The working conjecture from K'04 that there is a proof complexity generator hard for all proof systems can be equivalently formulated (for p-time generators) without a reference to proof complexity notions as follows: * There exist a p-time function $g$ stretching each input by one bit such that its range $rng(g)$ intersects all infinite NP sets. We consider several facets of this conjecture, including its links to bounded arithmetic (witnessing and independence results) and the range avoidance problem, to time-bounded Kolmogorov complexity, to feasible disjunction property of propositional proof systems and to complexity of proof search. We argue that a specific gadget generator from K'09 is a good candidate for $g$.

翻译：K'04 中的工作猜想是,所有验证系统都有一个复杂的实证生成器(p-time generations),可以等同地设计(p-time generations),而不必提及以下证据复杂性概念: * 存在一个p-time 函数,将每个输入量拉长一小点,使其范围达到$rng(g)$(g)$的交错无穷无尽的NP套件。 我们考虑了这一猜想的若干方面,包括它与受约束的算术(证人和独立结果)的联系,以及避免范围问题,与受时间限制的Kolmogorov复杂度,以及可能使建议性验证系统脱钩的属性和证据搜索的复杂性。 我们争论说, K'09 的某个具体的工具生成器是合金的好候选方。