Mathematical Semiotics and Descriptive-Retrodictive Modeling of Structural Collapse: A Case Study of the SAO Tower Incident

This study presents a descriptive-retrodictive model of the collapse of the State Audit Office (SAO) Tower in Bangkok on 28 March 2025. Mathematics is positioned here not as a physical cause, but as an interpretant that bridges empirical engineering data and symbolic order, following Peirce's triadic model. The physical cause of the collapse is established from official Thai investigations: corruption in procurement, a 15% underbid, a reduction of core shear wall thickness from 30 cm to 25 cm, the use of substandard materials, and forged engineering documents. These factors left the structure in an unfinished, torsionally vulnerable state when the Mw 7.7 Myanmar earthquake struck. On top of this empirical layer, the study identifies three closed mathematical chains. First, Nicomachus' Theorem: sum_{i=1}^{n} i^3 = T_n^2, where T_n = n(n+1)/2. For n = 9, T_9 = 45 and sum_{i=1}^{9} i^3 = 2025. Second, the Greek isopsephy of the lexical root psephizo equals 2025. Third, the integral from 0 to 45 of (-2x + 90) dx = 2025, interpreted as accumulated risk from tender to collapse. The study further organizes the investigation data into a 9 x 9 structure: nine cubic enumerations corresponding to nine groups of nine empirical findings. The study explicitly distinguishes the lexical form psephizo from the inflected form psephizei that appears in Luke 14:28, whose isopsephy is 1240. The model is therefore a retrospective semiotic reading, not a law of physical causality. Keywords: Mathematical Semiotics, Retrodictive Modeling, Nicomachus