...but great artists steal

For the umpteenth time, I've been presented with a three letter answer to the prompt "Branch" while doing the NY Times Crossword.
Despite my best efforts, the answer is always "Arm" and every time, I can't help but be drawn back to The Secret's verse 10 in which both of these words seem to play significant roles.
If these words are one and the same according to one of the most popularized puzzles in history, then why not in the Secret?
Wouldn't that be a hoot? The arm you find in line 3 is one and the same as the branch you later use as a locator during your steps?
People seem skeptical. Whenever I broach this topic, it seems to get the dismissal of a really out there concept. "Ya, Maybe, I guess"--leaning on bridges, statue arms, and tree branches as certainly more 'on brand' or 'likely.' But what do we really know?
Byron is writer. Words are his thing. Add to this that his primary exposure to puzzles in 1980 is most likely along the lines of The NY Times crossword and suddenly a concept in the same vein should maybe be viewed as more than just a possibility.
So let's say Arm and Branch are the same. Where else do these two words align?
Armed forces, Branches of the military.
Arms and branches of agencies overseeing various sectors.
Or in the NYT sense, it could indeed be a tree branch. I'm not ruling it out. (Though I would hope it's not a real tree...)
So!
Find the arm that Extends over the slender path
My friend Scott recently reiterated one of our favorite talking points: Line breaks. This line break certainly could indicate that the arm is not extending itself, but has some role associated with the slender path. People, myself included, love 'slender path' being the Verrazano Narrows. So who oversees that? Technically, the coast guard. But heck--Byron could have assumed the Navy. Either works.
And then we get to branches. We're looking for one branch of the v. But what if 'v'=5? What else has 5 branches?
Food for thought. The confirmations seem to be in place. Our initial 'arm' finding could indeed be the beginning of the end and indicate very little travel in this particular puzzle. So how could this manifest? One of the pilons of the East Coast memorial? A placard in South Brooklyn? There's no shortage of armed forces related memorials, monuments or imagery in NYC.