An "Aveil" at Shabbat Mincha

Question

An aveil (mourner) does not practice public aveilut (mourning) on Shabbat (Ketubot 4a), though he is still in aveilut and there is some impact on what he can and can't do.

Would the presence of an aveil in shul at mincha on Shabbat stop the community from saying the prayer Tzidkatcha? He is still an aveil to some degree and not saying tzidkatcha isn't a public expression of his mourning.

Additionally, would his being there even if he is not considered an aveil to that degree still obviate saying tzidkatcha? The rule seems to be "if the day was not Shabbat, would we say tachanun? If not, don't say tzidkatcha on Shabbat." But if the day was not Shabbat, then he WOULD be a full aveil and then we would be davening in a minyan with an aveil and would not say tachanun.

Answer 1

In Nitei Gavriel on Hilchos Aveilus (cheilek alef) perek 117 he notes that when davening Mincha by the house of an aveil, there are mixed minhagim.

The case for saying we do, appears to have more support (refer to footnote 3):

1. Pri Megadim, OC 131, Eishel Avraham, S"K 10 notes because "אין מידת הדין מתוחה" - "we do not invoke the attribute of judgment" and therefore we say tzidkoscha.
2. This reason is shared also with Shu"t Mili D'Avos, cheilek beis, siman 11, os 25 (5 lines down from the top).
3. Pri Megadim, OC 292, Mishbetzos Zahav, S"K 2 - writes another reason that even though ordinarily Tachanun is not said in a mourner’s house, if it would not be said it would be a public demonstration of mourning. This view is also shared in the Sefer Tosafos Shabbos S"K 2.
4. Kitzur Shulchan Aruch 76:15 says outright "אַךְ כְּשֶׁמִּתְפַּלְּלִים בְּצִּבּוּר בְּבֵית אָבֵל, אוֹמְרִים אוֹתוֹ, דְּאִם לֹא יֹאמְרוּהוּ, הֲוֵי פַּרְהֵסְיָא, וְאֵין אֲבֵלוּת פַּרְהֶסְיָא בְּשַׁבָּת." - "But when praying with a congregation in the house of a mourner, it is said, for if it would not be said it would be a public demonstration of mourning and public mourning is not permitted on Shabbos.". This is also related in Darchei HaChaim 21.
5. Also refer to Yosef Da'as 400 that says we do recite tzidkoscha - the rule that on days we don't say tachanun we don't say tzidkoscha, is predicated on when it is a day of simcha, however in the case of an aveil they are primarily feeling a sense of mourning. We only don't say tachanun in the house of mourner due to "מידת הדין מתוחה" but this is not the case with tzidkoscha.
6. Finally, the recitation of tzidkoscha was taken on (lit. 'acquired') upon the passing of Moshe Rabbeinu and Dovid HaMelech (who died according to the Zohar at Shabbos Mincha), and if this is the case then for sure it is fitting to say it in the house of mourner.

The support that he brings for those who don't say it - (see footnote 4) are as follows:

1. Eliyah Rabbah 292:17 - Interestingly, he rejects the point mentioned in no. 6 above (he also adds that Yosef also died during this period of time) and meticulously knock off each case. Firstly, as per the Midrash on Parshas Vayeilech, Moshe tried to argue his case for Hashem not to let him die. Hashem responded that if He were to keep him alive it would effectively turn the Torah into a forgery/lie as it says expressly that he died. So that's why we say "ותורתך אמת" to negate this claim. With regards to Yosef, the Gemara tells us that he died before all his brothers even though he was a greater tzaddik as he acted with pride (ga'avah). And such is the great issur of gaavah that the Rabbeinu Chananel on the Gemara explains that Yosef used as it were, the sceptre of the King of Kings Hashem who dons Himself with a sense of pride when performing miracles and wonders such as Krias Yam Suf (the splitting of the Reed Sea). This is why we say in Tzidkoscha "אשר עשית גדולות אלקים מי כמוך" - "That which You do is great, G-d who is like You" i.e. no human being is comparable to that of Hashem. Finally, with Dovid the Gemara relates that Dovid did not want to die on Shabbos, but Hashem answers "וְאֵין מַלְכוּת נוֹגַעַת בַּחֲבֶרְתָּהּ" - " And one reign does not overlap with another (and deduct from the time allotted it even a hairbreadth)". And this is why we say in Tzidkoscha "צדקתך כהררי קל" - "Your righteousness is like the mighty mountains".

He ends by writing:

כתב עולת תמיד בשם אבודרהם יש מקומות שאין אומרים צדקתך בבית האבל

The Olas Tamid writes in the name of the Avudraham that there are places that don't say tzidkoscha in the house of a mourner.

2. He notes that it is likewise the custom of several European communities not to say it - 1) פירארא (couldn't work out this one?) 2) Frankfurt & 3) Worms

Answer 2

In many places it is customary to have Shabbos Mincha service in the Aveil's house in which case it would not be appropriate to Say Tzidkoscho as we are supporting G-d's Judgement for returning the Sinners to Geihenom after Shabbos as the Abudraham Explains:

צדקתך צדק לעולם ותורתך אמת כנגד דינה של גהינם ששואלין תחלה למת למה לא עסקת בתורה שנקראת אמת

This is the very reason why we don't say tachanun in the Mourners house. Mishna Brura 131,4:

נהגו שלא ליפול על פניהם (כ) לא בבית האבל - היינו כל שבעה והטעם דאז מדת הדין מתוחה עליו וע"כ יש ליזהר מלהגביר מדת הדין
All seven days of mourning one does invoke the Attribute of Judgement of Hashem since it has affected the mourner by taking his relative away from him (This would include saying Tachanun during the week and Tzidkoscho on Shabbos).

If the Aveil goes to Shul ther is a Machlokes Haposkim whether the congregation should say Tachanun, Beis Yosef says only the Aveil should say it, where as the Knesses Hagedolah in hagahos says the whole congregation should not say Tachanun. Since Tzidkosecha is also tziduk Hadin (acclaiming G-ds Justice which could mean negative connotations about the dead) just like Tachanun so the same Machlokes should apply.