blessing - Where are we commanded to wrap ourselves in Tzitzit?

When we put on a tallit, we say a blessing (copied from here)

Barukh atah Adonai, Eloheinu, melekh ha'olam

Blessed are you, Lord, our God, sovereign of the universe

asher kidishanu b'mitz'votav v'tzivanu l'hit'ateif ba-tzitzit

Who has sanctified us with His commandments and commanded us to wrap ourselves in the Tzitzit.

I know that there is a commandment to attach the fringes to the proper garment (as the jewfaq site lists in its enumeration of the 613 mitzvot according to the Rambam, "To put tzitzit on the corners of clothing (Num. 15:38)") but what is the source for the idea that there is a specific commandment to wrap ourselves in the tzitzit? The text of the bracha seems to reflect an explicit command -- but what command?

This answer indicates "In Ashkenazic practice, the optimal blessing for a tallit -- to wrap oneself in tzitzit -- is said only on a talit gadol. For a *tallit katan", we're not sure it's quite up to that level, so it gets a lesser blessing, regarding the mitzva of tzitzit. " I'm not sure what any of this really means -- is there an extant commandment to wrap that is on a higher level than simply "asu lahem tzitzit"?

Additional notes -- the Shulchan Aruch (O"C 8:1) says, "One should wrap himself in the ציצית and make a blessing on them while standing" -- " יתעטף בציצית ויברך מעומד". But (8:3) "the טלית קטן (small Talit) garments that we have the custom to wear, even though there is no concept of wrapping (היתעטף) by them, one is יוצא his obligation of ציצית." So we fulfill the obligation without wrapping.

So, if so, where is there any additional textual obligation to wrap that would be reflected in the bracha?

Answer

(As background, know that there is an argument (see Tur OC 8) if a formal "Arab-style" wrapping is the only method of wearing a four-cornered garment which qualifies for the biblical command of Tzitzit. This is just a question of what the Torah commanded. Wearing four-cornered socks, for instance, or a four cornered scarf is not included in the Mitzva according to everyone and you'd be exempt from putting Tzitzit on them.)

So we have a blessing which uses what appears to be a very particular word describing the method of wearing clothing in its formulation. You can take this in 4 main ways:

1. 
   

   This shows that the opinion limiting the Mitzva to the formal Arab-style wrap is correct. (See Or Zarua quoted in Terumat HaDeshen #45.) We only find this limiting because our sartorial styles have changed in the last few millennia. According to this you have to wear any garment with Tzitzit in the formal Arab-style wrap fashion always if you want to fulfill the Mitzva. (Some are stringent for this opinion when not doing so would be a leniency such as to avoid a possibly invalid blessing said before donning a Talit.)

   
   
   


2. 
   

   The wording of the blessing is not intended to be fixed and when wearing Tzitzit not in the old fashioned formal Arab-wrap style you should say a different blessing like "LeHitlabbesh BaTzitzit" or maybe "Al Mitzvat Tzitzit". (See Maharam of Rothenberg quoted in Terumat HaDeshen ibid.) According to this there is no need ever to do the formal Arab-style wrapping, as long as you pay attention to the wording of your blessing.

   
   


3. 
   

   The wording of the blessing is fixed but just indicates the most common usage when it was composed, namely, the formal Arab-style wrapping. This is not unlike other Mitzvot where (at least according to this school of thought) we use the standard text even when in non-standard circumstances (eg. washing hands for bread by dipping in a Mikva gets an "Al Netilat Yadayim"). This is just a fixture of our liturgical system sans a Sanhedrin. (See Beiur HaGra to OC 8:6.) According to this there is [most likely] no need ever to do the formal Arab-style wrapping.

   
   


4. 
   

   This shows that the word "LeHit'ateif" isn't such a specific action and it doesn't have to mean formal Arab-style wrapping, but rather any type of wearing/wrapping. That which the Talmud (MK 24a) defines that word as a formal Arab-style wrap is either not how we rule (Beit Yosef OC 8) or was only intended for the laws of mourning (Mahari Abuhov cited ibid.). According to this there is no question from the language of the blessing and formal Arab-style wrapping isn't necessary for Tzitzit.

   
   

One way or another, the blessing is just describing the process of putting on the clothing with Tzitzit, and while the word it chose may seem very particular, the Mitzva is just what we always thought it was which is wearing a garment with Tzitzit in accordance with various legal details, whatever they may be; tying Tzitzit onto clothing is not strictly speaking a complete Mitzva (more of a Hekhsher Mitzva or the beginning of a Mitzva, however we decide to define that).

You are correct that the verb in the verses is related to making the fringes, but blessings don't always follow the verse exactly (eg. "Lehaniach Tefillin" not "Likshor Tefillin", "Likboa Mezuza" not "Likhtov Mezuza", or "Lehafrish Challah" not "Leharim Challah"). We apparently allow a bit of Oral Torah interpretation to frame exactly what Mitzva action we are performing when formulating the blessing.