Sk+1 = { x ∈ Sk | |fk(x) + δ| < rresonant }
rresonant = 1/φ² ≈ 0.381966
rresonant = 1/φ² ≈ 0.381966
Words persist if their field trajectory stays within the convergence radius of φ.
Words are scored by geometric field dynamics derived from three constants.
Each prompt deepens a persistent geometric library — outputs improve with use,
not retraining. Ask the same question twice and watch the field resolve further.
Words persist if their field trajectory stays within the convergence radius of φ.
GCL processes language through geometric field dynamics. A word becomes a named invariant when its symbol trajectory produces a bounded orbit near the golden ratio attractor — the same convergence criterion as the Mandelbrot set. No corpus. No training. No lookup tables.
Every constant in the system derives from π, φ, and the effective boundary 2.078. No learned weights. No training corpus. No embeddings.
Resolution scales with library depth. At cold start outputs are sparse. After a few questions on the same domain the field produces full five-word geometric sentences.