Symbolic Modular Field Invariants: Mathematical Tests and Empirical Validation

This research package explores the emergence of mathematical invariants in symbolic modular fields, focusing on their role in stabilizing memory across loop structures. Using a series of tests involving symbolic loops modulated by irrational constants—including the golden ratio (𝜙), √2, and the novel stabilizer ⟦κ⟧\llbracket \kappa \rrbracket[[κ]] derived from the Kuro Nova (KN) framework—we compute symbolic memory scores and identify a robust pattern of invariant behavior. This work supports the broader SMFT (Symbolic Modular Field Theory) effort, bridging symbolic AI, cognition models, and modular mathematics. Results suggest the presence of a conserved symbolic quantity that may serve as a foundation for memory architecture in artificial minds.