# Verification report

The analytic proof bounds every linear functional of uniform volume on
a symmetric event retaining at least 15/16 of a Euclidean ball. The
second moment follows from Cauchy--Schwarz and the exact fourth moment;
the exponential bound follows from the full nonnegative moment series.
The conditional psi2/L2 ratio is at most 2 sqrt(2).

Intersecting the ball with a cylinder gives an exact prescribed projection.
For the displayed C_n in dimension 64n^2, the projection is (1/2)B_1^n
and its directional ratio diverges at least as
sqrt(n+2)/(2 sqrt(2 log 2)). The coordinate estimate for B_1^n is known
prior work. The paper treats the projection subquestion only.

The standard-library checker reports 2770 passing exact integer/rational
conditions in both normal and optimized Python, with identical results.
Its finite domains are explicit in the source: ball moments up to order
80 in nine dimensions, cross-polytope moments for n=2,...,128, rational
projection witnesses, and dimension-bound checks. There are no random
or floating-point tests. These are regression checks, not a formal proof.

Adversarial self-audit addresses the normalization, all-direction quantifier,
conditional variance loss, exponential threshold, exact projection equality,
isotropic normalization and the difference between projected volume and
uniform measure on the image support. No mathematical gap is known in the
stated theorem. No independent reviewer or proof-assistant verification is
claimed. Bounded literature checks do not certify absolute priority.