Finite-Memory Prediction and Remote Feedback in Langton's Ant

A black read is old at memory depth D when its cell was absent from the preceding D visits. From any complete finite initial state, an algorithm finds the next old-black read or certifies its absence; for fixed D it runs in polynomial time in sparse binary input size. Finite arithmetic segments preserve every skipped write and the complete endpoint field. Geometric estimates give quadratic finite-event deadlines and total spatially and birth-filtered queries. Non-eventually-translating orbits must consume infinitely many black lifetimes that are simultaneously late-born, old and remote. A twenty-black family has unbounded feedback lifetimes with exactly 31 intervening old-black reads at D=128, establishing the essential role of spatial extent in lifetime bounds.