Statistical Validation of a Stochastic Nutrient-Risk Model for Variable Fresh-Food Inputs

Manuscript 2 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.22647610 — 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 Not peer-reviewed as of the date of publication, 8 September 2026.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.

Plain-language material. A non-technical account of this validation is at growlrr.com/1-million-bowl-test and growlrr.com/how-we-validated-homemade-pet-food, of the reliability framework at growlrr.com/pet-home-cooked-recipes-blog/nutritional-reliability-framework, and of feline taurine in home-prepared bowls — relevant to the delivery floor in §3.1 — at growlrr.com/pet-home-cooked-recipes-blog/cat-taurine-homemade. The public reference list behind these claims is at growlrr.com/pet-nutrition-references.

Data availability. The per-run outputs underlying every aggregate reported here are tabulated in Appendix B. The full audit corpus described in §5 is not deposited; it is available from the author on request.

Abstract

Conventional quality control for companion-animal formulations certifies a recipe against a single averaged composite: a deterministic point estimate. That method is blind to the variance of fresh agricultural ingredients, to manufacturing tolerance, and to the biological variation of the animal receiving the food.

This paper documents a stochastic alternative. Every raw ingredient is treated as a distribution rather than a scalar; five multiplicative lognormal noise sources are applied per simulated feeding day; and a day passes only if every floor nutrient is delivered at or above 90% of its NRC 2006 requirement, with no nutrient reaching 80% of its safe upper limit. The population statistic is the lower limit of a Wilson score interval on the pass proportion.

We describe a three-stage verification programme and report its results. A 10,000-draw provisional gate confirms that a formulation change has not broken a floor. An inherited 100,000-draw baseline over a four-fold stress envelope, run as a five-model cascade, returns Wilson-C95 99.996% for both species. A 1,000,000-draw full-population validation on the release-B-2.1.0 engine, accumulated as ten independent 100,000-draw runs with seeds spaced 1,000 apart, returns zero failures for both adult corrections, a pooled Wilson-95 lower bound of 99.9996%, N-limited, and a between-run standard deviation on the worst-nutrient mean of 0.042 (dog) and 0.057 (cat) percentage points of requirement.

Past zero observed failures a Wilson bound reduces to n/(n + z²) and is a function of draw count alone; the physical quantity it accompanies converges by roughly 5,000 draws. The 1,000,000-draw run is therefore reported for its replicate dispersion and its audit corpus, not for extra decimal places, and the bound is stated as N-limited every time it appears.

Keywords: BARC Protocol · residual correction · homemade dog food · homemade cat food · home-prepared diet · companion animal nutrition · Monte-Carlo simulation · stochastic validation · Wilson score interval · lognormal noise · nutrient adequacy · N-limited bound · replicate dispersion · reproducibility · NRC 2006

1. Introduction — point estimate versus distribution

In standard practice a formulation's safety is verified on paper by comparing a single averaged laboratory composite against a regulatory minimum. The method assumes every gram of raw material carries an identical nutrient content. Real macro-ingredients — chicken and mutton mince, fish, egg, curd, vegetables — vary with season, supplier, cut, processing and cooking retention.

The model described here replaces that assumption. Each nutrient in each ingredient is a distribution; each simulated feeding day is one draw from the joint distribution of a bowl plus its correction; and the question asked is operational rather than nominal: for what fraction of realistically varying daily bowls does the corrected diet clear every floor without approaching a ceiling?

2. Conventions

These govern every figure in this paper and in the series.

• A day passes only if every floor nutrient is delivered at ≥ 90% of its NRC 2006 requirement [1]. This is a joint criterion, not an average.
• A batch fails if any nutrient reaches ≥ 80% of its safe upper limit.
• The population statistic is the lower limit of the Wilson score interval [2] on the pass proportion, at z = 1.96 (the two-sided 95% interval). This convention is used for every figure in this paper.
• The release gate is C/R 95/99: the Wilson-95 lower bound must be ≥ 99% of days at ≥ 90% of requirement. Requirements are the NRC recommended allowances, cross-checked against the FEDIAF [3] and AAFCO [4] profiles where those bodies publish a value.
• With zero observed failures the bound reduces to n/(n + z²), a function of draw count alone. Such a bound is reported as N-limited.
• No percentage is quoted without its species, release, draw count and confidence basis.

