Square Hammer

There's a lot of reference to Freemasonry in this song.

On the title, "Square Hammer":

"The Masonic gavel is an emblem of authority used by the Master of the lodge to show his executive power over the assemblage by punctuating its actions.

In this capacity, order is maintained and a structured outcome to the proceedings is achieved.

The common gavel is also one of the working tools of the Entered Apprentice.

Operative Gavel

In the operative stonemason era, the common gavel was a tool used to hew (break) the rough edges from the stones (ashlars) in order to perfectly fit them into place.

Speculative Gavel

In speculative Freemasonry, the Masonic Gavel is used to symbolically divest the heart and consciousness of all the vices and superfluities (excesses) of life in order to ready ourselves as if we were living stones, open to be shaped into a spiritual being that is pleasing to our Creator.

A True Masonic Gavel

What does a true Masonic gavel look like? The head of the gavel is rectangular, flat on one end and can be slightly pinched or come to a point on the other end."

Source: masonic-lodge-of-education.com/masonic-gavel.html

Now, onto the lyrics - more specifically, the line: "Are you on the square? Are you on the level? Are you ready to swear right here, right now"

If you look at the poetry of Rob Morris (who was a Freemason), his most famous poem was called "The Level and the Square"

This poem starts off with:

"We meet upon the Level, and we part upon the Square, What words of precious meaning those words Masonic are, Come let us contemplate them, they are worthy of our thought, With the highest and the lowest and the rarest they are fraught.

We meet upon the Level, though from every station come, The king from out his palace, and the poor man from his home; For the one must leave his diadem outside the mason's door, And the other finds his true respect upon the chequered floor."

Finally, an interesting insight by a Reddit user named killcokidd on the Ghost subreddit:

"On the Square - When a stonemason cuts a block to use in the construction of a building, it must be perfectly shaped so that it will support the other blocks that surround it. The block’s sides must all be perfectly straight with no faults, so that it will do its part as just one small piece of a much larger building. To check the reliability of his workmanship, the stonemason uses a tool called a square shaped like a right angle, to determine whether the sides and angles of the stone are perfect. Freemasons use the term "on the square" to describe their trust in each other. A man who is on the square is honest and reliable, and is a strong part of the whole community around him. The term is also used to mean “just between you and me.” When one Mason tells another Mason something he’d like to be kept private, he’ll often say “This is on the square.”

On the Level - To a Freemason, means just that — all Freemasons are Brothers who meet on the same level, regardless of their social or economic status outside the lodge. Princes, presidents, and captains of business are no better or more important than bus drivers, plumbers, and paper boys when they sit in the lodge together. Masonry does not detract from a man’s accomplishments, nor does it exalt him above his Brothers because of his position outside the lodge."

It seems Ghost is delving into the clandestine underworld of Freemasonry and satirising that establishment the same way they do to organised religions.

Intelligent, fascinating, and a kick-ass song.