# Verification of the convex Hilbert domain counterexample

The four-page English manuscript constructs an open bounded convex balanced
domain in C direct-sum ell^2. It has nonempty Hilbert interior. At p_t=(t,0),
with delta=1-t, its squeezing function lies between delta/sqrt(10) and
1/sqrt(floor(delta^(-2))) <= sqrt(2) delta. The exact Hilbert distance to the
boundary is delta/sqrt(2). Hence its squeezing infimum is zero.

The written proof checks global holomorphic retractions, strict membership
of the open polydisc even at the equality endpoint, the local inverse supplied
by the original embedding definition, a finite Hilbert sign-average identity,
Schwarz derivative estimates, and explicit inner and outer ball inclusions.
It uses no infinite-dimensional compactness or nearest-point theorem.

Normal and optimized Python runs agree on 34237 exact Gaussian-rational
checks, including 278 rational centers, 2437 global domain samples and 120
sign-average tests with complete finite sign enumeration. These are supporting
consistency checks, not a proof by enumeration or proof-assistant certification.

All four pages were visually inspected. The saved TeX passed the built-in
compiler, and the portable archive was rebuilt with identical PDF content
streams and its checker rerun in both modes. Only the author name appears at
the top; Mercury Software GmbH and contact details are in a footnote. AI
assistance is disclosed in ordinary body text.

Question 5 is answered completely negatively; the separate Question 6 is not
resolved. The classical ball-polydisc norm obstruction is credited. This is
an originating-researcher self-audit, not external review. The bounded novelty
search did not locate the same example; absolute priority is not certified.