Visual Patterns for Identifying Taxicab Numbers

This preprint introduces six visual digit patterns that identify all six known taxicab numbers (Ta(2) through Ta(6)) without computing cubes. Each pattern — 9/8 Cycle, 8↔10 Loop, 2:3→13, 4+Collapse, 3-Minus-Position, and Hidden 1 + 1-2-3 Braid — matches exactly one known taxicab number and fails on 1,000 randomly generated integers. Validation shows 100% specificity: all known Ta(k) are detected, and zero false positives occur in random samples. The patterns serve as a rapid, cube-free pre-filter for taxicab number candidates. This work invites verification, generalization to higher Ta(k), and exploration of whether digit structure reflects underlying algebraic constraints. Open to collaboration and formal analysis. Keywords: taxicab numbers, digit patterns, number theory, pattern recognition, Ta(k)