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Summary The present study aims to outline new, more adjusted approaches of research addressing social complexity of past societies. In doing so, we use varied evidence to detect major ‘leap events’ in the history of ancient Egypt which were reflected by the state administration and its fluctuating complexity. The archaeological and inscriptional evidence shows that crucial changes in history had a non-linear, punctuated character. To reveal their true character, newly developed mathematical models have been applied. The analyses of early complex civilisations have made a noticeable progress recently. The current scholarship pays significant attention to a processual approach, description of the dynamics and its interpretation against the specific background formed by varied datasets originating from disciplines such as archaeology, history, art history, philology or environmental sciences to name but a few of the most relevant ones. Within this context, Old Kingdom Egypt evidence is reassessed using specific methods of analysis and interpretation. The ancient Egyptian Old Kingdom (2592–2120 BC), one of the earliest territorial states on this planet, is still frequently considered to be a homogenous continuum of isolated historical events manifested in various forms of architecture, art or religion. Some recent studies applied to its study put emphasis on a non-linear, ‘punctuated approach’ which appears to provide some new important perspectives on this traditional problem. The application of modern mathematical methods based on Hidden Markov Models and Social Network Analysis significantly changes this view. These methods have the potential to detail a vivid, heterogenous process of historical progress as a punctuated equilibria model, as a non-linear system with changing dynamics of its development in time. In this process, human agency, the rise and fluctuation of complexity and particular strategies of different social groups played significant roles and can be detected with the help of impartial approaches. The emerging picture can be used not only to describe the evolution of a past society but also for comparative purposes when studying the dynamics of past or present societies.

A study of the King’s daughter Sheretnebty, whose tomb-complex is situated in the non royal necropolis in Abusir South, raises many questions with regard to the history of the Fifth Dynasty (2,494–2,345 BCE). This paper provides an interpretation of the newly acquired evidence that emerged during the second season of exploration of her tomb-complex, which began in 2012 (ArOr 80). During this season’s work, two additional rock-cut tombs belonging to high officials were uncovered in the south-eastern part of the complex, and the finds included a set of limestone and wooden statues and fragments of the false-door of Sheretnebty. This newly discovered evidence enables us to identify tomb AS 68c as the most probable place of Sheretnebty’s burial. In addition, the discovered fragments of her false-door indicate that Sherentebty was the daughter of King Niuserre from the Fifth Dynasty.