Color Management at the Bits & Bytes Level

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Can someone familiar with both programming and color management
recommend reading material on my problem or where to go next? The answer is
probably too long for a post. Google searches have gotten me several million
responses and graphic artists forums are not aware of bits and bytes.

I have done a lot of programming and so am familiar with bits,
bytes, coding, file formats, and so on. Now I would like to tie it together
with color management.

I have finally gotten some grip on the overall color management
scheme; i.e. color spaces, color identified by 3 or 4 numbers, 3 or 4
numbers per pixel (1 number per color), color filters for scanners and
electron guns and phosphors for CRTs, even CMYK FM half toning, central Lab
hub for color management, etc. I'm just mystified by what is actually
recorded on disk and what is happening in memory when color management is
present and when it is not present. Suppose I take a scan of a photo and
save it as a TIF file. What do the numbers for each pixel in the file stand
for? Are they (1) the scanner sensor's RGB output or (2) the scanner sensor's
RGB numbers changed by a profile to some better RGB space or (3) does the
profile convert the RGB sensor numbers to the central Lab hub space? Also
what is the monitor showing me while I adjust the scanner controls? Again,
is it any of the preceding or it a more complex trail in RAM modified by a
monitor profile? Where do Microsoft Word and Adobe Photoshop get the
signals to send to the Monitor's electron guns and how do they get there?

In general, what space, what profile and what optimization do the
physical numbers on disk and in RAM represent and when and how does the
profile modify them?

I'm like the kid in my math class who raised his hand when the
teacher announced a mid term exam. He said "Teacher, I understood
everything you said except for that equals symbol"