Empirical confirmation of bosonic wealth statistics in Bitcoin UTXOs

TL;DR

This study empirically confirms that Bitcoin UTXO ownership distributions follow bosonic occupancy statistics, indicating a fundamental informational driver of inequality in digital economies.

Contribution

It provides the first empirical validation that Bitcoin wealth distributions adhere to bosonic statistics, bridging theoretical predictions with blockchain data.

Findings

A geometric model accurately describes ownership distributions.

Jensen-Shannon divergence is below 0.08 in 99.74% of cases.

Inverse-temperature parameter aligns with theoretical mean-temperature relation.

Abstract

Digitalisation transforms money from distinguishable physical objects into fungible informational units. A recent theoretical framework predicts that such indistinguishable wealth obeys bosonic occupancy statistics, leading to geometric ownership distributions and enhanced inequality. Using Bitcoin blockchain data, we test this prediction on 63 UTXO denominations across 72 monthly snapshots (2018--2023). A one-parameter geometric model describes the ownership distributions, reproducing both mean holdings and their temporal evolution; Jensen--Shannon divergence values lie below $0.08$ in $99.74\%$ of cases. The inferred inverse-temperature parameter satisfies the analytic mean--temperature relation to better than $0.1\%$ in every sample -- a self-consistency test that two-parameter alternatives cannot pass -- and remains within a narrow band across eight orders of magnitude in denomination and over six years. Bitcoin UTXO ownership statistics are therefore consistent with bosonic occupancy laws, suggesting that the informational nature of electronic money may act as a structural driver of inequality in digital economies.