Geometry G v4 — A Minimal Cognitive Geometry and Its Empirical Testbed

Geometry G v4 presents a fully operational, falsifiable cognitive geometry designed to test whether a stable internal vertical axis modulates perception of ambiguous shapes. Version 2 consolidates the formal structure, expands the reference implementation, and provides a complete experimental testbed enabling independent researchers to evaluate the framework without interpretive drift. Keywords and Subjects Heat kernels; Plancherel measures; Selberg trace formula; solvable two‑dimensional gauge theory; harmonic analysis; representation theory; spherical functions; Casimir operators; symmetric spaces; geodesic–holonomy correspondences; spectral geometry; finite‑group analogues; TQFT gluing operators; structural engines; adaptive engines; Carlo Reset Operator; axiom–equation mapping; Carlo Field progression; multi‑volume NOTEBLOCK systems; symbolic languages; cosmological architectures; mythic frameworks; identity mapping; narrative engines; creative structural systems; emergent‑structure synthesis; structural compendia; universe‑scale mapping; forward‑trajectory planning. Contact: [email protected]