Diels–Kranz (DK) numbering is the standard system for referencing the works of the pre-Socratic philosophers, based on the collection of quotations from and reports of their work, Die Fragmente der Vorsokratiker (The Fragments of the Presocratics), by Hermann Alexander Diels. It was first published in 1903, was later revised and expanded three times by Diels, and was finally revised in a 5th edition (1934–7) by Walther Kranz and again in a sixth edition (1952). In the system, each author is assigned a number, with entries divided into three groups:
- A: testimonia, ancient accounts of the authors' life and doctrines
- B: ipsissima verba (literally, exact words, sometimes also termed "fragments"), the exact words of the author
- C: imitations, works which take the author as a model
- Testimonia are: commentary on the works of the Presocratics, accounts of their lives and of their philosophical views. The collection includes a German translation of the Presocratic quotations, but not of the testimonia.
- IEP: "Diels-Kranz Numbering System"