Accepting din earns the chesed of Sukkos

בגמ' לך ה' החסד כו' מעיקרא תשלם לאיש כמעשהו ולבסוף לך ה' החסד כו'.

In the Gemara: "To You, Hashem, is the chesed…" — at first [the pasuk states] "You repay each man according to his deed," and at the end "To You, Hashem, is the chesed."

The Gemara notes a tension in the verse: it begins with strict reward "according to one's deeds" (din) but concludes by attributing everything to Hashem's chesed.

דאיתא עלה במחשבה לברוא במדת הדין וראה שאין העולם מתקיים שיתף עמו מדה"ר.

For it is taught: it arose in [Divine] thought to create [the world] with the attribute of strict judgment (middas ha'din); He saw that the world could not endure, [so] He joined the attribute of mercy (middas ha'rachamim) with it.

Creation could not stand on pure justice alone, so Hashem blended in mercy — the very tension the Gemara found in the pasuk.

וכ"ז מתקיים בחג הזה אחר ימי הדין.

And all this is fulfilled in this festival [of Sukkos], after the days of judgment.

Sukkos comes right after the Yamim Noraim — the "days of din" — and embodies this very transition from judgment to mercy.

הקב"ה מפייס את בנ"י בחג הסוכות.

Hashem appeases Bnei Yisrael on the festival of Sukkos.

After the awe of judgment, Sukkos is Hashem's gesture of reconciliation and closeness toward His people.

לאשר בני ישראל הם מוכנים לקבל המשפט.

Because Bnei Yisrael are prepared to accept the judgment.

Bnei Yisrael willingly submit to Hashem's judgment rather than resist it.

וכל איש ישראל מסכים למשפטי ה' אמת.

And every Jew assents that the judgments of Hashem are true.

Each Jew affirms in his heart that Hashem's verdicts are entirely just.

ולכן זוכין אח"כ למדת החסד והרחמים.

And therefore they afterward merit the attribute of chesed and rachamim.

Precisely because they accept the din, Bnei Yisrael are then granted Hashem's kindness and mercy.

ואמת שיש משפט גם במדת החסד.

And it is true that there is a judgment even within the attribute of chesed.

Even chesed is not given indiscriminately — it too involves a form of mishpat.

דהיינו לשפוט האדם אם יכול לקבל החסד כראוי שלא לבוא לידי גסות כו'.

That is, to judge whether a person is able to receive the chesed properly, so that he does not come to coarseness (gassus) [of spirit].

The "judgment within chesed" weighs whether a person can absorb kindness without it leading him to arrogance or spiritual coarseness.

ומשפט זה מיוחד רק לבנ"י.

And this judgment is unique to Bnei Yisrael alone.

Only Bnei Yisrael are subject to this refined judgment of chesed, since only they are prepared to receive kindness in holiness.

לכן איתא כי המשפט נגמר בשמיני עצרת והוא משפט הנ"ל בבחי' החסד כמ"ש:

Therefore it is taught that the judgment is completed on Shemini Atzeres — and this is the aforementioned judgment in the aspect of chesed, as explained.

The judgment is finalized on Shemini Atzeres precisely because it is this special "judgment within chesed," reserved for Bnei Yisrael, that brings the whole season of din to its merciful conclusion.

Summary: The verse's movement from "repaying each according to his deed" to "Yours is the chesed" mirrors creation itself, where Hashem joined mercy to justice so the world could endure. After the Yamim Noraim, Hashem appeases Bnei Yisrael on Sukkos: because they willingly accept His true judgment, they then merit chesed and rachamim. Yet even chesed contains a judgment — unique to Bnei Yisrael — testing whether one can receive kindness without coming to coarseness, and this is the judgment completed on Shemini Atzeres.