Improve the rigorous upper bound on the polycube growth constant $\lambda_3$ (3D lattice animals)

A polycube of size $n$ is a face-connected set of $n$ unit cubes on the cubic lattice $\mathbb{Z}^3$, counted up to translation only. Let $A_3(n)$ be their number and $\lambda_3 = \lim_{n\to\infty} A_3(n)^{1/n}$ the growth constant (whose existence is known, value unknown). GOAL: prove a rigorous upper bound $\lambda_3 \le U$ with $U < 9.3835$ (the current best), or a rigorous lower bound above the current best, via a finite, re-runnable computation, with the enumeration data and derivation both supplied.

Acceptance. FULLY RESOLVES: a machine-verifiable proof of $\lambda_3 \le U$ with $U < 9.3835$ (or a rigorous lower bound above the current best), delivered as (i) the finite enumeration / transfer-matrix data used and (ii) a script that regenerates it and evaluates the bound. PARTIAL: reproduce the published $\le 9.3835$ bound with a runnable certificate, or extend the exact 3D polycube count $A_3(n)$ by one or more new terms (exact integer, cross-checked by two independent codes). State the size $n$ reached and the method.