P-mode: how does it select the initial camera settings?

AI says the settings are dependent on the metered brightness but then gets coy about exactly how say 13 EV translates to a specific initial aperture and shutter combination that exactly matches 13 EV - before the twiddling of those starts up ...

As we all know, a given EV translates to many, many different combinations of aperture and shutter, any of which gives the same exposure.

We also know that EV = log2((N^2)/t) so (N^2)/t = say 2^13 = 8192 but still 8192 is a combination of N and t ** and does not specify either one.

For the purpose of this discussion, I would prefer ISO to be invariant and set at 100.

** where N = the f/number and t = the shutter time

That, is a really interesting question in 2025 !
Are they going by the book, are they factoring in their own lenses, who knows ?
I must fire it up in my youngest cam (A7RIVa) to see where it has matured to.
It would be nice to know Panic mode has evolved.
First but, I have to derust the selector off A.

Looking forward to any results.

All the data you need is or should be in the instruction manual that comes with your camera.

AI queries do not generally waste my time.

Not helpful because all the data I need is not in my manual.

Testing my Sigma SD9/17-50mm zoom, the initial camera setting is the largest aperture f/2.8 and the metering sets the shutter time anywhere between the camera limits of 15 sec and 1/6000 sec, presumably as a function of the AE sensor illuminance for a particular scene. So if the scene exposure value is the aforesaid 13 EV, and the lens is set to f/2.8 then the shutter time would be set to 2^13 / 2.8^2 = 1/1044 sec

A bit like how my separate light meters work (Sekonic, Weston batteryless).

Altering either the SD9's aperture or the shutter time adjusts the other setting appropriately to keep the EV constant.

The SD9 is old (2003) with no ability to set other aperture/shutter limits other than those built-in and has no auto-ISO either.

I am a Nikon shooter so I will speak about Nikon cameras though I am sure other brands are similar.
There is a program in the camera which has a predetermined combination of SS/A for the EV level and based on the scene brightness it chooses the combination. By rotating rear command wheel you can overwrite this combination with another one. Thom Hogan provides in his books an initial table for each EV value.

Unfortunately Hogan's books cost a buck or two. I found one for the D70 free on-line but it had no such table in it. I found one for a Z but it only had the index pages. A pity because the said table would have been highly interesting ...

This is a table from Thom Hogans book on Nikon Z 8 camera.
Program Exposure Table (at ISO 100)
EV Aperture Shutter Speed
0 f/1.4 2 seconds
1 f/1.4 1 second
2 f/1.4 1/2
3 f/1.4 1/4
4 f/1.4 1/8
5 f/1.7 1/12
6 f/2 1/15
7 f/2.4 1/23
8 f/2.8 1/30
9 f/3.5 1/45
10 f/4 1/60
11 f/4.8 1/90
12 f/5.6 1/125
13 f/6.7 1/180Version 2.00
14 f/8 1/250
15 f/9.5 1/350
16 f/11 1/500
17 f/13 1/750
18 f/16 1/1000
19 f/16 1/2000
20 f/16 1/4000 * maximum value; for brighter scenes camera uses 16.3 value

...
P.S. I asked AI about Thom Hogan's testing and got:

Seems reasonable as they match typical exposure values for such scenes. AI quoted a similar table for Canon.

Cool !!
We were typing at the same time ...