Base-Invariant Detection of Mathematical Constants in Universal Communication Systems

We present a formal computational method for detecting mathematical constants in encoded messages without prior knowledge of the number base used by the encoder. This problem arises in scenarios where sender and receiver cannot establish a shared coordinate system---including interstellar communication (SETI/METI), archaeological cryptanalysis, and cross-cultural information exchange. We prove that mathematical constants can be detected with arbitrarily high confidence by testing measurements against all plausible bases and identifying convergence patterns. Our detection algorithm achieves polynomial time complexity $O(|B| \times |S| \times |C|)$ and perfect parallelization. We establish theoretical bounds on detection probability, false positive rates, and provide extensive experimental validation. Applications extend beyond xenocryptography to include data format recovery, legacy system interpretation, and multi-modal sensor fusion.