ZUSE Automat Agent: Empirical Law Discovery in Elementary Cellular Automata

Version v1.8 adds the Fase 31–32 compact-state-variable analysis of the T=15 oscillator family. Fase 31 searches for a shorter descriptor of the T=15 shape family than the full temporal background orbit. No compact background-only descriptor among length-2..4 circular subpattern counts, parity, run lengths, first-one position, or short orbit prefixes predicts all 13 global shape families. The only exact background-only descriptor is orbit_prefix_24, which is effectively the full temporal background orbit rather than a compact symbolic law. Conditioned on the ECA rule, however, the circular multiset of length-4 background subwords (subpatterns_len4) separates all 10 backgrounds per rule into unambiguous shape-family buckets. This identifies the shortest non-orbit descriptor candidate found so far. Fase 32 tests the key rotation-equivariance prediction of that descriptor. Across all seven non-trivial rotations of each of the 20 representative backgrounds, fixed IC placement almost completely fails: only 3 of 140 rotations produce T=15, and only 1 matches the predicted family. When IC/background alignment is preserved by co-translation, all 140 of 140 rotations produce T=15 and all 140 match the predicted family. The resulting compact state variable for the confirmed representative set is: (rule, subpatterns_len4, IC/background alignment) This closes the current T=15 symbolic arc: the mechanism is established as a five-state defect cycle under F^3, exact black/white conjugation is proved analytically, sparse truth-table support is rejected, fixed local block derivation is rejected, finite shape families are identified, and the compact state variable controlling those families is now isolated. The co-translation result is a rotation-equivariance validation on known representative backgrounds and their rotations, not a claim of prediction over unseen backgrounds. ZUSE Automat Agent is a deterministic, policy-driven discovery loop for elementary cellular automata. It builds an empirical atlas of cycle laws, world families, basin fragility, and background-conditioned oscillator dynamics using fixed evaluators and reproducible scripts. The discovery loop itself is deterministic. Language-model assistance was used only after execution for interpretation and documentation, not for world selection, law evaluation, scoring, or acceptance of empirical results. All results are reproducible from deterministic scripts with no stochastic components in the discovery loop. Repository:https://github.com/conchaestradamiguelangel-droid/zuse-automat-agent