= Wringing-film uncertainty
\b[Wringing-film uncertainty] is the uncertainty contributed by differences or changes in the effective contact layers formed during <gauge block wringing>. Because the defined length of a <gauge block> includes a wringing-layer convention, the issue is the difference between calibration and use, not automatically an extra layer correction added to every certificate value.
For a stack of $n$ blocks wrung to an auxiliary plane, let $w_i$ denote each calibrated effective layer contribution and $w'_j$ the contributions from the $n-1$ internal contacts plus the base contact in use. The residual contact correction is
$$
\Delta_w=\sum_{j=0}^{n-1}w'_j-\sum_{i=1}^{n}w_i.
$$
Its <standard uncertainty> requires a model for these differences. NIST's handbook describes dependence on surface condition, fluid and elapsed time, and notes residual uncertainty when an unknown block's layer is transferred through comparison with a master.<The Gauge Block Handbook by Ted Doiron and John S. Beers>[Appendix B, Physics of Wringing Films and defined-length discussion]{ref}
An original model for $n$ effective contact differences writes $\delta_j=b+\epsilon_j$, with one shared zero-mean contribution $b$ of variance $u_b^2$ and independent contact contributions $\epsilon_j$ of variance $u_\epsilon^2$. Then
$$
\Delta_w=nb+\sum_j\epsilon_j,\qquad
u^2(\Delta_w)=n^2u_b^2+nu_\epsilon^2.
$$
The common term grows quadratically in variance because every contact contains the same contribution. Treating all contacts as independent would omit their <covariance>.
For three contacts with stipulated $u_b=3\,\mathrm{nm}$ and $u_\epsilon=2\,\mathrm{nm}$, the combined standard uncertainty is $\sqrt{9\cdot9+3\cdot4}=\sqrt{93}\approx9.64\,\mathrm{nm}$. Assuming independence for three marginal uncertainties $\sqrt{13}\,\mathrm{nm}$ instead gives $\sqrt{39}\approx6.24\,\mathrm{nm}$. The numerical difference comes entirely from the assumed shared effect; these values are illustrative, not a general wringing specification.
Repeatedly separating, preparing and rewringing contacts can characterize a repeatability contribution. Repeated detector readings of an unchanged stack do not sample new wrings. Averaging independent rewrings may reduce a random contact term while leaving a shared calibration or preparation contribution. Film evolution and <thermal expansion> during handling must also be distinguished from readout noise.
Report surface preparation, reference geometry, elapsed time and the treatment of shared effects. A stack that adheres firmly can still have a length contribution relevant to a small uncertainty target. <Wringing-film covariance model> assumptions therefore belong with the result, rather than being hidden inside an unspecified repeatability number.
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