How common is it for one entity to have a 3+ year technological lead on its nearest competitor?

In practice, it is often hard to tell the difference between "far ahead of the competition" and "off on a weird tangent". You could make the case that NASA is 50 years ahead of the competition in manned lunar space travel, and at the time being ahead of the Soviets was a huge part of the appeal. But over time manned space travel was all but abandoned because there didn't seem to be enough value in it. The USAF is in a similar position with stealth aircraft; competing countries never heavily invested in stealth and radar improvements have made it increasingly obsolete.

If you're three years ahead of intelligent, well-funded competition, they may be waiting to see if the game is worth the ante.

An example of a 10+(!) year technology lead is computational discrete topology. Every large-scale geospatial, graph, et al analysis system is based on it — you can’t build one without it — but there is virtually no literature on how it works and a practical expression of the theory is robustly non-obvious. The same few people continue research and design every kernel for companies/governments. AGI and autonomous systems specifically drive much demand for this tech currently, since it is needed to reason about relationships/behaviors in space-time at scale.

There is no company behind this tech currently but I’ve heard rumors of one being created. It could have a strong feedback loop, not just due to tech exclusivity but because a platform-level implementation would effectively provide a consensus model of physical reality for machines.

Tangentially, I am aware of AGI research programs working from first principles that have made impressive theoretical CS advances while completely under the radar. It is difficult to determine if any have 3+ year leads on any other program though since that assessment implies global visibility.

Distinguishing between a technological lead and ineffective competition is also important. An example is database engine technology. Some proprietary databases are orders of magnitude more efficient/scalable than any open source comparable, which looks qualitative, but is widely recognized as a product of design quality rather than any technological lead. (see also: Google’s data infrastructure)

Google immediately jumps to mind. The search result quality combined with the infrastructural investment required to execute on copying Google seems like it would take even an entity with no budget constraints more than 3 years, and that’s just search; Google also has maps, email, etc. Does your question assume any budget constraints? (I’ve been using DuckDuckGo as my default search engine for a few weeks and the results are obviously substantially worse than Google. And DDG has been trying pretty hard for over a decade, but with less than unlimited resources but still a lot.)

Xerox PARC in the 70s and early 80s had a head start on inventing the personal computer revolution. PARC was well-funded, and they spent a fair amount of money building computers so each researcher had one on their desk. A little later, PCs were made in such quantity that it was no longer possible to stay ahead and have better equipment than businesses and consumers could buy. At PARC, they invented ethernet, the desktop metaphor, WYSIWYG editing, and much else. they didn't invent the mouse, but they built platforms and environments that made really great use of it.