U-Bit Collapse in Arnault Composites (v1.0)

This repository contains the paper and dataset accompanying the arXiv preprint: U-Bit Collapse in Arnault Composites: Probing the Boundary of Strong Lucas PseudoprimesBowman Hall, January 2026 Overview This work presents a large-scale computational study of composite integers constructed using the Arnault framework and engineered to pass multiple Miller–Rabin primality tests (through base 11). The study investigates whether such composites exhibit any measurable progress toward evading the strong Lucas probable prime test, a core component of the Baillie–PSW primality test. To quantify deviation from expected Lucas sequence behavior, the paper introduces the U-bit collapse metric[ \delta = \log_2 n - \log_2(U_d \bmod n), ] where ( n + 1 = d \cdot 2^s ) with ( d ) odd. Across 200 Miller–Rabin–resistant composites of approximately 350 bits, no significant Lucas collapse is observed. All samples fail the strong Lucas test, with collapse values concentrated near zero, providing empirical evidence for the orthogonality of the Miller–Rabin and Lucas components of Baillie–PSW.