Din of Rosh Hashanah, chesed of Yom Kippur

איתא בגמ' ולך ה' החסד כו' בתחלה לאיש כמעשהו ולבסוף החסד.

It is taught in the Gemara: "And to You, Hashem, belongs kindness" (Tehillim 62:13) — at first Hashem pays each man according to his deeds, and afterward comes the chesed (Sanhedrin 100a).

The Sefas Emes draws on Chazal's reading: judgment first measures a person exactly by his actions, and only then does Hashem add His chesed beyond the strict accounting.

וכן הוא המדה בר"ה הוא המשפט וכמ"ש צדיק ה' בכל דרכיו.

And so is the order: Rosh Hashanah is the judgment, as it is written, "Hashem is righteous in all His ways" (Tehillim 145:17).

Rosh Hashanah expresses the attribute of strict mishpat — Hashem as the righteous Judge who weighs every deed.

וביו"כ הוא הסליחה בחסד וזה וחסיד בכל מעשיו כי החתימה ביוה"כ הוא סוף מעשה המשפט לכן הוא בחסד.

And Yom Kippur is the forgiveness through chesed — this is the continuation of the posuk, "and He is kind in all His deeds" — for the sealing on Yom Kippur is the conclusion of the act of judgment, and therefore it comes with chesed.

The same posuk holds both halves: "righteous in all His ways" is Rosh Hashanah's din, and "kind in all His deeds" is Yom Kippur's chesed, which seals the verdict mercifully because it is the finishing of the judgment.

ושלא כמדת ב"ו שקשה לתקן המעשה יותר מתיקון הרצון.

And this is unlike the way of flesh and blood, for whom it is harder to repair the deed than to repair the will.

For a human being, fixing one's intentions is easier than undoing an act already done; with Hashem the order is reversed.

ובאמת היא הנותנת ע"י שגלוי לפניו ית' שבמעשה א"א לב"ו להתקיים בדין לכן שיתף עמו החסד במעשה.

And in truth this very fact is what brings it about: because it is revealed before Him that in the realm of deed no human could survive strict judgment, He therefore joined chesed together with the deed.

Precisely because action is the hardest area for a person to rectify, Hashem mercifully attaches chesed to the judgment of one's deeds, so that no one is condemned by din alone.

אבל הדרך והמשפט בצדק שכן צריך להיות עכ"פ באדם שיכונו דרכיו והנהגותיו במשפט אמת.

But the path and the judgment remain in righteousness, for so it must be — at the very least a person's ways and conduct should be aligned according to true mishpat.

Even though Hashem adds chesed, a person's own job is to direct his ways and behavior to accord with true justice and ratzon Hashem.

הגם שא"י לגמור במעשה כראוי כמ"ש במ"א מזה:

Even though one cannot fully complete the deed as it ought to be, as I have written elsewhere on this matter.

A person is not expected to achieve flawless action; his task is the sincere alignment of his will and his ways, and Hashem's chesed completes the rest.

Summary: Building on Chazal's teaching that Hashem first judges by deeds and then adds chesed, the Sefas Emes maps Rosh Hashanah onto strict din ("righteous in all His ways") and Yom Kippur onto chesed ("kind in all His deeds"). Because the realm of action is where no person could withstand pure judgment, Hashem joins chesed to the deed at the sealing; man's own avodah is to align his ways with true justice even when he cannot perfect the action itself.