3. Methods — the noise model

Five multiplicative, strictly positive, lognormal variance sources are applied per draw. The convention is multiplicative because the underlying variation is proportional rather than additive, and bounded below at zero.

Evaluation runs across the full allometric envelope — dog 2.5–110 kg with the metabolic multiplier sampled over [1.2, 1.8], cat 2.5–10 kg over [0.9, 1.3] — so the consequence of weight-class dosing (a fixed unit count delivers less per calorie to a more active animal) is sampled rather than assumed [Manuscript 3].

Two grocery constructions share the same correction, noise and pipeline: a smooth-day model, the same diverse bowl every day, and an alternate-day rotation model, which rotates the protein between days. Rotation is the harder pattern, because it exposes troughs that a smooth average hides.

3.1 Cooking-retention factors — model parameters, not measurements

Cooking retention is not one coefficient applied uniformly. Each nutrient carries its own retention factor: the fraction of the raw content assumed to survive preparation, applied to the grocery base before any correction is added.

These factors are estimates and should be read as such. They are drawn from the general food-science and feed literature on cooking and processing losses; they have not been measured on these bowls, on this product, or in any kitchen, and no result reported here should be taken as evidence for any individual value. They are inputs to the model, in the same category as the composition tables — a stated assumption whose consequences are then explored, not a finding.

The model is built on the premise that they are uncertain. Each retention factor is a stochastic input rather than a constant: it is redrawn on every simulated day with a coefficient of variation of 0.20, rising to 0.80 in the fourfold-stress arm. A result that survives the stressed arm has therefore survived retention behaving very differently from the assumed central value, which is the point of stressing it. Nothing in the reported reliability figures rests on any one factor below being right.

The values below are the assumed central values.

Thiamine is assigned a retention of zero. It is the most heat-labile nutrient in the panel, and rather than model a partial loss the engine assumes the cooked base delivers none of it, requiring the correction to supply the entire requirement. This is deliberate over-provision: if any thiamine does survive preparation, the animal receives more than the floor rather than less. It is also why thiamine appears at a literal 0% of requirement in the uncorrected arm of the ablation [Manuscript 8].

Taurine is handled by a delivery floor rather than by retention alone. Its retention factor is 0.60, but the correction additionally gap-fills taurine to a floor of 2.3 times the NRC recommended allowance in cats and 4.0 times in dogs, computed against what the food and the remainder of the correction already supply — so the rule can only ever add, never displace what the diet provides. The asymmetry is deliberate and rests on three properties specific to this nutrient. Taurine is water-soluble and carries no established safe upper limit, so it is excluded from the safe-upper-limit panel entirely and a generous floor costs nothing in ceiling headroom. Its deficiency endpoints in cats — dilated cardiomyopathy and central retinal degeneration — are severe and, in the retinal case, irreversible. And in the canine arm it was the second-largest contributor to near-floor draws under fourfold stress, so raising the floor removed a variance source rather than adding a safety margin that was not needed.

The general rule the engine follows is therefore conditional rather than uniform: where a nutrient has a meaningful ceiling, the correction sizes to the requirement and the margin to the ceiling is computed and reported [Manuscript 6]; where a nutrient has no established ceiling and a severe deficiency endpoint, it sizes to a generous floor instead.

This is a structural difference from an uncorrected fresh-feeding calculation. A diet planned from raw composition values — whether raw-fed, or home-cooked but costed against a table of uncooked ingredients — counts nutrients the pot has already destroyed. The heat-labile vitamins are where that error is largest, and for thiamine it is total.

