order on agents and a logic, locally Boolean and generally non-Boolean, that is provably homomorphic to the Lebesgue logic of probabilistic belief. The namesake of the Institute.

Hoffman, Prakash, Chattopadhyay, 2025. Observer mechanics: Bennett, Hoffman & Prakash, 1989.

04 / 04

Recursive Trace Logic

RTL extends trace logic with a hierarchy of Markov kernels that govern changes to the state space itself: a Policy Level for state-space transitions, a meta-policy Level, and beyond. This is a framework in which spacetime, perception, and first-person experience are conjectured to emerge, including the eight conjectures of physics, the neural interface, phenomenology and spiritualism, and new technologies.

Whitepaper, 2026. Active inference parallels: Clark, 2017; Parr, Pezzulo & Friston, 2022.

Trace Logic

Mathematics of the Trace Logic

A conscious agent is a Markov kernel acting on its own measurable space of experiences. If one defines observer-windows on that kernel, a partial order emerges on the space of agents, which is called the Trace Chain Theorem.

The asymptotic statistics of trace chains are conjectured to reproduce, in the appropriate limits, the mathematical structures of relativity, quantum theory, and the Standard Model of physics, but may also derive the mathematical structure of perception, inference, and conscious experience itself.

The Recursive Trace Logic extends the theory to first-person dynamics: the agent's own act of inferring, updating, and constructing its interface. It connects the trace logic to active inference and the predictive-processing literature without committing to a materialist substrate.

The trace logic is the framework. Below is the program of work it makes possible: physics, then neuroscience, metaphysics, and technological innovation. Each step validates the framework and opens new ground.

The Eight Conjectures

A framework for deriving the foundations of physics

Eight physics conjectures the program is pursuing.

01 / 08

Special Relativity

Minkowski space emerges as the limiting behavior of Markov chains representing n-cycles as n → ∞ under certain conditions.

02 / 08

General Relativity

Curved spacetime emerges as the limiting behavior of special classes of non-cyclic Markov chains under certain conditions.

03 / 08

Cosmology

Cosmology and cosmic evolution arise as properties of long samples of certain classes of Markov trace chains.

04 / 08

Planck-Scale Failure of Spacetime

The breakdown of spacetime at the Planck scale is a consequence of the increase of energy with number of states in a trace.

05 / 08

Quantum Wavefunction and Born Rule

Quantum wavefunctions of free particles, and the Born rule, can be recovered from the asymptotic behavior of enhanced Markov chains.

06 / 08

Elementary Particles

Each of the elementary particles in the Standard Model can be identified with a particular class of Markov chains.

07 / 08

Scattering Amplitudes

Scattering amplitudes arise from properties of relevant Markov chains, with ABHY associahedra appearing as subpolytopes of the Markov polytope.

08 / 08

Entanglement

Disjoint traces of an ergodic Markov chain create spacelike-separated observers with hidden interactions, giving rise to quantum entanglement.

Beyond physics

The full reach of the program

Deriving spacetime physics is the first step. RTL is then applied to the structure of subjective experience, in conversation with neuroscience and contemplative traditions, and finally to the unimaginable technologies the new epistemology makes possible.

Neuroscience

Engineering the observer interface

The brain, in the trace-logic framework, is a component of the interface through which experience is produced, not the substrate of experience itself. This follows the desktop-icon metaphor where the icon is not where the computation occurs. RTL will enable quantitative predictions on the neural correlates of consciousness, via identifying, inside the interface, what neural states and perturbations produce what experiences. It also provides a principled framework for studying altered states pharmacologically, physiologically, and through direct stimulation, such as our research collaboration with Noonautics on DMT phenomenology.

Metaphysics

A mathematical framework for spirituality

The non-dual ontology of the trace logic aligns naturally with diverse contemplative traditions, including Buddhism, Vedanta, and Daoism, that have long held the dualisms of mind/matter, self/world, and real/imagined to be products of an adaptive process rather than features of reality. RTL offers, a novel, mathematically precise framework in which long-standing questions of these traditions can be examined. We do not import contemplative claims as data; we use the mathematics to clarify which questions are well-posed and how answers might be distinguished.

Technology

A new science of reality, and technology

Paradigm shifts in science have always been accompanied by new technologies. RTL points to three near-term frontiers. First, in generative physics, one can search for phenomena predicted by the trace structure but not by materialist reductionism, including possible connections to dark matter. Second, we can form mathematically precise tools for modulating, modeling, and engineering experience, extending the same leverage the physics conjectures gave us over matter to the domain of experience itself. Third, we envision a microchip epistemology in which conscious-agent networks inform new computational architectures beyond today's models.