Trace logic / the 2026 research program
Only what
returns.
What remains of a world
you can only partly observe?
After the Trace Institute’s
October 8, 2026 whitepaper
and Traces of Consciousness · 2025
A world of possibilities.
Hover to stir the particles. Click a state to begin there.
Each cluster represents a possible experience in this model. The lines show where the chain can go next. Choose a starting point, then press Play to follow its journey.
A Markov chain gives probabilities for the next state, given the present one.
The second probability includes hidden journeys.
Take your time. You control the story.
Begin at s₀. Follow a path, then watch what survives.
02 / Hidden paths, visible effects
Absence leaves
a trace.
A visible transition includes every possible excursion through hidden states before the next return. The trace matrix sums those possibilities.
Entries are percentages. Every row sums to 100% before rounding. Highlighted cells show the latest chain step and completed return.
Underlying chain
row → column| from ↓ | s₀ | s₁ | s₂ | s₃ | s₄ | s₅ |
|---|---|---|---|---|---|---|
| s₀ | 14.0 | 46.0 | 8.0 | 18.0 | 8.0 | 6.0 |
| s₁ | 6.0 | 14.0 | 46.0 | 8.0 | 18.0 | 8.0 |
| s₂ | 8.0 | 6.0 | 14.0 | 46.0 | 8.0 | 18.0 |
| s₃ | 18.0 | 8.0 | 6.0 | 14.0 | 46.0 | 8.0 |
| s₄ | 8.0 | 18.0 | 8.0 | 6.0 | 14.0 | 46.0 |
| s₅ | 46.0 | 8.0 | 18.0 | 8.0 | 6.0 | 14.0 |
Whole window
row → column| from ↓ | s₀ | s₁ | s₂ | s₃ | s₄ | s₅ |
|---|---|---|---|---|---|---|
| s₀ | 14.0 | 46.0 | 8.0 | 18.0 | 8.0 | 6.0 |
| s₁ | 6.0 | 14.0 | 46.0 | 8.0 | 18.0 | 8.0 |
| s₂ | 8.0 | 6.0 | 14.0 | 46.0 | 8.0 | 18.0 |
| s₃ | 18.0 | 8.0 | 6.0 | 14.0 | 46.0 | 8.0 |
| s₄ | 8.0 | 18.0 | 8.0 | 6.0 | 14.0 | 46.0 |
| s₅ | 46.0 | 8.0 | 18.0 | 8.0 | 6.0 | 14.0 |
Qₛ = Qₛₛ + Qₛₕ (I − Qₕₕ)⁻¹ Qₕₛ
S: visible states · H: hidden statesDirect transitions + all hidden excursions.
This inverse exists for every window in our strictly positive chain.
- s₀
- s₀
Recent visits, oldest → newest. Dimmed visits are hidden. A changed window starts a fresh record at s₀, or its lowest visible state.
03 / A window that can change
Who chooses
what is possible?
The 2026 whitepaper proposes a hierarchy: a kernel governs transitions; another governs changes to the state space. Enable the policy level above to try a small, two-level example.
At a visible state, the next step has a 25% chance of using policy R to select a window. Hidden excursions finish first. A changed window restarts at s₀; retaining a window keeps the current state. These rules and probabilities are choices for this study.
Policy paused · 0 policy steps
Window-selection policy
row → column| from ↓ | Narrow | Open | Whole |
|---|---|---|---|
| Narrow | 55.0 | 35.0 | 10.0 |
| Open | 25.0 | 50.0 | 25.0 |
| Whole | 10.0 | 35.0 | 55.0 |
This study follows the Trace Institute’s A Science of Reality: Observers, Interfaces, and Traces, dated October 8, 2026: basic trace logic in section 3 and the proposed recursive extension in section 4.
The trace calculation also follows Traces of Consciousness by Donald Hoffman, Chetan Prakash and Swapan Chattopadhyay, in its September 5, 2025 preprint revision.
The states in this theory represent possible experiences. Our six-state example is independent of Observer’s four-world-state example; it is not a reconstruction of physical space. The particles make abstract states visible.
Our six-state chain, window presets, policy probabilities, restart convention, guided example and particle forms are illustrative choices. You can also build a custom observation window by clicking the states. Reset repeats the same sample sequence. This is a finite demonstration of the mathematics; claims about consciousness and the emergence of physics remain part of an ongoing research program.
Read the 2026 whitepaper Trace Institute · October 8, 2026 · Research whitepaperRead Traces of Consciousness Hoffman, Prakash & Chattopadhyay · September 5, 2025 · Preprint