A second discount applies only to the vegetable component: phytate and oxalate binding lowers the absorption of plant-borne minerals relative to animal-borne ones, at iron 0.35, zinc 0.50, copper 0.65, calcium 0.55, manganese 0.60 and phosphorus 0.55. The vegetable fraction is fed for fibre and satiety and the correction owns the minerals, so the effect on the result is small — plant minerals are not credited at face value.

3.2 Computational implementation

The model is implemented as TypeScript modules executed under Node.js (v26 at the time of the reported runs), as a self-contained program with no external numerical or statistical dependencies. Every routine that bears on a reported figure — the pseudo-random generator, the sampling transform, the Wilson interval and the aggregation — is implemented in the codebase rather than delegated to a library, so that the arithmetic behind any result can be inspected without resolving a dependency tree.

Pseudo-random generation uses mulberry32, a 32-bit seeded generator. It is deterministic: a given seed reproduces a run exactly, which is what allows the paired-arm ablation to hold everything constant except the correction [Manuscript 8], and what makes the replicate structure of the 1,000,000-draw run meaningful. It also has the corresponding limitation, stated in §7: a nested sweep on one stream is not independent replication, which is why the replicate dispersion is taken from ten independently seeded runs rather than from the sweep.

Sampling uses the Box–Muller transform to generate normal deviates, converted to a mean-corrected lognormal so that multiplicative noise is strictly positive and does not shift the mean of the quantity it perturbs. Lognormal rather than normal is deliberate: a nutrient's delivered quantity cannot go negative, and the error in a grocery weight or an assay is proportionally rather than additively distributed.

Reproducibility. Seeds, draw counts, stress multipliers and configuration are recorded with every result reported here (§2). The engine source is not deposited (see the cover note's disclosure boundary), so a reader can reproduce the procedure from this description but cannot regenerate these exact draws; the audit corpus in §5 is deposited so that the reported aggregates can be checked against the per-run outputs they came from.

Use of AI assistance. Claude, a large language model developed by Anthropic [5], was used as a coding and analysis assistant during the development of the model and in the preparation of this series: in writing and refactoring implementation code, in auditing the manuscripts for internal consistency, and in checking reported figures against the engine's output. It was not used to generate results: every quantitative value reported in this series was produced by executing the model. The author is responsible for the content.

4. Results — the staged verification programme

Staging is by draw count, according to what each stage is for.

4.1 Stage 1 — the 10,000-draw provisional gate

Run whenever the formulation changes, to confirm the change has not broken a floor. On the release-B-2.0.0 adult corrections, following the calcium re-architecture [Manuscript 1]:

Only the first of these is consistent with zero failing draws at N = 10,000; the other two reflect a handful of sub-90% draws in the stress and cat conditions, which is exactly what a provisional gate exists to see. All three clear the 99% gate.

4.2 Stage 2 — the inherited 100,000-draw baseline

On the release-A-1.0.0 adult corrections (adult-correction formulation, identifier 842353e5, fixed 3 August 2026; identifiers are defined in §6.4), a five-model cascade — smooth-day snapshot, smooth-day tissue reservoir, rotation snapshot, rotation reservoir, and a joint release gate — at 100,000 draws per stress point:

Wilson-C95 99.996% both species; Wilson-C99.99 99.985% (dog) and 99.977% (cat); zero safe-upper-limit breaches.

This remains the only result computed on a C99.99 basis in this programme (§6.4). The stress envelope is in Appendix A: smooth-day reliability is flat at 99.996% across ×1 to ×4 for both species, while alternate-day rotation degrades gracefully but stays above the gate even at four times realistic kitchen variance (cat 99.391%, dog 99.421%), with the degradation knee beyond the ×4 ceiling.

Because the correction is delivered identically every day regardless of which protein was served, rotation moves the macronutrient profile without moving the correction's micronutrient contribution. This follows from the architecture rather than being tested by the run.

