The bris as Yom Kippur's seal

ומ"ש לעיל כי הציצית רומז לברית מילה.

And what was said above, that the tzitzis alludes to the bris milah.

The Sefas Emes picks up an earlier point: the mitzvah of tzitzis carries within it a hint to the covenant of milah — both are signs marking a Yid as belonging to Hashem.

רמז לדבר בההוא עובדא במס' מנחות שבאו הציצית לאותו תלמיד להצילו מחטא ערוה ואמר שכ' בפ' ציצית ב"פ אני ה' אלקיכם.

A hint to this is found in that incident in Maseches Menachos, where the tzitzis came to a certain student to save him from the sin of arayos (forbidden relations), and he said that in the parsha of tzitzis it is written twice "Ani Hashem Elokeichem" ("I am Hashem your God").

In the Gemara (Menachos 44a), a man's own tzitzis rose up and stopped him from sin. The Sefas Emes notes that the parsha of tzitzis repeats the phrase "I am Hashem your God" twice, tying the garment of mitzvos to guarding against arayos.

ובאמת גם בפ' עריות כתיב ב"פ אני ה' אלקיכם.

And in truth, in the parsha of arayos as well it is written twice "Ani Hashem Elokeichem."

The same double declaration of "I am Hashem your God" appears in the parsha that lists the forbidden relations — linking the two parshiyos at their root.

ואפשר שלכן קורין בפרשת עריות ביוהכ"פ למנחה.

And it is possible that this is why we read the parsha of arayos on Yom Kippur at Minchah.

The custom of reading the laws of arayos at Minchah of Yom Kippur is rooted in this shared phrase, drawing the holiness of the day specifically toward guarding kedushah.

ורמז ב"פ אני ה' אלקיכם כמ"ש אני ראשון ואני אחרון.

And the hint of the two times "I am Hashem your God" is as it is written, "I am first and I am last" (Yeshayahu 44:6).

The doubling corresponds to Hashem being both the beginning and the end — "first" and "last" — the One who encompasses all of existence from start to finish.

ובנ"י יש להם חלק בראשית ואחרית והמילה עדות והכל הולך אחר החותם.

And Bnei Yisrael have a portion in both the beginning and the end, and the milah is the testimony, and everything follows the seal.

The bris milah is the "seal" (chosam) stamped upon a Yid, bearing witness to his bond with Hashem. Since "everything follows the seal," it is the milah that secures Bnei Yisrael's share in both the first and the last.

גם רמז לדברים הנ"ל ממ"ש הקב"ה לאברהם בך חותמין שיום החתימה ביוהכ"פ בזכות בריתו של אברהם אע"ה כנ"ל]:

There is also a hint to the above matters from what the Holy One, Blessed is He, said to Avraham, "With you they seal" — that the day of the sealing on Yom Kippur is in the merit of the bris of Avraham Avinu, peace be upon him, as above.

Chazal teach that the closing brachah of Shemoneh Esrei is "sealed" with Avraham ("magen Avraham"). The Sefas Emes connects this to the chasimah (final sealing of judgment) on Yom Kippur, which comes about through the merit of Avraham's bris — the eternal seal of the covenant.

Summary: The Sefas Emes weaves together tzitzis, the bris milah, and Yom Kippur through the doubled phrase "Ani Hashem Elokeichem." The bris is the "seal" testifying to Bnei Yisrael's bond with Hashem — first and last — and it is in the merit of this covenant of Avraham that the final sealing of judgment on Yom Kippur is granted.