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一个可接受输出关系 $R$，唯一重要的状态区分是等价类 $s \sim_R s' \iff \mathrm{Adm}_R(s)=\mathrm{Adm}_R(s')$。每个精确正确性断言都归结为相同的商恢复问题，而不可行性关注的是基础问题的可处理性，而非其表示形式。精确指的是与 $R$ 一致，而非零错误确定性或规范中不存在近似/随机化。精确语义商定理将可接受输出等价性识别为通过精确相关性认证恢复的规范对象。决策、搜索、近似、统计、随机化、范围和分布保证均是该定理的实例化。可处理族具有有限原始基，但优化器商可实现性最大，因此商形状无法表征前沿。我们证明了对于定理强制精确认证封闭律下不变的、可高效检查的结构谓词存在元不可能定理。零失真摘要、商熵界和支持计数解释了这一点。通过作用无关的对目标仿射见证，四个障碍族中的同轨道分歧迫使矛盾产生。因此，在封闭封闭域上，不存在正确的问题可处理性分类器能对这些族给出精确表征。限制在封闭封闭子域上仅能通过消除轨道间隙提供帮助。统一严格间隙控制保留了完整的优化器商，而任意小的扰动可能翻转相关性和充分性。封闭轨道一致性由正确性强制决定，相同的计算成本障碍延伸至优化器计算、载荷/搜索以及定理支持的外部或传输输出。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。