4.3 Stage 3 — the 1,000,000-draw full-population validation

Run 29 August 2026 on the release-B-2.1.0 engine (build 3077c230; formulation block, bill of materials, diet and dose ladder unchanged from B-2.0.0), for the two adult corrections only — dog and cat maintenance.

Design. Ten independent runs of 100,000 draws each, with seeds 42, 1042, … 9042 spaced 1,000 apart so that no derived stream can collide between runs, pooled exactly on pass and total counts.

Every individual run returned 100,000 of 100,000, with a per-run Wilson-95 lower bound of 99.996%. Per-run detail is in Appendix B. With zero observed failures the bound is closed-form — n/(n + z²) — so the pooled figure follows directly from the draw count and requires no estimation.

Accumulated, not brute-forced. A single 1,000,000-draw process does not complete on the reference hardware; it exhausts the heap. The run is therefore accumulated from ten independent seeded runs — which is how the practice always worked, but which became reportable only once the streams were independently seedable. Before that, ten runs would have been bit-identical repeats and no dispersion could have been computed. Total wall clock was approximately four minutes.

Basis of the palatant contribution. Commercial palatant suppliers do not disclose nutrient composition, so the palatant's contribution is characterised by the authors from its constituent breakdown [Manuscript 4]. Every figure in this paper is computed on that basis.

4.4 Scope of the 1,000,000-draw run

The 1,000,000-draw validation covers the two adult maintenance corrections and nothing else. The growth, reproduction and large-breed configurations are evaluated separately and were deliberately not re-run at that scale: they add no new active and no new excipient, they already clear the gate at 10,000 draws, and a 1,000,000-draw run against provisional manufacturing tolerances would be invalidated the moment the manufacturing sheet locks. They are verified at 10,000 draws and bridged by equivalence to the adult-core convergence plateau.

All five were re-tested to the B-2.1.0 standard on 29 August 2026:

All five clear the C/R 95/99 gate. The dog reproduction co-blend is formulated with a growth-biased ratio so that its phosphorus delivery matches a lactating dam's requirement; the composition and its delivered values are given in Manuscript 1 §5.1.

5. The audit corpus

Two artefacts accompany the 1,000,000-draw run: the pooled and per-run JSON records, and a 200,000-row audit corpus. The per-run records are reproduced in Appendix B; the corpus itself is not deposited and is available from the author on request.

The corpus is 10,000 rows per run per species, sampled without replacement by a deterministic sampler that is independent of the engine's own random streams — so the published file is itself reproducible — then merged across all ten seeds and shuffled. The shuffle is load-bearing: unshuffled, the file is ordered by seed, and any analysis on a prefix would silently be reading one run instead of the span.

Columns: run, seed, species, node index, floor percentage, binding nutrient, grade, calcium-to-phosphorus ratio, safe-upper-limit score, and all 28 floor-nutrient percentages, at three decimal places. Integrity as delivered: 200,000 rows; exactly 20,000 per seed; seeds interleaved throughout; minimum floor percentage 99.704, consistent with 1,000,000 of 1,000,000 clearing the 90% floor.

What the corpus exposes. Delivered nutrient percentages per draw — not ingredient identities, forms or masses. A determined reader can subtract public grocery composition and approximate the correction's nutrient contribution, though not its ingredient forms. This is accepted.

6. Discussion — how to read these numbers

The following applies to any figure quoted from this work.

6.0 What a reliability figure actually says. Every figure of this kind in the series has the same structure, and it is worth stating once in full because two different percentages appear in it and they are easy to conflate.

Each simulated feeding day either passes or fails. It passes only if every nutrient in the panel simultaneously reaches at least 90% of its NRC (2006) requirement — one nutrient short is a failed day, however comfortable the rest are. Across n such days the model counts passes, and the Wilson score interval converts that count into a lower confidence bound on the underlying proportion of days that would pass.

