Notes on acceptable bundles I

Abstract

The notion of acceptable bundles plays a fundamental role in the Simpson--Mochizuki theory. This paper presents a detailed study of acceptable bundles on a punctured disk. In addition to its expository aspects, we introduce a new invariant and provide arguments that differ from those of Simpson and Mochizuki.

62 pages, v2: Title change; minor revisions. For Part II, see arXiv:2604.05233 [math.AG]