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(GeoOptimizer - pure thermodynamic optimization, no Adam, no gradients, no floats). Result: 6/6 mathematical verification tests PASS Symplectic condition det(T₃ᵏ) ≡ 1 (mod 13) Exact p-adic arithmetic Banded geometric attention O(N log N) Deterministic Zariski audit at every epoch But… nothing learned. Loss remained flat (~0.323), entropy frozen at 2.768. Why? Because the old hard entropy cap is still running. The model is mathematically perfect, but it doesn't have room for real data binding yet. It's like a pure crystal - beautiful, but not yet illuminated. Next step: Remove/soften S_G_MAX and let thermodynamic optimization run free. Algebra is alive. We learn slowly but exactly. #GeoLLM #IntegerAI #Z13eta #AlgebraicIntelligence