Starting from almost nothing
Instead of assuming particles or fields, the paper begins with just a few very basic requirements about reality:
- You must be able to tell things apart (distinguishability)
- That distinction must be finite and recordable
- The system must be self-contained (no hidden external references)
- And it can’t rely on a pre-existing background like space or time
These are not exotic assumptions—they’re the minimum needed for anything like physics to exist at all.
What survives these constraints?
The paper then systematically tests every possible “primitive structure” you could imagine building reality from.
- Continuous structures? Fail—you can’t measure them with infinite precision
- Larger multi-state systems? Fail—they always contain simpler yes/no distinctions inside them
- Structures that depend on external references? Fail—they aren’t truly fundamental
- Incomplete or open systems? Fail—they can’t define themselves
After eliminating every alternative, only one structure remains:
A system with exactly two states, each defined by its relation to the other.
This is called the Fold.
What is a Fold?
At its simplest, a Fold is just a yes/no distinction:
- this vs that
- 0 vs 1
- one state vs another
But importantly, it’s not just a label—it’s a self-contained relational structure. Each state only exists in terms of how it differs from the other.
It turns out this tiny structure carries exactly one bit of information—the smallest possible unit of distinction.
The surprising result
The core result of the paper is:
If you want a physically meaningful theory at all, the simplest building block must be a Fold—and there is no alternative.
This is what’s called a no-alternative theorem.
It doesn’t just say “Folds work.”
It says:
Anything else either reduces to a Fold or fails to meet the basic requirements of physics.
Why everything looks binary
The paper goes further and shows something even more striking:
Every measurement we can ever perform breaks down into a sequence of yes/no questions.
No matter how complicated a system is—whether it has many possible states or even a continuous range—any real observation we make can only extract information in binary steps.
So even if the underlying reality were more complex, what we can actually observe always reduces to:
- yes / no
- this / not this
In other words:
All measurable reality is built from Folds.
What this means
This result changes how we think about the foundations of physics.
Instead of starting with particles or fields, the paper suggests:
Reality may be built from the smallest possible acts of distinction—simple yes/no relations—from which everything else emerges.
Particles, fields, spacetime, and even quantum states would then be larger structures built out of these basic units.
What the paper does—and doesn’t claim
It’s important to be precise.
The paper does not claim:
- that the universe must be binary at every level
- or that deeper, richer structures don’t exist
What it does claim is:
Any part of reality that can be observed, measured, or recorded must ultimately reduce to these binary distinctions.
The takeaway
If you boil the entire paper down to one idea, it’s this:
You can’t build physics without distinctions—and the simplest possible distinction has only two states.
And once you accept that:
That two-state structure—the Fold—is the only possible starting point.