OSHUN: ingredient science built around measured hair geometry

Bee Rosa Davis

Research note · Version 0.3 · Updated 8 October 2026

OSHUN is a research program for textured-hair formulation: measure the fiber an ingredient encounters, preserve that context with the experimental response, and make predictions only where the model has support. Its current study and interactive ingredient checker investigate that architecture using public human-skin permeability data, while specifying the hair measurements needed for the next stage.

TL;DR

The question: How can ingredient models account for the geometry of textured hair—and explain when the available measurements do not support an answer?

What the work does: OSHUN combines a context-preserving data model, a skin-permeability feasibility study and an interactive ingredient checker. It compares predictions with and without experimental context, explains ingredient-level refusals, and specifies a controlled panel for measuring hair geometry and response.

What is still open: The present measurements are human skin. Testing the hair hypothesis requires a controlled fiber panel; establishing curl definition, breakage or other product benefits would require additional endpoints.

THE RESEARCH IN CONTEXT

OSHUN begins with a formulation problem: an ingredient interacts with a particular material under particular conditions. For textured hair, the proposed material description includes measured fiber shape, twist and surface structure. The goal is to give those properties a place in the data and model, so that a prediction can be tied to the substrate it actually describes.

Its current empirical starting point is skin permeability—the rate-related coefficient describing transport through a skin barrier. The Potts–Guy baseline uses molecular weight and a partition coefficient, which describes a compound’s preference for oil-like versus water-like environments. OSHUN asks what happens when body site, skin layer and donor solution remain attached to the observations instead of disappearing into one pooled fit.

The companion makes the representation problem tangible. A formulator can inspect an ingredient’s model inputs and nearby measured compounds, or see why a prediction is refused. The study then uses those gaps to specify a hair-fiber measurement program. Skin transport, hair-fiber response and finished-product performance remain separate questions; the project’s architecture connects the research steps without treating them as interchangeable results.

AVAILABLE RECORD

Independent research: a feasibility study, an interactive ingredient checker and a proposed controlled hair-fiber panel. The measured results concern human skin; hair-response and finished-product performance remain untested.

TECHNICAL FIGURE

source-derived technical plate

Public measurements and recorded error estimates with retained subset sizes. These are not paired gains on one unchanged population.

Prediction error alongside the changing sample

Saved conditioning comparison

Fit / conditioning | Measurements retained | Dropped | Context cells | RMSE (log Kp) | R²

No conditioning | 534 | 0 | 1 | 1.2583 | 0.0210

Refit here | 534 | 0 | 1 | 1.1454 | 0.1887

+ vehicle | 441 | 93 | 8 | 1.1038 | 0.2737

+ full protocol | 311 | 223 | 15 | 0.9912 | 0.3727

The first row applies the published Potts–Guy equation; subsequent rows refit with leave-one-out evaluation. Full conditioning retains 311 of 534 measurements. Because the populations differ, the lower RMSE is not a paired estimate of improvement on the same cases.

oshun.json — Saved project data; values read directly

Inside the full-protocol strata

Saved subgroup results

Body site / layer / vehicle | n | RMSE (log Kp) | R²

abdomen | epidermis | unspecified | 75 | 1.1558 | 0.0229

abdomen | epidermis | PBS | 37 | 0.8826 | 0.4683

abdomen | epidermis, dermis | unspecified | 28 | 0.9255 | -0.1202

abdomen | dermis | unspecified | 24 | 1.3003 | 0.2924

thigh | epidermis, dermis | unspecified | 22 | 1.2689 | 0.2932

unspecified | epidermis | unspecified | 21 | 0.4399 | 0.8374

Selected strata retained in the companion data, not all 15 cells. Negative R² values remain visible; conditioning does not make every subgroup predictable.

oshun.json — Saved project data; values read directly

The formulation question behind the project

Choosing a conditioning agent is not only a question about the molecule. It is also a question about the surface it encounters, the surrounding formulation and the outcome being measured. OSHUN asks how to keep those relationships available to the model rather than reducing an ingredient to one prediction that is reused for every substrate.

For textured hair, the proposed inputs are physical measurements such as cross-sectional ellipticity, twist density, fiber diameter and cuticle scale density. These describe geometry and surface structure directly. The proposed model would use those measurements rather than demographic categories or self-reported curl types.

The project has three connected parts: a study of what experimental context changes in an existing dataset, an ingredient checker that exposes the limits of prediction, and a controlled-panel design for collecting the missing hair data. The formulation goal motivates all three, but permeability is only one endpoint; it does not by itself measure curl definition, breakage, moisture retention or finished-product performance.

