We study the fundamental problem of fairly dividing a set of indivisible goods among agents with additive valuations. Here, envy-freeness up to any good (EFX) is a central fairness notion and resolving its existence is regarded as one of the most important open problems in this area of research. Two prominent relaxations of EFX are envy-freeness up to one good (EF1) and epistemic EFX (EEFX). While allocations satisfying each of these notions individually are known to exist even for general monotone valuations, whether both can be satisfied simultaneously remains open for all instances in which the EFX problem is itself unresolved. In this work, we show that there always exists an allocation that is both EF1 (in fact, the stronger notion EFL) and EEFX for additive valuations, thereby resolving the primary open question raised by Akrami and Rathi (2025) and bringing us one step closer to resolving the elusive EFX problem. We introduce a new share-based fairness notion, termed strong EEFX share, which may be of independent interest and which implies EEFX feasibility of bundles. We show that this notion is compatible with EF1, leading to the desired existence result.

翻译：本研究探讨在具有可加性估值的主体间公平分配不可分割物品这一基础问题。其中，"任意物品无嫉妒性"（EFX）是核心的公平性概念，其存在性证明被视为该研究领域最重要的开放问题之一。EFX有两个重要的松弛概念："单物品无嫉妒性"（EF1）与"认知EFX"（EEFX）。尽管已知即使对于一般单调估值，单独满足任一概念的分配总是存在，但对于所有EFX问题本身尚未解决的实例，两者能否同时满足仍是开放问题。本工作证明：对于可加性估值，总存在同时满足EF1（实际上是更强的EFL概念）与EEFX的分配，从而解决了Akrami与Rathi（2025）提出的首要开放问题，使我们向解决难以捉摸的EFX问题迈进了一步。我们提出了一种新的基于份额的公平性概念——强EEFX份额，该概念本身可能具有独立研究价值，且能推出捆绑分配的EEFX可行性。我们证明该概念与EF1具有兼容性，由此导出了期望的存在性结果。