Alex Honnold has not freed the nose with or without a rope. His nose speed record partner, Tommy Caldwell, is one of only a handful of people who have.

Lynn Hill's first free ascent of The Nose was a monumental achievement, for a woman or a man.

It's confusing because The Nose describes both the feature on El Cap, and the route that takes the plum line up that feature. Honnold's Free Solo of the Nose was on a route called Freerider.

That's why I said, "in a comparable style". The FA was done on aid, as was Alex's speed ascent with Tommy.

But not completely comparable. The FA had to establish anchors, drill in bolts, figure out the route. More standing on the shoulders of giants, than anything I think.

Then, it's just optimization.

Honnold's Free Solo of the Nose was on a route called Freerider.

I think the confusion may be your own? The Nose is well, The Nose. Honnold climbed a route off to the side on a feature called (initially) the Salathe Wall.