Why 137? A hydrogen atom spans 137 Compton wavelengths -- one electron orbit contains 18,800 Compton "ticks." Are these brute facts or signatures of a cosmic Central Limit Theorem converting quantum noise into classical atoms? The cosmological constant is an even stronger candidate: 10^122 horizon pixels produce the observed dark energy. Honest about gaps. https://doi.org/10.5281/zenodo.20182909
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Statistical Genesis of Appearance — A First-Principles Investigation
This document investigates a single hypothesis: The dimensionless numbers encoded in the fine-structure constant --- $1/\alpha \approx 137$ and $1/\alpha^2 \approx 18{,}800$ --- are not brute facts of nature. They are the quantitative signatures of a layered statistical process, a Central Limit Theorem operating at multiple strata, that converts fundamental quantum noise into the stable, classical appearance of atoms. We do not prove this hypothesis. We clarify what it means, what would constitute evidence for and against it, and how it connects to broader questions about the statistical origins of physical law.




