Deterministic Overdose Escalation Limits in Feline and Canine Nutritional Formulations: A Closed-Form Margin-of-Safety Analysis

A diet can be adequate on day one and unsafe over a year, and it can be safe at the label dose and unsafe when an owner doubles it. This paper addresses both questions with models that are deliberately separate from the stochastic adequacy framework, because they answer different questions: the stochastic model asks whether a formulation is robust to a chaotic bowl; these ask whether it is robust to time and to dose. Three models are reported. A tissue-reservoir model buffers each nutrient by an exponential moving average parameterised by its storage half-life, and shows that integrating over the storage horizon can only raise the effective floor relative to a single-day snapshot. A one-compartment kinetic model replaces that reservoir with explicit homeostatic absorption regulation and first-order clearance, every parameter taken from published literature, and reduces exactly to the reservoir when no regulation is credited — so it can add mechanism but cannot contradict the floor. A deterministic over-dose escalation holds the bowl constant and increases the unit count one at a time, in closed form, to locate the first safe-upper-limit crossing. The results converge on one structural finding. Because the correction is delivered dry and unheated it carries no manufacturing overage for thermal loss, so its day-zero base sits low and the gap to every ceiling is wide by construction. On the release-A-1.0.0 block an owner must feed roughly three times the label dose every day before any nutrient reaches its safe upper limit, and the first nutrient to do so is a benign bulk mineral in both species — calcium in the cat at 15 units against a 5-unit label dose, iodine in the small dog at 14 — not a cumulative hepatotoxin. Copper, vitamin A and vitamin D — the actives whose chronic toxicity is best described in the veterinary literature [2] — sit far beyond binding, precisely because they are ceiling-guarded by design. The kinetic model supplies a candidate mechanism: under the cited absorption exponent, modelled tissue copper compresses toward a set-point from both directions, holding the modelled feline median at 116% of requirement against 153% under a linear reservoir.