The Donkey on the Edge Vol. I · The Evolution · Paper I · Result III May MMXXVI
The Donkey on the Edge
Result the Third

Haar class scaling

For bulk states drawn from the Haar class (uniformly random pure states), entropy disagreement scales as 0.608 times d_B to the negative three-halves power. The prefactor is analytic. This is the regime relevant to black hole interiors.

Theorem 5.2Haar ClassExact Prefactor

Two Ways of Reading the Same Finding

Paper Voice

For bulk states drawn from the Haar class (uniformly random pure states), the entropy disagreement scales as:

ESASB0.608dB3/2+O(dB2)\mathbb{E}|S_A - S_B| \approx 0.608 \cdot d_B^{-3/2} + \mathcal{O}(d_B^{-2})

The prefactor 0.608 is analytic. No fitting. Simulations match. This is the regime relevant to black hole interiors and holographic codes for chaotic quantum dynamics.

Donkey Voice

A plain-language companion to the result above, in the Donkey voice. The full essay lives in the field notes; this column carries the short version.

The G-chord / symphony analogy, full essay ›
See also