Nutrient Adequacy and Biological-Architecture Classification: A Two-Axis Framework for Evaluating Variable Fresh-Food Diets in Companion Animals

Standard regulatory compliance models evaluate companion-animal diets with a single scalar test: does each nutrient clear a defined floor? That test is indifferent to the source of the nutrient and to the long-term appropriateness of the food supplying it. We argue that the quality of a companion-animal diet resolves along two independent axes — biological appropriateness and nutritional adequacy — and that conflating them is the central confusion in the fresh-feeding debate. We define BARC (Biologically Appropriate, Residually Corrected) as a diet meeting both requirements: a fresh-food base clearing published quantitative boundaries for appropriateness, and a calculated residual correction closing the measured gap to an established nutrient target (NRC 2006, and by extension FEDIAF and AAFCO profiles). Neither alone qualifies. We give the boundaries numerically, derive the four diet states the two axes produce, and demonstrate with a deterministic point-estimate model why a one-axis check is insufficient: a meat-free, grain-based bowl can read "adequate" while its total sulfur amino acids sit at roughly 111% of the recommended allowance and collapse to 61% when a single animal-protein component is removed — a structural failure no micronutrient correction can repair. We also set out the quantitative reason the two axes come apart in a modern household. Requirements for mass-tied nutrients track body mass; intake tracks calories. A free-ranging carnivore running a multiple of a sedentary pet's maintenance energy receives that multiple of every micronutrient against a requirement of the same order, so an ancestral recipe is adequate at ancestral energy throughput and incomplete at domestic throughput. We show that the organ-meat lever conventionally offered to close that gap is mathematically closed: in a cat bowl the vitamin A ceiling is reached at a liver fraction of roughly 16%, while the manganese floor is not reached until roughly 47%.