Not quite accurate - it's more like halfway between them.
"Fragile" was recorded between mid-August and mid-September (concerts resumed on September 24, before which there was a week or so of rehearsals).
"America", as you state, was recorded in early February 1972. But that's not "just prior" to "Close To The Edge", which was recorded throughout June into July 1972. Yes were on a North American tour in February/March, reconvening for working sessions in April/May then entering Advision Studios sometime in late May or early June.
In a way, "America" even belongs to "The Yes Album" period, since the arrangement was put together during the writing sessions for "The Yes Album", and was only performed live until Tony Kaye's departure. Rick Wakeman had never played it when they decided to record it, and apparently found it too much work as Bruford plays the Mellotron chords on the final section. Wakeman only got to play it during the first couple of shows after Alan White had joined, then it was shelved and was never played again until the SLO shows in 1996.
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