I'm a little late to this discussion, but have been aware of the Celera for a while. I just read an article that popped into my news feed today. Quote by the company CEO:

He describes the aircraft as "...four to five times the efficiency of other turboprop aircraft, and seven to eight times the efficiency of jet aircraft" -William Otto Jr., CEO

Does this mean that it uses 10-12.5% the fuel of a jet yet still flies just as fast or faster, and has the same range or greater?

In the same article the plane is described as being able to fly 400 knots and have a range of 4,500 miles.

I find these to be dubious claims. Does anyone know for sure if the Celera follows the same laws of physics as other airplanes?

Link to the article:
https://www.cnn.com/travel/article/celera-500l-business-aircraft-future/index.html

The Celera 500L first flew in 2018 and has since completed about 50 test flights. So far it has only reached a top speed of about 180 miles-per-hour and an altitude of 17,000 feet,

but a more powerful version of the engine, to be installed soon, will enable faster speeds and higher altitudes, closer to 40,000 feet.
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to a speed of 460 miles-per-hour

because they lack an ignition source to keep their fires lit, diesels are restricted in how high they can fly, even with twin turbochargers and hot glow plugs
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The latest Diamond DA42-VI with its twin Austro diesels and supplemental oxygen is a prime example. It has a service ceiling of just 18,000 feet — which also happens to be the single-engine ceiling for the airplane.

Diamond says it has flown the DA42’s Mercedes-Benz-produced Austro engine to 30,000 feet without ill effect, but for now they are limited by certification from venturing into the rarefied air of the flight levels. Diesels can be prone to flaming out at high altitude where the air is less dense — if it’s cold enough and the air is thin enough, a successful restart could be in doubt.
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jet-A, jet-A-1 and even straight diesel fuel. Of course, when it’s cold, diesel fuel can turn to Jell-O. Without a fuel preheater or recirculation system, that could pose problems at extremely low temperatures. If you’re going to be flying where it’s really cold with an aero diesel, it’s probably best to go with jet-A mixed with Prist anti-ice additive — as long as it’s approved for use in your engine.

Not much in the way of details here where it counts
That with 500+ HP then

from 180 miles-per-hour and an altitude of 17,000 feet to 460 at 40,000 feet with?? "a more powerful version of the engine"

In the near future, the diesel engine could be replaced with an electric or hydrogen one, to make the plane emissions-free. "

It’s just a piston aircraft with massive turbocharging designed to fly at a bazillion feet which is ultra efficient. This is not magic. The problem is getting up there in a reasonable amount of time, which they haven’t solved.

It’s just a piston aircraft with massive turbocharging designed to fly at a bazillion feet which is ultra efficient. This is not magic. The problem is getting up there in a reasonable amount of time, which they haven’t solved. What they seemed to have solved really well is making it look super goofy and combining that with misleading claims which results in a very high click through rate for online publications.

This is to say nothing of deicing, ultra reliable pressurization system at those dangerous altitudes, and reliably maintaining laminar flow.

interesting article I hope they can make it work reliably..

Laminar flow is notorisly hard to make happen reliably.

dealing with ice could be an interesting problem. perhaps heated wings.

Gliders have wipers that run the length of the wings to remove bugs as they disrupt the laminar flow.

I wonder if the gain from wiping the bugs off is that much more than the penalty you pay from the drag at the root when they're stowed, the drag when they're in operation, and the weight.

As for the A03’s ability to offer enough power to get Celera to its 450-mph cruise speed at altitude Slater says, “Making 500 horsepower at 40,000 feet would take an insane amount of turbocharging, turbo pressure. It’s not something I’ve seen before outside of tractor-pulling engines which can have up to 200 pounds of boost at sea level.”

But the A03 won’t make a full 500 horsepower at altitude. Even with multiple turbos Slater notes that RED only claims the ability to make 500 hp at 25,000 feet, not at 40,000 feet. He points out that the limitation is not unique. A turboprop engine like the ubiquitous Pratt & Whitney PT-6, which has a 750 to 850 maximum shaft horsepower rating at sea level produces less than 300 hp at 28,000 feet.

Here's a PT6