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

Manuscript 6 of 8 in the BARC Protocol specification series · Release B-2.1.0 · September 2026

Author. Prasanna M, Growlrr Foods Pvt Ltd, Chennai, India. Correspondence: support@growlrr.com. ORCID: 0009-0003-6812-347X.

DOI. 10.5281/zenodo.22647616 — the concept DOI, which always resolves to the current version of this record · Published. 8 September 2026 · Licence. CC BY-SA 4.0 · Status. Not peer-reviewed as of the date of publication, 8 September 2026.

Competing interests and funding. The author is the founder of Growlrr Foods Pvt Ltd, a pioneer and proponent of the BARC Protocol for pet foods. BARC stands for Biologically Appropriate, Residually Corrected, and is conceptualised as an open protocol under a Creative Commons Attribution–ShareAlike licence, for like-minded collaborators around the world to formulate and develop. Growlrr Foods Pvt Ltd develops and commercialises a BARC-based residual-correction product, BowlBalancer. The work was funded entirely by the company; no external funding was received. No independent laboratory, institution or reviewer has verified the results reported here. Readers should weigh these facts alongside the analysis, which is published in full — including its limitations and open items — precisely so that it can be checked.

Framework. This work applies BARC — Biologically Appropriate, Residually Corrected — an open protocol for correcting a biologically appropriate fresh base to a published nutrient standard, released under a Creative Commons Attribution–ShareAlike licence (CC BY-SA 4.0) at growlrr.com/barc-protocol (concept DOI 10.5281/zenodo.22648597) so that others may formulate and develop against it. BARC is the protocol; the correction specified and validated here is one implementation of it.

Terms. A glossary of the statistical and nutrition vocabulary used across this series — requirement, floor, safe upper limit, Wilson bound, N-limited, draw, stress multiplier, retention factor, trituration and the rest — is in the series cover note (10.5281/zenodo.22647606), section 4.1.

Computational tooling and AI assistance. The model is implemented in TypeScript under Node.js with no external numerical dependencies. Claude (Anthropic) was used as a coding and analysis assistant in developing this work and preparing these records; it was not used to generate results, all of which were produced by executing the model. See the series cover note (10.5281/zenodo.22647606), section 6.1.

Plain-language material. The corresponding public account of completeness and safety is at growlrr.com/is-growlrr-complete. The public reference list behind these claims is at growlrr.com/pet-nutrition-references.

Scope of §3. The deterministic escalation is computed on the release-A-1.0.0 formulation block. The subsequent calcium re-architecture [Manuscript 1] reduced correction-borne phosphorus, which moves the phosphorus crossings later; the escalation has not been re-computed on that basis, and §3.4 sets out what this means for each nutrient.

Abstract

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.

Keywords: BARC Protocol · residual correction · homemade dog food · homemade cat food · home-prepared diet · companion animal nutrition · toxicokinetics · safe upper limit · margin of safety · overdose modelling · homeostatic absorption · hepatic copper · tissue reservoir · one-compartment model · non-thermal formulation

1. Introduction — why these models are separate from the stochastic framework

Mixing them produces category errors, so they are reported apart.

2. Methods — the companion model on the time axis

This paper covers the dose axis. The time axis — whether adequacy survives once tissue stores buffer it, and whether accumulating nutrients stay bounded over months — is the subject of [Manuscript 5], which reports a tissue-reservoir model and a one-compartment kinetic model with homeostatic absorption, together with the full cited parameter set.

Two of its results are load-bearing here and are quoted rather than re-derived. First, copper is the deliberately ceiling-guarded nutrient of this formulation, held closest to its floor from above so that every other nutrient sits higher. Second, under the cited absorption regulation the modelled tissue copper compresses toward a set-point rather than tracking intake upward, plateauing near 155% of requirement even under a three-fold over-supply.

Those results explain why the nutrients owners worry about are not the ones that bind in the escalation below. They are not repeated here.

3. Results — the deterministic over-dose window

3.1 Question and design

If an owner deliberately over-doses — the same bowl, extra units — how many whole units above the recommended dose before the first nutrient crosses its safe upper limit, and which nutrient is it?

The bowl is held constant and only the unit count U rises, so delivery is linear and the model is closed-form with no random component:

delivered(U) = food + U × correction-per-unit; breach when delivered ≥ requirement × SUL%

Nutrients with no established toxicity ceiling — thiamine, riboflavin, pantothenate, cobalamin, taurine, choline — are excluded by construction. Two deliberately conservative subjects are used: the 4 kg cat (the anchor, requirement multiplier exactly 1.0) and a 4 kg small dog — the lowest body mass that still takes a real dose, and therefore the least tissue to buffer an overdose per kilogram, scaling to 0.357 of the 20 kg anchor. Both sit at the recommended 5 units per day.

3.2 Why the margin is wide by construction

Extruded and retorted foods undergo severe thermal degradation in manufacture and must front-load labile vitamins to clear a shelf-life target. That overage narrows the distance between the delivered dose and the safe upper limit before an owner does anything at all.

