Topology is the algorithm: phrase-footprint geometry gates whether memory accumulation confers focal-lesion resilience

The cognitive-reserve hypothesis proposes that accumulated learning protects against focal brain damage, but clinical data cannot separate the number of memories acquired from the spatial extent they occupy. We examined this question in Hexcortex, a weight-free neuromorphic architecture in which memory traces occupy identifiable locations in a hexagonal microcolumn substrate. In an angular-gyrus analog (14,160 columns), we recorded firing during a stream of two-word phrases while ablating 0-100% of the association cortical columns within a temporal memory-trace zone, using scattered and contiguous lesions (230 recordings). To separate memory count from footprint, each single-phrase substrate was retrained to approximate the other phrase's memory count while retaining its own input-zone fingerprints exactly at the byte level. This produced a balanced 2 x 2 design across eight shared lesion seeds. An initial analysis showed asymmetric drift at 75% contiguous ablation that appeared to follow memory count. The factorial analysis separated the two factors. Resilience was determined primarily by footprint rather than by the number of memories formed (7->1: F(1,7) = 2527, p < 0.001). The interaction was the largest effect at the trained transition (1->0: F(1,7) = 944, p < 0.001): additional memory improved resilience in the wide-footprint substrate (? = +0.145, dz = 8.9) but not in the narrow-footprint substrate (? = -0.002, p = 0.19). We describe this pattern as footprint-saturation reserve: accumulated memory improves resilience while footprint headroom remains. Footprint and phrase identity co-vary in this experiment, and the measurements concern neural patterns rather than behavioral resilience.