Capital letters in "Theorem", "Conjecture" etc [duplicate]

This is my first post and as you can probably guess I am a mathematician so I have no clue about grammar. I am writing a mathematical document at the moment and I would appreciate some advice on my usage of capital letters. Can somebody please confirm if the following are correct?

1) "We know by T​heorem 4.6.1 that..."

2) "the following c​onjecture, due to..."

3) In order to prove the "Mckay-Stevens $k$-covering C​onjecture, once needs to show that..."

I'm particularly confused about 3).

Many thanks for any help

There is no standard used throughout mathematics. Not even throughout English-speaking mathematics. Some recommend "Pythagorean Theorem" and others recommend "Pythagorean theorem".

Find your own comfortable conventions and use them. And when a journal or publisher has a different convention, follow it without objection. (There may be more important things to reserve your objections for.)

Those all look correct, to me. Those are examples of proper nouns.

Capitalization

The reason that you would capitalize your first example is because it refers to a specific theorem, namely 4.6.1. Example number two is referring to a theorem less specifically. The third example is capitalized because it refers, again, to a specific theorem.

Capitalization of Hyphenated Compounds

Capitalization of hyphenated compounds in titles is a question of style. You should almost always capitalize the first part, in titles. The second part would be capitalized if it is a noun, proper adjective, or carries equal or more force than the first part. Don't capitalize the second word if it is a participle that is modifying the first word. ^[source]

Your example is an example of where the second word is modifying the first. In that case, you would not capitalize the word covering.

Journal Style Guidelines

I also agree with what GEdgar said about following the rules of the paper you are publishing in. If the journal you intend to publish in has a style guide, use it! If there is not a style guide, the best rule of thumb is to maintain uniformity in your style. This advice is taken from a style manual written by the American Mathematical Society.