A dry, unheated correction requires no manufacturing overage [Manuscript 4]. It sizes to the requirement at manufacture, so its day-zero base sits low and the ceiling buffer is wide by construction rather than by generosity. This is a structural consequence of the delivery format, not a formulation choice made for safety margin.

3.3 Result — release A-1.0.0 block, 3 August 2026

The binding limit is a benign bulk mineral in both species — calcium in the cat, iodine in the small dog — with wide, well-tolerated windows, not a cumulative hepatotoxin. The nutrients owners actually worry about sit far beyond binding: feline copper reaches its limit only at +82 units, vitamin A at +235, vitamin D at +3,267; canine vitamin A at +56, copper at +58, vitamin D at +285. They never lead because they are ceiling-guarded by design [Manuscript 5].

The small dog is the tighter case, as intended: it breaches one unit sooner than the cat, on iodine, confirming that the study selected the conservative subject.

Full per-nutrient windows are in the Appendix.

This is a deliberate-overload stress map, not a dosing instruction. The label dose stands.

3.4 Reading these figures against the current formulation

The calcium re-architecture [Manuscript 1] left the delivered calcium target unchanged but reduced correction-borne phosphorus by 61 to 64%. Two consequences follow directly:

• The phosphorus crossings are conservative for the current adult formulation. Less correction-borne phosphorus means the crossing moves to a higher unit count, not a lower one.
• The calcium crossings are unaffected in principle, the calcium target being unchanged, and calcium is the binding nutrient in the feline case.

The figures are therefore reported on the release-A-1.0.0 basis, which is the conservative one for the nutrient that binds first in the canine case and neutral for the one that binds first in the feline case.

4. Discussion — what the two axes establish together

The escalation reported here shows that the first ceiling reached under gross mis-dosing is a benign bulk mineral at roughly three times the label dose, and that the cumulative actives sit far beyond binding. The time-axis models of [Manuscript 5] show why: those actives are ceiling-guarded by design, and regulated absorption compresses the one that matters toward a set-point rather than letting it accumulate.

Together the two axes bound the correction from above, as the stochastic framework [Manuscript 2] bounds it from below. Safety is a property of the ceiling as much as the floor, and neither a single-day snapshot nor a dose escalation alone can establish it.

5. Limitations and open items

• The escalation is computed on the release-A-1.0.0 formulation (§3.4), which is conservative for phosphorus and neutral for calcium.
• Safe upper limits were accessed through secondary summaries of NRC 2006 [1] and must be verified against the primary volume, with the specific tables named, before any label claim.
• Nutrients without established ceilings are excluded from §3 by construction, so the analysis speaks only to nutrients that have one.
• These are models. No animal study is reported here, and none should be inferred. A non-invasive household observation study is planned; see the series cover note, Limitations and future work.
• Healthy animals only. Not a clinical or therapeutic system, and no disease claim is made.
• Not peer-reviewed as of the date of publication (8 September 2026). Should it later be reviewed or independently replicated, that will be recorded in a subsequent version of this record.

6. Conclusion

The dose axis is treated deterministically: units are escalated until the first nutrient reaches its safe upper limit, and the margin is the multiple of the label dose at which that occurs. 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 distance to every ceiling is wide by construction rather than by tuning.

On the modelled configuration an owner must feed roughly three times the label dose every day before any nutrient reaches its limit, and the first to do so is a bulk mineral in both species — calcium in the cat, iodine in the small dog — rather than a cumulative hepatotoxin. Copper, vitamin A and vitamin D sit far beyond binding, because they are ceiling-guarded by design.

These are deterministic point estimates on a modelled diet, not observations of over-dosed animals, and the margins describe the correction rather than any bowl an owner might additionally supplement.

References

1. National Research Council (US), Committee on Animal Nutrition. Nutrient Requirements of Dogs and Cats. Washington (DC): The National Academies Press; 2006. doi:10.17226/10668
2. Seawright AA, English PB, Gartner RJW. Hypervitaminosis A and deforming cervical spondylosis of the cat. J Comp Pathol. 1967;77(1):29–39. doi:10.1016/S0021-9975(67)80003-4

Appendix · Per-nutrient over-dose windows, release A-1.0.0

Closed-form, no random component; food held constant; +1 unit per day escalation from the recommended 5 units per day. Safe upper limits are expressed as a percentage of requirement.

Cat · 4 kg (anchor). First whole-unit breach at 15 units (+10, 3.0× dose) — calcium.

Dog · 4 kg (small, conservative). First whole-unit breach at 14 units (+9, 2.8× dose) — iodine.

How to cite

Prasanna M. (2026). Deterministic Overdose Escalation Limits in Feline and Canine Nutritional Formulations: A Closed-Form Margin-of-Safety Analysis (Manuscript 6 of 8, Release B-2.1.0). Growlrr Foods Pvt Ltd. Zenodo. https://doi.org/10.5281/zenodo.22647616

The series

This manuscript is one of eight deposited together under release B-2.1.0, with a series cover note carrying the concept DOI and the full DOI list. All eight apply the BARC Protocol, published openly and separately at growlrr.com/barc-protocol.