The lead supervisory authority (LSA) is determined by the location of the controller's "main establishment" for a specific cross-border processing activity. According to GDPR Article 4(16), while the main establishment is presumed to be the place of central administration (Germany), this can be rebutted. If decisions on the purposes and means for a specific processing activity are made in another establishment that has the power to implement them, that establishment becomes the main establishment for that activity. In this scenario, the SaaS application was "defined and implemented" by the Polish establishment, indicating that decisions regarding its data processing were made there. Therefore, the Polish supervisory authority is the LSA for this specific service.

A. The supervisory authority of Germany at the federal level. This is incorrect because the decision-making power for the specific SaaS processing resides in Poland, not at the company's central administration in Germany.
B. The supervisory authority of Germany at the regional level. This is incorrect for the same reason as option A. The location of the central headquarters is superseded by the location where processing decisions are made.
D. The supervisory authority of the European Union. This is incorrect as there is no single supervisory authority for the entire EU. The GDPR establishes a system of national supervisory authorities coordinated by the European Data Protection Board (EDPB).

1. General Data Protection Regulation (EU) 2016/679, Article 4(16)(a): "‘main establishment’ means: (a) as regards a controller with establishments in more than one Member State, the place of its central administration in the Union, unless the decisions on the purposes and means of the processing of personal data are taken in another establishment of the controller in the Union and the latter establishment has the power to have such decisions implemented, in which case the establishment where such decisions are taken is to be considered the main establishment".

2. European Data Protection Board (EDPB), Guidelines 8/2022 on identifying a controller or processor’s lead supervisory authority, Version 2.0, 24 May 2023, para. 23: "In order to rebut the presumption that the place of central administration is the main establishment, it is necessary to demonstrate both that: 1. the decisions on the purposes and means of the processing are taken in another establishment; and 2. this other establishment has the power to have such decisions implemented."

3. Drechsler, L. (2018). The lead data protection supervisory authority under the GDPR: a gateway to the one-stop-shop mechanism. International Data Privacy Law, 8(4), 347–359. Section 3.1 discusses how the main establishment is not always the central administration, but can be the "centre of decision-making with regard to data processing operations." (https://doi.org/10.1093/idpl/ipy021)