A replication. Measured 1–2 September 2026, published 2026-09-23. 3,578 sleep and meditation apps, German iOS App Store.
In August 2026 we measured the cooking-app category of the German App Store as completely as we could reach it, and reported that 81% of recipe apps never appear in the store's own results for the obvious query, and that 77% of the apps listed as Gratis charge money once opened.
The first serious objection to that result is the right one: cooking apps may be special. It is an old, crowded, fragmented category. So we picked a second one designed to break the finding if it was breakable — sleep and meditation apps: anchored by a few large subscription products rather than fragmented, a different vocabulary, a different buying pattern. If price opacity were a symptom of fragmentation, it should weaken here.
The rules were frozen before counting, exactly as in the first category, and every later change is dated with the error that motivated it (protocol).
| Cooking | Sleep & meditation | |
|---|---|---|
| Apps in the classified category | 941 (≥991 incl. price-unverified) | 3,578 |
| Absent from the single obvious query | 81% (579 of 715, rezepte) | 88% (1,013 of 1,155) |
| Reachable only through the similar-apps graph | 28% (276 of ≥991) | 68% (2,423 of 3,578) |
| Listed as Gratis | 96% (907 of 941) | 96% (3,417 of 3,578) |
| …of those read, charge through in-app purchases | 77% (697 of 907) | 77% (2,581 of 3,351) |
| Median highest single in-app purchase, among apps that charge | €39.99 | €39.99 |
| Largest single in-app purchase behind Gratis | €599.99 | €1,199.99 |
Both recall rows are computed the same way in both categories: the first over the apps the sweep itself classified, against one query; the second over the whole closed category. The obvious query is rezepte for cooking and schlaf for sleep; using meditation instead gives 86% (995 of 1,155). An app counts as charging in-app when at least one item on its product page's purchase list is priced above €0. Two sleep apps list only €0.00 items and are not counted; no cooking app does.
Two categories chosen for their dissimilarity, measured about two weeks apart with the same frozen instrument, return the same 77% and the same median — to the cent.
We claim: the specific objection that cooking is unrepresentative does not survive contact with the second category, on the price findings. The first attempt to refute the result failed to refute it.
We do not claim that this is now general. It is two categories, not twenty. Both are consumer-facing and both sit on the same storefront. A category with professional buyers or a handful of strong brands is still unmeasured. We would rather someone other than us ran the third one.
The prediction we made was wrong, in the interesting direction. We chose a concentrated category expecting that if discovery failure were a symptom of fragmentation it would weaken here. It did not weaken. On the comparable measure the second category is less discoverable than the first — 88% absent from the obvious query against 81%, and 68% reachable only through the recommendation graph against 28%. Concentration at the head of a category does not make its tail findable; on this evidence it coincides with a larger invisible tail, not a smaller one.
We do not annualise. €1,199.99 is the price of one purchasable item as Apple publishes it. The developer labels it a yearly subscription; we report that label and do not convert it, because Apple does not publish billing periods reliably enough to convert anything.
A September draft of this section, written the day after the measurement, carried two wrong numbers. Both were caught when the figures were recomputed from the raw data for publication, and neither ever reached the site:
1. The maximum was given as €999.99. It is €1,199.99 — a German meditation app listed as Gratis with a €1,199.99 item. The draft figure appears to have been read off an incomplete pass; the app was present in all three classification versions and was never borderline. 2. The cooking free-listed share was given as 92%. It is 96% (907 of 941) — the same as the sleep category, not four points below it.
A third, corrected the same day it was published (2026-09-23). The first version of this page and of §6 of the working paper compared this category's 68% against cooking's 81% as though they were one measure, and concluded that the second category is more discoverable. They are two different measures and the conclusion was backwards. Cooking's 81% is absence from a single query (rezepte), counted over the apps the sweep classified; the 68% is the share of the whole closed category reachable only through the recommendation graph. Computed like for like, the second category is less discoverable on both: 88% against 81% for the single obvious query, 68% against 28% for graph-only reachability. The table above now carries both measures for both categories. The error was ours, it was live for about an hour, and it inverted the finding — which is exactly why we recompute headlines from raw data rather than from our own prose.
A fourth, corrected 2026-10-14. This page and §6 of the working paper said the two categories were measured seven weeks apart. They were about two weeks apart: cooking from 19 August to 1 September, sleep on 1–2 September. The figure was never measured; it was written.
None of the four changed a price headline. We publish them because a project whose entire claim is honest measurement does not get to quietly fix its own arithmetic, and because the pattern is the one we keep finding in ourselves: the errors show up in the summary, not in the pipeline.
Every figure above is recomputable from the scripts in `sleep/` against public Apple endpoints. No API key, no paid tooling, no access anyone else lacks.
```bash cd sleep python3 build_corpus.py # 25-query German sweep python3 classify.py # category classification python3 closure_hopn.py # hops over the similar-apps graph python3 apply_v3.py # uniform precision filter across all hops ```
If something here is wrong — particularly if you build an app that appears in the data — write to korrektur@openappindex.org. Every notice is checked and corrections are published with a date, including the four above.
Method, classification rules and their dated amendments: `openappindex-sleep-category-protocol.md`. The cooking measurement this replicates: `working-paper.md` §4, and openappindex.org/methode.html.