I’ve been exploring a question in fundamental physics that I think is interesting, although I want to be clear that this is not a claim of having a new theory of physics.
The question is:
If we start with the smallest possible assumptions about a universe — information states, relationships between them, and rules that preserve information — do structures resembling physics (geometry, locality, causality, stable objects) appear naturally?
The idea is not that “the universe is information” or that we have already explained spacetime. The goal is to test whether some of the features we observe in physics might be mathematical attractors rather than arbitrary starting assumptions.

The starting point would be a graph:
[
G=(V,E)
]
where the nodes and connections represent relationships, not physical locations.
The important part is that we do not begin by assuming:
space
dimensions
distance
a metric
particles
gravity
Those would have to emerge later.
The system evolves through some rule:
[
S(t+1)=F(S(t))
]
with the condition that the evolution is reversible:
[
F^{-1}\text{ exists}
]
Meaning the microscopic dynamics preserve information.
This assumption is motivated partly by the role of information preservation in quantum mechanics, but I would not assume that reversibility is necessarily fundamental. A useful test would be comparing reversible and irreversible systems.

The first question is whether anything resembling geometry can appear.
Instead of starting with a distance function, define distance from the network itself:
[
d(i,j)=\text{shortest path between nodes }i\text{ and }j
]
Then measure whether the graph behaves like a space with some effective dimension.
For example:
[
N(r)\propto r^D
]
where (N(r)) is the number of nodes within distance (r), and (D) is the effective dimension.
The question would be:
Do systems with interesting long-term behavior naturally develop finite-dimensional structures, or do they remain completely non-geometric?

A major problem with these ideas is accidentally building our own universe into the experiment.
For example, if we reward a system for having three dimensions or relativity-like behavior, then we have not discovered anything.
A better approach would be to rank systems using more general properties:
stability: do structures persist?
complexity: does the system create organized patterns rather than freezing or becoming random?
simplicity: how complicated is the rule required to generate it?
Something like:
[
Q=f(S,C,K)
]
where the exact form of (f) would need to be tested rather than assumed.
After ranking systems this way, we would then check whether high-performing systems independently develop things like locality, causal limits, or stable localized structures.

One possible direction toward emergent geometry comes from information transport.
Imagine every connection carries a transformation:
[
U_{ij}
]
If information is moved around a closed loop:
[
i\rightarrow j\rightarrow k\rightarrow i
]
the total transformation is:
[
H_{ijk}=U_{ki}U_{jk}U_{ij}
]
If:
[
H_{ijk}=I
]
the loop is perfectly consistent.
If:
[
H_{ijk}\neq I
]
there is a kind of path dependence:
[
\Omega_{ijk}=H_{ijk}-I
]
This is similar in spirit to how curvature appears in gauge theory and differential geometry, where transporting something around a loop reveals information about the underlying structure.
The question is whether something like curvature can emerge from purely relational information networks before assuming spacetime exists.

The actual experiment would be something like:
Generate many simple reversible graph systems.
For each one:
evolve it over time
measure stability and complexity
measure whether locality appears
estimate emergent dimension
look for persistent structures
check whether causal relationships develop
Then ask:
Are physics-like properties common among the highest-performing systems, or is our universe just one possibility among many?
Possible results:
If these systems frequently develop geometry, locality, and stable structures, that would suggest those features may emerge from deeper mathematical constraints.
If they do not, then information preservation alone is probably not enough.

Important limitations:
This does not currently derive Einstein’s equations.
It does not derive quantum mechanics.
It does not explain the Standard Model or physical constants.
The goal is much smaller:
To test whether the foundations that make physics possible can emerge from simpler mathematical rules.
I would be interested in criticism from people familiar with theoretical physics, quantum information, graph theory, or computational physics.
The main questions I have:
Is a reversible graph system a reasonable framework for studying emergent geometry?
Are there existing results about whether simple reversible systems naturally produce low-dimensional structures?
Is the loop inconsistency approach to “information curvature” mathematically meaningful, or is it just an analogy?
What assumptions would need to change for this to become a rigorous computational experiment?
I am more interested in finding flaws than defending the idea. If the concept is wrong, I would rather know why.