Canonical guarded zero-head cells have uniform reciprocal valuation means

Write $L_n=\log n$, $s_n=n/\log n$, $y_n=\lfloor n^{2/9}\rfloor$, and $\mathcal P_{n,W}=\{p\text{ prime}:W<p\le y_n\}$. Fix a finite head-prime indexing set, patterns, physical intervals, and a guard ledger with fixed promotion and bank parameters. Let $W>1$ contain every pattern prime. There exist $A_z>0$ and $N_0$ such that for every finite band space and bridge at $n\ge N_0$, cutoff $W$, and exactly the canonical guarded sample (with separated physical intervals and nonempty remaining cells),

The expectation is under the uniform guarded cell law. The constant is independent of the bridge, band partition, prime, and physical sign.