Bitcoin arithmetic, symbol definitions, from private key to public address

(Note, please see EDIT below.) I title this with “arithmetic” because “mathematics” is an abstraction for arithmetic and a mathematical function can be broken down into arithmetic. I need the arithmetic.

The top level question / goal: I am trying to understand the arithmetic in how a private key is translated into a public key. Presume my wallet has generated a private key for me. What are the steps the wallet (and/or the bitcoin nodes) use to create the public key that it uses to deposit coins into?

I have found and read multiple articles, but am not recognizing the steps. But before going there, I need to solidify the meanings of a few symbols. Start with this post found from a search: What is the math behind Bitcoin's elliptic curve?

Q, k I don’t know what these represent.

G from another post I find this: “The generator point G, or a ECDSA public key, is a pair of coordinates x and y, for which the above equation holds.” I presume this mean some specific point on the curve, which is composed of the x and y value. Is this correct? What is intended by “generator point?”

n is a variable, often meaning repeat some operation this many times.

From other places I find these items along with what I suspect they mean. Please correct me where I am wrong.

X: upper case, the private key

x,y: lower case a point on the curve,

p: lower case, the largest prime smaller than 2^^256

P: upper case, I don’t know

Thank you for your time and patience.

Edit: found this site: How do you get a Bitcoin Public Key from a Private Key

It looks pretty good. Looks like G is our originating point on the ecliptic curve. Is this correct.

If is save my private key, on a thumb drive or somewhere else, and my cold storage wallet (is that a correct name?) completely fails, and I put my private key into a new wallet, will it be able to access all the coin I put into the account used by my failed wallet?



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