The two percentages are:

• The confidence level — how sure the statement is. C95 is 95% confidence; C99.99 is 99.99% confidence, a far more demanding standard and correspondingly a lower bound.
• The proportion bound — what the statement is that sure about: the fraction of feeding days clearing every floor.

So the headline result reads, in full:

From 1,000,000 simulated feeding days, we are 95% confident that the true proportion of days on which every nutrient reaches at least 90% of its NRC 2006 requirement is at least 99.9996%.

It does not mean 99.9996% confidence. Three further limits apply to every such figure:

• It is a property of the model, not of an animal. The population is simulated feeding days generated from published composition tables and stated assumptions. No animal has been fed.
• With zero observed failures the bound is limited by N, not by the diet. It then reduces to n/(n + z²) and reports how many draws were run. Such figures are labelled N-limited wherever they appear.
• The floor is 90% of requirement, not 100%. A passing day is one where no nutrient falls more than a tenth below its allowance, which is a tolerance, not a guarantee of full delivery.

6.1 The between-run standard deviation and the pooled bound measure different things, and neither is a biological confidence statement. With zero observed failures the bound is n/(n + z²). A bound of 99.9996% at 1,000,000 draws and 99.996% at 100,000 draws are the same evidence reported at two sample sizes. The dispersion figures — 0.042 and 0.057 percentage points across independently seeded streams — are replicate-based, which a nested sample on a single stream cannot produce. They quantify how stably the sampler reproduces its own inputs, and will shrink with √N whether or not those inputs are correct; they are a statement about the simulation, not about the animal.

6.2 The physical quantity converges long before the bound does. The table below is a single configuration — the canine smooth-day arm of release A-1.0.0, zero failures at every draw count — chosen so that only N varies down the column. The corresponding figure for release B-2.1.0 is 135.32 (§4.3); the two differ because the formulation changed at B-2.0.0, not because N changed.

{{CHART:convergence|Additional draws buy a tighter bound, not a better diet. The Wilson lower bound climbs with N because it is a function of N; the physical quantity it is bounding — the mean delivery of the worst nutrient — moves 0.2 percentage points across a fortyfold increase in draws. Canine smooth-day arm, release A-1.0.0, zero failures throughout.}}

Worst-nutrient delivery moves 0.2 percentage points across a fortyfold increase in N. The bound rises monotonically because it is a function of N. Additional draws purchase decimal places, not evidence.

6.3 The only defensible phrasing.

✅ "Zero failures observed in N = 1,000,000 draws; Wilson-95 lower bound 99.9996%, N-limited." ❌ "99.9996% reliable." ❌ "More reliable than at 100,000 draws."

6.4 The two identifiers used in this paper. Results are traced to the exact code and formulation that produced them by two internal build identifiers, quoted so that any figure here can be tied to a specific artefact rather than to a version name alone. 3077c230 is the software build of the validation engine at release B-2.1.0. 842353e5 identifies the formulation of the adult corrections, fixed 3 August 2026 and unchanged from release A-1.0.0 through B-2.1.0 — so a result computed on that formulation with the earlier bone-mineral calcium system belongs to A-1.0.0 and is labelled as such wherever it appears. Neither string carries meaning beyond identification.

6.5 No C99.99 figure is reported for the 1,000,000-draw run. Arithmetic on the zero-failure formula gives approximately 99.9985% at z = 3.891, but that is a calculation performed outside the model rather than a result the run produced, and it is not published as one. The inherited 100,000-draw baseline (§4.2) remains the only C99.99 figure of record.

7. Limitations and open items

• No empirical referent. Every figure here is a model output; no animal has been fed and no finished lot assayed. A non-invasive household observation study is planned to begin closing this, and results will be reported when they exist (series cover note, Limitations and future work).

