ZUSE Automat Agent: Empirical Law Discovery in Elementary Cellular Automata

Version v1.15 integrates Fase 44 and Fase 45: algebraic normal form (ANF) analysis of the dense T=15 causal cone. Fase 44 audits the 25-input, 12-step causal cone using exact bit-packed truth tables and Möbius transforms to obtain algebraic normal form coefficients. Across the 20 minimal T=15 representatives, 174 active outputs are analyzed. Active-output ANF degree ranges from 14 to 24; no output reaches the formal degree-25 ceiling. Active-output monomial counts range from 9,376 to 17,758,052. The result is LOW_OUTPUT_ANF_DEGREE_FOUND: the cone is not algebraically uniform. Fase 45 shows that this variation is highly structured. Active-output degree follows: degree = 24 - abs(rel_pos) + epsilon, with epsilon in {0,1} with zero exceptions over 174 active outputs. Monomial counts obey an almost exact spatial decay law: log10(monomials) ~= 7.241925 - 0.307283 * abs(rel_pos) with R^2 = 0.998197. The slope is close to -log10(2), meaning that monomial count decays almost by a factor of two per cell away from the defect center. This gives the first positive algebraic structure after the previous ROBDD negative results: the T=15 cone remains dense and input-complete, but ANF exposes a spatial complexity gradient centered on the active defect. All results are reproducible from deterministic scripts. Repository:https://github.com/conchaestradamiguelangel-droid/zuse-automat-agent