Mathematical Semiotics of Cubit Variation as the Root of Length Discrepancy in the Durupinar Noah's Ark Formation: A Comparative Study of 51.41 cm vs 52.4 cm

This study addresses the length discrepancy of the Durupinar Formation, which is commonly cited as 506 ft versus 515 ft. Both figures claim to derive from the same biblical dimension of Noah's Ark in Genesis 6:15, namely 300 cubits in length, 50 cubits in breadth, and 30 cubits in height. This study shows that the discrepancy does not originate from differences in field measurement, but from differences in the definition of one cubit used in the conversion. This study uses a comparative quantitative method and mathematical modeling. Two cubit standards are compared: (1) 51.41 cm, as an anthropometric cubit proposed in this study, and (2) 52.4 cm, as the Royal Egyptian Cubit. The 51.41 cm cubit yields a total length of 154.23 m or 506.0 ft, while the 52.4 cm cubit yields a total length of 157.20 m or 515.7 ft. The difference is 2.97 m or 9.74 ft, and this difference is entirely a product of the cubit conversion factor. The study then validates the side-wall area using two models, the box model and the parabola model. In the first test with L = 506.0 ft, the difference between the two models is only 0.6 ft2 (0.005%). In the second convergence test with L = 506.5 ft, which is the parabola peak value, the difference between the two models becomes 0. This shows that the two models converge at the same point. From the perspective of mathematical semiotics, the numbers 506, 506.5, 20.6, 22.44, 11.28, and 33.72 are not read as coincidental numbers, but as signs that mutually reinforce each other within the same modeling system. This study concludes that standardization of the definition of one cubit must be done before further interpretation of Durupinar scan data (GPR, drone, LiDAR, and resistivity). Keywords: Noah's Ark, Durupinar, Cubit, Royal Cubit, Mathematical Semiotics, Parabola Modeling, Genesis 6:15