CohortScope · Rijksmuseum Rembrandt corpus · findings dossier

The millimetre problem

We built a pipeline to flag which Rijksmuseum “Rembrandts” look anomalous against firmly-attributed ones. It does not work. This page is the record of how we established that, and of the one finding that outlived it: the images almost everyone analyses are far too coarse to see a brushstroke, and nothing downstream can repair that.

Method closed — negative result 5 pre-registered outcomes

What was tested

Five held-out outcomes, each fixed in writing before the data existed

Every threshold, seed and decision rule below was committed to the repository before the works it judges were acquired or scored. When a locked rule cost us samples, we recorded the loss instead of amending the rule.

weak and fail are the pre-registered tiers, not editorial summaries. Full statistics, confidence intervals and per-artist breakdowns are in the linked reports.

How the result was reached

Every alternative explanation, tested and closed in order

A negative result is only worth anything if the obvious objections have been answered. Each step below became askable only once the one before it was settled.

The finding that outlived the method

A pixel has to mean something

A 17th-century oil brushstroke is roughly 0.3–3.0 mm wide. To resolve one you need several pixels across it. The original pipeline fetched every painting at a fixed pixel width of 1500, regardless of whether the canvas was 15 cm or 5 metres — so what a pixel measured varied wildly, and nobody had written the number down.

What each stage actually saw, in millimetres of canvas per pixel

Log scale. The green band marks brushstroke width (0.3–3.0 mm) — a stage whose pixels land inside or beyond it cannot represent handling at all, only composition and colour.

Not one work of 108 reached 0.30 mm/px by the time it entered the network. The model that was supposed to compare brushwork had never been shown any.

The detail was already published and free to request. It was discarded at download time, before any modelling decision was made.

The decisive test

Was 0.20 mm/px simply the wrong scale?

Fixing the scale confound was necessary but not sufficient — so we swept it. Both signals were re-run across a 2× range of physical resolution, on a population held fixed across floors so that the only thing changing was how many millimetres a pixel covers.

Separation against resolution

Handcrafted features CNN embedding

The curves are flat, not noisy-but-trending. The answer is no: over a 2× range bracketing the locked floor, neither signal separates firm Rembrandts from their pupils at any resolution this collection can support.

And it cannot be pushed further here. Nine works in the entire corpus have imagery finer than 0.05 mm/px, and zero support a full-range sweep for the embedding. The imagery to test a finer hypothesis does not exist in this collection.

The uncomfortable control

How the painting was photographed predicts better than the pipeline does

In every pupil test we ran the same control: can a single column of acquisition metadata separate the two classes better than the whole two-signal method? It can, four times out of four.

Test	Metadata column alone	Its AUC	Full pipeline	N

Chance is 0.500. This is why each report is marked confounded: a result a metadata column can match is not evidence about paint. It is evidence about digitisation campaigns.

The reusable deliverable

Which questions can your imagery actually answer?

This is the part that survives the negative result. For every work we can say whether published imagery supports texture analysis at 0.20 mm/px — and when it does not, exactly why. Reporting a work as unanswerable is more useful than scoring it on inadequate pixels.

Per-work adequacy

Sorted coarsest first — the least answerable at the top.

← coarsest published imagery · not answerable · use the arrows finest · answerable →

Object	Artist	Title	Canvas	Published	Analysed	Into CNN	At 0.20 mm/px

Click any card above or any row here to see the painting alongside its numbers. Published is the finest the museum's IIIF server offers; analysed is what the original pipeline downloaded; into CNN is what survived its resize and crop. The gap between the first and last columns is the whole story.

Standing on it

What we are not claiming

This is evidence about this method, on this corpus, at the resolutions this collection can supply. It is not a claim that no visual method can distinguish a Rembrandt from a pupil, and it is not a claim that any specific painting is or is not by Rembrandt. Held-out group sizes are 35–67 works: well powered to detect a large effect, poorly powered for a small one. Failing to find an effect is not the same as showing there is none.

The cohort that defines “normal” is 17–23 paintings, and it is size-biased — the resolution floor excludes the largest works, including The Night Watch, and the tiling rule excludes the smallest. Any normal fitted here describes the middle of Rembrandt's output, not its range.

Everything above is reproducible from the repository: each stage refuses to overwrite its own output without --force, and every reported figure on this page is read out of a committed artifact at build time rather than typed in.