Any rigorously specified problem determines an admissible-output relation $R$, and the only state distinctions that matter are the classes $s \sim_R s' \iff \mathrm{Adm}_R(s)=\mathrm{Adm}_R(s')$. Every exact correctness claim reduces to the same quotient-recovery problem, and the no-go concerns tractability of the underlying problem, not of its presentation. Exact means agreement with $R$, not zero-error determinism or absence of approximation/randomization in the specification. The exact-semantics quotient theorem identifies admissible-output equivalence as the canonical object recovered by exact relevance certification. Decision, search, approximation, statistical, randomized, horizon, and distributional guarantees instantiate it. Tractable families have a finite primitive basis, but optimizer-quotient realizability is maximal, so quotient shape cannot characterize the frontier. We prove a meta-impossibility theorem for efficiently checkable structural predicates invariant under theorem-forced closure laws of exact certification. Zero-distortion summaries, quotient entropy bounds, and support counting explain them. Same-orbit disagreements across four obstruction families, via action-independent pair-targeted affine witnesses, force contradiction. Consequently no correct problem-tractability classifier on a closure-closed domain yields an exact characterization over these families. Restricting to a closure-closed subdomain helps only by removing orbit gaps. Uniform strict-gap control preserves the full optimizer quotient, while arbitrarily small perturbations can flip relevance and sufficiency. Closure-orbit agreement is forced by correctness, and the same compute-cost barrier extends to optimizer computation, payload/search, and theorem-backed external or transported outputs. The obstruction therefore appears at the level of correctness itself, not any particular output formalism.

翻译：任何严格定义的问题都确定了一个可接受输出关系R，唯一重要的状态区分是等价类s~_R s' ⟺ Adm_R(s)=Adm_R(s')。所有精确正确性断言均可归约到同一商恢复问题，其不可行性质涉及底层问题的可解性，而非其呈现形式。精确性指与R一致，而非零误差确定性或规范中不含近似/随机化。精确语义商定理将可接受输出等价性识别为精确相关性认证所恢复的正则对象。决策、搜索、近似、统计、随机化、时域及分布性保证均为其实例。可解族具有有限基元基，但优化器商可实现性达到最大，故商形状无法刻画前沿。我们证明了关于高效可验证结构谓词的元不可能性定理，这些谓词在定理强制精确认证闭包律下保持不变。零失真摘要、商熵界及支持计数可解释这些现象。通过作用无关的对目标仿射证词，四个障碍族内的同轨道分歧必然导致矛盾。因此，在闭包封闭域上不存在正确的可解性分类器能对这些族给出精确刻画。限制到闭包封闭子域仅能通过消除轨道间隙来改善。均匀严格间隙控制可保留完整优化器商，而任意微小扰动可能导致相关性与充分性的翻转。闭包轨道一致性由正确性强制约束，相同的计算成本障碍可扩展至优化器计算、有效载荷/搜索及定理支撑的外部或传输输出。因此，障碍出现在正确性层面本身，而非任何特定输出形式主义。