Autonomous Discovery of Fundamental Mathematical Constants via Unified Complexity Theory: UCT Sequence Probe v3.2.1

Mathematical sequences encode fundamental constants within their structural patterns. This work presents the Unified Complexity Theory (UCT) Sequence Probe v3.2.1, a computational framework that autonomously extracts these constants from raw sequence data without prior knowledge or assumptions. Principal Results:- Catalan base "4" identified with 0.018% relative error (N=512)- Golden ratio φ measured with 0.038% relative error (N=512)- EXACT regime classification (Λ=1.000, χ=0.000) achieved for Catalan numbers- Prime-Schröder structural connection observed- Complete analysis runtime: 7.75 seconds The framework incorporates seven distinct mathematical models with complexity-aware scoring, automatic model selection, and fundamental constant detection across 512-point sequences. Results support the UCT prediction that error scales as ε ~ 1/√N, projecting sub-0.01% precision at N=1024. This work demonstrates UCT as a computational tool for mathematical structure analysis, with potential applications in AI interpretability, algorithmic information theory, and automated theorem discovery. Interactive Demo:The framework can be evaluated in Google Colab (no installation required):https://colab.research.google.com/drive/1_5nhd-IfavxaSFKFi2BoMDjXpBKF0eoB?usp=sharing Package Contents:- Full paper- Production Python implementation- Complete data- Interactive Colab demo notebook Related Work:UNIFIED COMPLEXITY THEORY: Mathematical Foundation, Rigorous Proofs, and Universal Validationhttps://zenodo.org/records/17844198