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The calibration of radiocarbon measurements is based on a number of mathematical assumptions that are rarely considered by users of the various available calibration programs. As 14C ages take on mathematical properties best known from quantum physics, a quantum theoretical approach provides a useful basis to evaluate the reliability of processes of calibration and Bayesian modelling of radiocarbon datasets. We undertake such an evaluation here through a consideration of the mathematics of calibration, the normalization process, and through an archaeological case study. We demonstrate that the normalization function deemed necessary for 14C histogram shape-correction is identical to the default prior widely used in Bayesian calibration. We highlight flaws in default Bayesian calibration algorithms which may affect archaeological studies that are overly reliant on high calibration precision, especially when based on relatively small (N<100) sample sizes. The observed differences between algorithms have consequences for radiocarbon models that claim sub-generational (~25–30 calendar years) precision. [ABSTRACT FROM AUTHOR]

The region of the upper Neckar and Ammer river valley is situated on the south-westernmost periphery of the overall distribution area of the earliest LBK in Europe. In a small side valley of the Ammer, we have been able to investigate in the past few years the two sites 'Lüsse' and 'Unteres Feld' which have provided important information about the beginning and development of the Early Neolithic in southwestern Germany. From these two sites, we have a sequence of features from all phases of the LBK. Radiocarbon data obtained from short living samples (charred seeds, animal bones from ungulates and human bones) were combined with pottery stylistic data from the same features to construct an age-model that can be applied, simultaneously, on site-level (locally) as well as on supra-regional level. The data series was first analysed using the GaussWM-algorithm in the CalPal program (Version, 2019.5), by application of an assumed linear (equal phase-length) age-model, and then using OxCal (Version 4.3), by application of Bayesian Boundary analysis. Both methods come to practically identical results. The pottery stylistic development of the LBK can henceforth be described, locally, by application of the five Ammer Valley stages (AV 1-5), and which are in turn synchronised with the widely applicable chronological system of Meier-Arendt (1966) which itself has five phases (I-V). Although generally similar, the two systems show certain differences but which only become apparent due to the achieved high temporal resolution of a few decades. An important observation is that in the Ammer Valley material with typological features of the earliest LBK (AV 1) can also be found in more recent LBK contexts, apparently undisturbed. In the upper Neckar region, in contrast, it is the Flomborn style (AV 2 and 3) that appears alongside the old pottery traditions. Put together, the old pottery traditions persisted for an exceptionally long time, in the newly founded settlements in the Ammer Valley. [ABSTRACT FROM AUTHOR]