We study how exact Solvability Complexity Index (SCI) statements should be formulated for families of computational problems rather than for single problems. While the equality \(\mathrm{SCI}_G (\mathcal P)=k\) is unambiguous for an individual computational problem \(\mathcal P\), the family setting requires one to distinguish family-pointwise exactness, witness-space sharpness, and worst-case exactness. We formalize this trichotomy, prove that witness-space sharpness coincides with worst-case exactness but is, in general, strictly weaker than family-pointwise exactness, and give a canonical source-family example witnessing the strictness. We then establish two positive upgrade theorems: an abstract pullback principle and a concrete finite-query criterion guaranteeing that witness-space sharpness upgrades to family-pointwise exactness. Next, we introduce a decoder-regular finite-query transport preorder on SCI computational problems, prove that it is a preorder, derive a transport-saturation sufficient criterion extending the principal-source package, and show that the associated transport degrees need not form a lattice in full generality. We analyze the natural decoder classes \(\mathscr R_{\mathrm{cont}}\) and \(\mathscr R_{\mathrm{Bor}}\): on the full class the corresponding quotients are not upper semilattices, while on the nondegenerate subclass the preorder is upward and downward directed. Finally, we exhibit two natural positive families realizing the principal transport mechanism: exact integration on compact intervals and a fixed-window spectral decision family obtained by block-diagonal stabilization.

翻译：我们研究如何针对计算问题族而非单个问题精确表述可解性复杂性指数（SCI）语句。虽然对于单个计算问题 \(\mathcal P\)，等式 \(\mathrm{SCI}_G (\mathcal P)=k\) 是明确的，但族设定要求区分族逐点精确性、见证空间尖锐性和最坏情况精确性。我们形式化这一三分性，证明见证空间尖锐性与最坏情况精确性一致，但通常严格弱于族逐点精确性，并给出一个典范的源族实例以证明该严格性。随后我们建立两个正向升级定理：一个抽象的拉回原理和一个具体的有限查询判据，保证见证空间尖锐性可升级为族逐点精确性。接着，我们在SCI计算问题上引入一个解码器正则的有限查询传输预序，证明它是一个预序，推导出一个超越主源包的传输饱和充分判据，并展示相应的传输度在一般情况下未必构成格。我们分析自然解码器类 \(\mathscr R_{\mathrm{cont}}\) 和 \(\mathscr R_{\mathrm{Bor}}\)：在全类上，相应商集不是上半格；而在非退化子类上，该预序是向上和向下有向的。最后，我们展示两个实现主传输机制的自然正向族：紧区间上的精确积分和通过块对角稳定化获得的固定窗口谱决策族。