"the rich" — The adjective “rich” is a fused modifier-head AdjP, and “the rich” is a fused modifier-head NP. — Is this parse correct?

Question

the textbook "The Cambridge Grammar of the English Language", page 529:

from the passage above, I'm drawing the following conclusion:

(1) the rich
The adjective “rich” in (1) is a fused modifier-head AdjP.

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the textbook "The Cambridge Grammar of the English Language", pages 518-519:

(2) Peter the Great
“The Great” in (2) is a fused modifier-head NP.

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I'm combining the information from (1) and (2) and getting:

(1) the rich
The adjective “rich” is a fused modifier-head AdjP.
“The rich” is a fused modifier-head NP. — Is this correct?

(2) Peter the Great
The adjective “Great” is a fused modifier-head AdjP. — Is this correct?
“The Great” is a fused modifier-head NP.

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Update:
I'm asking it because I've seen the term "fused modifier-head AdjP" for the first time and I want to know whether I've understood it correctly or not.

Answer 1

If you follow the reference to Ch. 5, §9.3, I think you’ll find the answer (which I believe is yes) on p. 417:

9.3 Fusion of internal modifier and head
^. . .
(f) Modifier-heads with special interpretations
^. . .
[29]
^. . .
ii [The r̲i̲c̲h̲] cannot enter the kingdom of Heaven.
^. . .
Note also the fused-head restrictive modifier in proper names like Ivan [the T̲e̲r̲r̲i̲b̲l̲e̲].
_{Source: The Cambridge Grammar of the English Language}