From Hyper-Catalan Geodes to Resonant Intelligence_ A Structural Reinterpretation of Constructive Algebra

CODES Framework Abstract: This paper reinterprets Wildberger & Rubine’s constructive algebra—especially their hyper-Catalan geodes and rejection of radicals—as structurally resonant expressions of coherence within the CODES framework. By mapping their geometric methods onto the Phase Alignment Score (PAS) model and structured emergence, we show that their mathematical logic aligns with resonance-based intelligence (RIC). This convergence reframes constructive math not as a limitation of abstraction, but as a return to physically coherent symbolic modeling, where infinity is not a truth but a phase error. The paper closes by proposing a symbolic compression pipeline from hyper-Catalan logic into resonance-native AI substrates.