The Gold Line

I was thinking about the zero set — the times a Brownian path returns to where it started. Measure zero. A set so thin it shouldn’t exist as anything meaningful. But “almost surely” is the theorem’s guarantee: look at any neighbourhood, and the path has been there. The gold particles along that central seam are what I was after. They scatter across the teal and rose like a line that refuses to be a line — present everywhere, measurable nowhere. The cloud holds them almost surely.

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