Here is the third claim listed in the paper above (I cut out some of the middle part as it was just embroidery, you can read it above):
Here is a fuller explanation of this claim from the book:
Unsettled? What Climate Science Tells Us, What It Doesn’t, and Why It Matters
by Koonin, Steven E.
ISBN 9781950665792
Figure 2.3 illustrates some of those details. It shows how the amount of heat radiation leaving the top of the atmosphere varies with the radiation’s color (that is, the spectrum of infrared radiation). Were there no atmosphere, the spectrum would correspond to the smooth gray line in the graph, a curve which is described by the basic physics of the Stefan-Boltzmann law. The area under that curve corresponds to the cooling power of the radiation. The lighter, jagged gray line shows what the spectrum would look like with all major greenhouse gases present except CO2 (so with CO2 at 0 ppm). Combined, these gases reduce the radiation’s cooling power by about 12.1 percent. All of the line’s ups and downs arise from the detailed properties of the various greenhouse gas molecules, most importantly water vapor, but also methane and ozone. The solid black line shows a further 7.6 percent reduction in cooling power (increase in insulation) when CO2 is present at 400 ppm (about today’s concentration). Finally, the dashed black line shows an additional 0.8 percent loss of cooling power when the CO2 concentration is raised to 800 ppm, roughly twice what it is today; this change is barely visible in the sides of the large dip. There are two takeaways from this graph. One is the complexity of the spectra—hundreds of thousands of molecular properties, many measured in the laboratory, go into creating these simulated spectra, which agree very well with satellite observations. Second, although the effect of CO2 at today’s concentration is significant (7.6 percent), doubling it doesn’t change things much (an additional 0.8 percent) due to the “painting a black window” effect we’ve already discussed.
The book citation actually goes back W. Happer the author of the article we are discussing. He is actually a well known expert in this particular field.
Some of the specifics are different between the two sources, which I attribute to language ambiguity and timeframes.
1 - Specifically, the article says current concentrations of CO2 decrease heat radiation to space by about 30% while the book says in similar language that this is 7.6%. I think this is due to a difference in what is included in each calculation… in the article it is advantageous for this percentage to be as large as possible to make the next section seem as small as possible, even trivial… I will leave it to the reader to decide if this is intentional misdirection or just a simple ambiguity.
2 - The article states that the additional reduction in heat radiation of doubling CO2 from 400 to 800 is 1%, the book states that this reduction is 0.8%. I think this is simply a case of different studies done at different times producing slightly different but comparable results.
The last part of article states:
In the book this is stated as “painting a black window” has a smaller affect. I think this should be obvious from the information included above. A change of CO2 from 0ppm to 400ppm reduces heat radiation by 7.6% (per the book) while a change of CO2 from 400ppm to 800ppm reduces heat radiation by 0.8% (again per the book).
Now, before you go off on me and call me a climate change denier (or worse), you need to realize that a 0.8% reduction in heat radiation is actually a big deal and agrees, generally, with the heat increases that are expected.
My final say on this article is that generally the actual measurable claims made are accurate. However, the juxtaposition of the 30% decrease in heat radiation (and the possibly misleading description of it) from CO2 concentrations with the additional 1% decrease in the same from higher CO2 levels was an intentional misleading presentation, serving to minimize the impact of that statement.
So, if you read all of this, congratulations, you have a high tolerance for pain 
) I prefer to live by the Precautionary Principle since even low probability events can have high impact and there are so many unknowns.
You post something on Twitter (or X) with no details and a link that does not work. Then you post a copy of the Twitter posting here as “evidence”.