• The model cannot see a misweigh. Potency and fill are modelled as lognormal coefficients of variation, which does not represent the discrete fat-tail failure of a decimal error on a microgram-scale active. That risk is controlled by process — assayed dilute premixes, geometric dilution, per-lot finished-unit assay [Manuscript 4] — not by this model. Monte-Carlo-adequate is not, by itself, safe.
• Deterministic seeding makes every result reproducible, which is a strength for audit and a limitation for inference: the convergence sweep of §6.2 is a nested sample on one stream and yields no between-replicate variance. Only the ten-seed run does, and only for the two adult corrections.
• Bioavailability and retention distributions are literature-derived and documented qualitatively rather than as a per-nutrient table of primary sources. The phytate discount factors have not been independently re-verified against a primary source at this release.
• Safe upper limits were accessed through secondary summaries of NRC 2006 and should be verified against the primary volume before any label claim.
• 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.

8. Conclusion

The validation reported here treats nutritional adequacy as a distributional property rather than a single-bowl calculation. A five-axis noise model perturbs biological variation, grocery composition, cooking retention, purified-active assay and fill, and the corrected diet is evaluated across simulated feeding days rather than against an average day.

On the release-B-2.1.0 configuration, 1,000,000 simulated feeding days produced no day on which any nutrient fell below 90% of its NRC allowance, giving a Wilson-95 lower bound of 99.9996% — a figure limited by the number of draws rather than by the diet's behaviour, and labelled as such throughout. Reliability holds flat from realistic day-to-day variability to fourfold it on a settled feeding pattern, and clears the 99% acceptance criterion even on the harder alternate-day rotation at fourfold stress.

Two qualifications carry as much weight as the result. The retention factors are literature-derived assumptions rather than measurements on these bowls, which is why the model varies them stochastically rather than fixing them. And every figure is a model output: no animal has been fed, and the model shares its composition inputs with the diet it evaluates.

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. Wilson EB. Probable inference, the law of succession, and statistical inference. J Am Stat Assoc. 1927;22(158):209–212. doi:10.1080/01621459.1927.10502953
3. FEDIAF. Nutritional Guidelines for Complete and Complementary Pet Food for Cats and Dogs. Brussels: FEDIAF; 2024. https://europeanpetfood.org/self-regulation/nutritional-guidelines/ (This is the edition on which the nutrient tables used here are based; a 2025 edition was published on 8 September 2025 and is not the basis of these runs.)
4. Association of American Feed Control Officials. Dog and cat food nutrient profiles. In: AAFCO Official Publication. Champaign (IL): AAFCO; 2016. (The 2016 profiles are the edition used by the model.)
5. Anthropic. Claude [large language model]. Anthropic PBC. https://www.anthropic.com/claude (accessed 8 September 2026).

Appendix A · Stress envelope, release A-1.0.0, 100,000 draws per point

The ×k multiplier scales the biological (kitchen) coefficient of variation. Wilson-C95, z = 1.96, seed 42.

{{CHART:stress-envelope|Reliability against stressed kitchen variability. The multiplier scales the day-to-day coefficient of variation of the biological, grocery and retention inputs; it does not change the dose. On a settled daily pattern reliability is flat from realistic variability to fourfold it. The alternate-day rotation arm degrades, but remains above the 99% release gate at every point tested.}}

On the single-protein bound the adult corrections also clear, with copper the near-floor nutrient at roughly 129% (cat) and 138% (dog) of requirement.

Appendix B · The 1,000,000-draw run, every replicate

Release B-2.1.0, engine build 3077c230, 29 August 2026. floorMean is the mean over draws of the worst nutrient's delivery as a percentage of requirement; p5 is the 5th percentile; min is the lowest single draw.

The lowest single draw across the whole exercise sits at 97.5% (dog) and 107.2% (cat) of requirement — above the 90% floor by a margin that is itself informative.

How to cite

Prasanna M. (2026). Statistical Validation of a Stochastic Nutrient-Risk Model for Variable Fresh-Food Inputs (Manuscript 2 of 8, Release B-2.1.0). Growlrr Foods Pvt Ltd. Zenodo. https://doi.org/10.5281/zenodo.22647610

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.