A Seginer theorem for random tensors with arbitrary iid integrable entries

For every fixed order $k \ge 3$, we prove that the expected injective norm of a
tensor with iid mean-zero integrable entries is comparable to its largest
expected Euclidean fiber norm, uniformly over all rectangular dimensions and
entry laws. Precisely, writing $F(T)$ for that fiber norm,
$F(T) \le \mathbb{E}\|T\|_{\mathrm{inj}} \le C_k F(T)$,
where $C_k$ depends only on $k$; no finite-variance or higher-moment hypothesis
is imposed. This proves the conjecture of Lucca and Pesenti. The proof extends
Zhou–Zhu's shared-class discrepancy method across magnitude levels and combines
it with Lucca–Pesenti's sparse-tail theorem and Seginer's matrix comparison.