Integer determination of the Antikythera calendar ring hole count

Determine whether the total number of equally spaced holes in the full front-dial calendar ring of the Antikythera mechanism is an integer; if it is, identify the specific integer value of N.

Background

This paper performs a Bayesian analysis of high-resolution X-ray measurements of hole positions beneath the Antikythera mechanism’s front-dial calendar ring to infer the total number of holes, N, in the original complete ring. The authors model tangential and radial positional errors and marginalize over fragment translations and rotations to obtain credible intervals for N.

Their results strongly favor approximately 354 holes over 360 or 365, and they assess probabilities for integer values using both MCMC and nested sampling methods. However, despite these constraints, they explicitly state that they cannot definitively establish that N is an integer nor identify a unique integer value, leaving the integrality and precise count unresolved.