Marco Mandap proposed a framework that treats agricultural soil as a four-dimensional tensor: two spatial axes, a time axis spanning rotation cycles, and a nutrient channel axis carrying nitrogen, phosphorus, and potassium simultaneously. Crop rotations become force vectors applied to this tensor, with the soil's resistance varying spatially according to texture — sandy patches yield more readily than clay. In simulation, a three-year corn-soybean-wheat rotation on a heterogeneous grid produced a mean stress of 0.63 after one cycle, peaking at 0.91 in sandy regions. Phosphorus depletion dominated in roughly one-fifth of zones, reaching 17.9% versus nitrogen's 10.8% — a finding that single-nutrient analysis would have missed entirely.
The through-claim is that multivariate coupling creates invisible hotspots. When nutrients are tracked independently, each appears within acceptable bounds. Only when all three are examined together, in spatial context, do the zones of compound stress emerge. The field does not fail because any single nutrient is critically low; it fails because several are simultaneously stressed in the same place. The tensor representation does not just improve precision — it reveals a category of vulnerability that lower-dimensional analysis structurally cannot see.
This is a general property of coupled systems monitored through marginal statistics. Hospital readmission rates look manageable when tracked per condition; the patients who cycle back are those with multiple marginal risks converging. Network outages seem random when monitored per node; they cluster where several degraded links share a path. The instrument that separates variables for clarity also amputates the interaction term where the real risk lives.
(arXiv:2603.12881)