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It's an interesting conjecture, but what about the anomalies? There are over a hundred planet systems discovered by Kepler with various levels of confirmation. None of them are mentioned here. The essay only lists 9 systems. How do the rest compare? Are there anomalies in unconfirmed systems? Why were these systems chosen; was it a random selection?

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You need a system with more than two planets. A system with only two planets is going to be linearly spaced on any type of scale.

Once you've filtered out systems with two or fewer planets, you need orbital measurements with decent precision to tell whether a plot of planet spacing is actually linear on a log scale or not. Measuring a planet's orbit requires a decent amount of observation (since we can't measure star/planet mass directly and don't usually measure period directly), so unconfirmed systems likely don't have good measurements.

It's likely that most of the unmentioned systems get filtered out by one of the above two criteria.

Also, even if we detect a system with N > 3 exo-planets, we often cannot tell if there are more than N, but below the threshold of detectability, making the plots incomplete and incorrect.

The post explains exactly why these systems were chosen: because they have the most planets. This is every known system with 6 or more planets (according to the OP).

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