Use of definite article (ה) in יהי רצון … מצות התלוים

Question

The paragraph after the ברכה (b'racha) of ציצת (tzitzis) ends with the expression " וְתַרְיַ"ג מִצְות הַתְּלוּיִם בָּהּ".

My question is why does the word "התלוים" start with "ה"? It appears like the "תלוים" is part of a definite noun phrase.

יְהִי רָצון מִלְּפָנֶיךָ. ה' אֱלהַי וֵאלהֵי אֲבותַי. שֶׁתְּהֵא חֲשׁוּבָה מִצְוַת צִיצִית לְפָנֶיךָ כְּאִלּוּ קִיַּמְתִּיהָ בְּכָל פְּרָטֶיהָ וְדִקְדּוּקֶיהָ וְכַוָּנותֶיהָ. וְתַרְיַ"ג מִצְות הַתְּלוּיִם בָּהּ. אָמֵן סֶלָה

("Da'at Sidur Ashk'naz")

Answer 1

To be clear, Hebrew is my mother tongue.

1. ה is frequently used as ש (which) in Hebrew, meaning מצוות שתלויות etc. For example we say "הנותן ליעף כח", meaning "שנותן ליעף כח" because the original verse is without ה at all.

2. Another reason is that in medieval (and Mishnaic) Hebrew this form is also frequent like שבת הגדול, and the contemporary proper Hebrew form would be definitely המצוות התלויות.
   BTW the fact that is does not align gender (should read מצוות התלויות) just proves it is a mistake.

Answer 2

I hope I'm not oversimplifying this, but intuitively the phrase in question sounds like a normal definite noun phrase, if a little obscured by the abbreviation "תרי"ג". The object being described is probably not מִצְות but תַרְיַ"ג מִצְות.

There are many cases in which the article is not needed in a definite noun phrase, such as when they are possessives or nouns in construct state. For example, the following are fine:

אֶל אַהֲרֹן וְאֶל אֶלְעָזָר וְאֶל אִיתָמָר בָּנָיו הַנּוֹתָרִים (Vayikra 10:12)

וַיְהִי לִבְנֵי מְנַשֶּׁה הַנּוֹתָרִים (Y'hoshu'a 17:2)

Perhaps another case that does not need the article to be definite numbered groups of things, as in the case at hand. [NUMBER THING] phrases behave a lot like construct noun phrases. The number words undergo very similar transformations as do nouns in construct, such as the final "ה" turning into a "ת", the suffix "ים" shortening to just "י" and the suffix "ות" not changing at all.

But unlike regular construct noun phrases, a numbered group of things may act more like a single word than like a noun phrase, as in an alternative nusach Ashk'naz version of the same paragraph, which includes

ועשיית כל התרי"ג מצות התלוים בה (cf. Sidur Ya'ave"tz)

It's quite common in Hebrew for construct state nouns to be treated in this sense as single words (e.g. "הבית ספר החדש"), so it should be all the easier to treat [NUMBER THING] phrases as such, even though the overwhelming majority of the time before ~1900 (at least in print) they weren't.

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Summary (AKA defense of my as yet uncertain intuition): If you accept that

1. "תַרְיַ"ג מִצְות" is one word and
2. תַרְיַ"ג is just a number and
3. a number can mark definiteness

then everything is fine.