Keep each measurement attached to its experiment

The study ingests 550 usable huskinDB records, of which 534 fall within its declared modeling domain. Each record preserves the compound, molecular descriptors, measured permeability, body site, skin layer, donor solution and source reference. Repeated observations remain distinct records in GIGI rather than being averaged into a single value for the compound.

The conditioning experiment keeps the two-descriptor regression family fixed and changes which recorded context the fit may use. The published Potts–Guy equation gives an RMSE of 1.26 log units on the 534 in-domain rows; a global refit gives 1.15. Fits within donor-solution groups give 1.10, and full body-site, layer and solution groups give about 0.99.

The retained population changes: donor-solution fits cover 441 records, and full-protocol fits cover 311. The decrease therefore cannot be read as a like-for-like improvement on all 534 measurements. Some groups perform poorly, and the study reports those results. Its useful lesson is to preserve and inspect context—not that adding context guarantees a better prediction.

What the ingredient checker actually does

In the companion, a reader selects ingredients or loads a preset curl-cream ingredient list. For eligible compounds, the browser compares the Potts–Guy equation with an inverse-distance-weighted neighbor estimate drawn from the measured skin records. Opening a result exposes its descriptors, neighboring measurements and arithmetic.

The checker separates two reasons to decline a prediction. A defined molecule can fall outside the declared molecular-weight or partition-coefficient range. A polymer, hydrolysate or mixture may instead lack the single molecular structure the model requires. The first is a coverage problem; the second calls for a different representation, not merely another coefficient.

The paper’s separate 29-ingredient deck yields 12 refusals: eight ingredients without a single defined structure and four outside the descriptor range. That is 41.4% of the study deck, not a measured failure rate for a finished curl cream. The browser preset is a smaller selection, and its refusal count is computed from the ingredients selected.

A returned value is a skin-permeability estimate within this demonstration. It is not a recommendation to use the ingredient, a safety assessment or a prediction of how well a hair product will work. The useful output is an inspectable estimate—or a specific explanation of what the model cannot represent.

A confidence idea that did not earn its place

The study also asked whether dispersion across a compound’s repeated measurements could rank its prediction error. The proposed section-curvature statistic is used here as a finite-sample dispersion measure, not as a demonstrated differential-geometric invariant. Its signal weakened and then reversed as the test required more repeated measurements.

Those repeats came from different laboratories and protocols. Their variation can reflect laboratory disagreement rather than a controlled change in substrate. The proposed confidence signal was not validated on this dataset; the failed test is one reason the next experiment needs a controlled panel.

The hair-fiber experiment the program calls for

The proposed panel uses one laboratory and one protocol, with donor fibers deliberately spanning measured geometry. It records continuous covariates, including ellipticity, twist density, diameter, cross-sectional area, cuticle scale density and water content. Humidity is controlled, and prior chemical treatment is recorded as an exclusion criterion.

Each ingredient would be measured across donor substrates so that response could be compared as geometry changes. The primary comparison uses the same rows for a fixed-descriptor model with and without measured geometry; no sparse group may be dropped to make the conditioned result look better. A randomly permuted geometry label is the negative control.

The panel also tests whether refused queries really have higher errors and whether the failed dispersion-based confidence signal becomes useful under controlled measurements. These are specified experiments still to be run. They make the route from a skin-data feasibility study to textured-hair research explicit.

THE NEXT RESEARCH STEP

Run a single-protocol pilot to estimate the variance needed for the panel’s power calculation, then compare conditioned and unconditioned models on identical hair-fiber measurements. Keep ingredient response separate from the later product-performance endpoints a formulator would need.

TEACHING CONSTRUCTION (not project measurements)

Keep the published baseline equation fixed when inspecting the saved record. Distinguish modeling recorded context from causally changing the substrate. Compare errors on a common evaluation set before attributing a reduction to an added contextual feature.

predicted log Kp = 0.71 log P − 0.0061 MW − 6.3

log P: The molecular partition descriptor used in the baseline.

MW: Molecular weight under the baseline convention.

Evaluation population: The same declared observations for a paired model comparison.

Suppose two models have reported errors of 1.0 and 0.5, but the second excludes half the observations. The numbers do not by themselves show an improvement on the original task. A paired comparison needs both models evaluated on the same retained observations.

SOURCE RECORD

OSHUN interactive ingredient checker: https://www.davisgeometric.com/oshun/

OSHUN study (PDF): https://www.davisgeometric.com/oshun/oshun-study.pdf

Measured-data illustration: https://www.davisgeometric.com/research/figures/membrane.html

Source versions: https://www.davisgeometric.com/research/account-source-records.json

No new experiments are reported in this research note.

Illustrated study: https://www.davisgeometric.com/research/figures/draft-ingredient-science.html