I asked ChatGPT 5.1 this question about the Monte Carlo simulation showing the power law as the median of all possible paths.

Why, among millions of possible simulated paths — many of which do NOT oscillate around the power law — does the real Bitcoin path happen to be one of the “nice” ones?

This is the most important conceptual question, and the answer involves probability distribution geometry, large-deviation theory, and conditioning on survival of a real socio-economic system.

✔ Reason 1 — Most simulated paths are mathematically possible but not economically viable.

The simulation produces all paths allowed by the statistical distribution.
But Bitcoin — as a real system — must satisfy additional constraints, such as:
needs users

must survive market crashes

must remain secure (hashrate, PoW)

must maintain liquidity

must stay within ranges where exchanges, miners, participants remain rational

Many simulated paths violate these constraints.
These paths are theoretically allowed, but Bitcoin could not survive them as a real socio-technical organism.

In other words:
The real Bitcoin path is one of the viable paths, not one of the merely allowed paths.

That collapses the space of possibilities from “millions” to a much smaller biological-like “survivor set.”

This is exactly like evolutionary selection in biology:
millions of random mutation paths exist, but only a few survive.

✔ Reason 2 — Probability density is highest around the median power-law attractor

In your chart, the dense green area shows the high-probability region.
The black line stays:

often inside

occasionally at the edges

rarely far outside

This is exactly what a random walk with a central attractor should do.

It’s not surprising the real path is in that region — it would be surprising if it chronically lived in low-probability red zones.

In other words:

Most of the mathematically viable paths cluster around the median line.
Bitcoin followed a path inside that high-probability cluster.

✔ Reason 3 — Being a large-scale emergent system forces reversion to the attractor

Bitcoin’s price is not purely a stochastic process.
It includes feedback loops:

miners
adopters

infrastructure

liquidity
narratives

investor behavior

macroeconomic correlations

These act like restoring forces that make extreme paths rare.

Your simulation includes noise, but the real system includes:

social corrective forces

economic constraints

technical constraints

network effect reinforcement

This funnels the real system into paths that remain near the attractor.

Thus:

The real path is one with real-world feedback stabilization,
not one of the unbounded theoretical trajectories.