The Avos as channels of the divine midos

כתיב עם חסיד תתחסד כו'.

It is written: "With the devoted one (chasid) You show devotion (tischasad)…" (Tehillim 18:26).

The Sefas Emes opens with the pasuk that Hashem deals with each person measure-for-measure, mirroring back the midah a person embodies.

הצדיקים הם כלים אשר על ידיהם מנהיג הקב"ה העולם בחסד ורחמים.

The tzaddikim are the vessels through which the Holy One conducts the world with chesed and rachamim.

Tzaddikim serve as the kelim (channels) by which Hashem's kindness and mercy flow into the world.

ולהיפוך אצל רשעים אמרו חז"ל הן הן המזיקים.

And conversely, regarding the resha'im, Chazal said: "They themselves are the destroyers (mazikim)."

Just as tzaddikim channel goodness, the wicked become the conduits through which harm and destruction enter the world.

עם חסיד תתחסד הוא החסד שמתגלגל בעולם על ידי אברהם אבינו ע"ה.

"With the devoted one You show devotion" — this is the chesed that flows through the world by means of Avraham Avinu, alav hashalom.

Avraham is the embodiment of chesed; through his midah, Hashem's kindness is drawn into the world.

גבר תמים הוא יצחק עולה תמימה וע"י מתגלה משפט ה' בעולם.

"With the wholehearted man [You are wholehearted]" — this is Yitzchak, the "perfect offering (olah temimah)," and through him the mishpat (justice) of Hashem is revealed in the world.

Yitzchak, who was bound on the altar as a flawless korban, embodies the midah of gevurah/din, the channel for Hashem's justice.

עם נבר הוא האמת שמתגלה בעולם ע"י יעקב אבינו ע"ה.

"With the pure one [You show purity]" — this is the emes (truth) revealed in the world through Yaakov Avinu, alav hashalom.

Yaakov, of whom it is said "titen emes l'Yaakov," is the channel for the midah of truth in the world.

עם עקש תתפתל הוא עשו ועמלק.

"With the crooked one You act with cunning" — this is Esav and Amalek.

The "crooked one" of the verse corresponds to Esav and his descendant Amalek, who receive back the twistedness they bring into the world.

ומקדימין פ' שקלים זכותו של אברהם אבינו בת נדיב.

And we read Parshas Shekalim first — [corresponding to] the merit of Avraham Avinu, "the daughter of the generous one (bas nadiv)."

The half-shekel of Shekalim, given with generosity, draws on the zechus of Avraham — the "nadiv" (generous one) whose midah is chesed.

וזכור הוא בחי' יצחק כמ"ש ז"ל אפרו של יצחק צבור ע"ג המזבח כמו שדרשו שלכן כתיב וזכרתי כו' בריתי יעקוב כו' וביצחק לא כתיב זכירה כי אפרו צבור.

And [Parshas] Zachor is the aspect of Yitzchak, as Chazal said: "the ashes of Yitzchak are heaped upon the altar," as they expounded — that this is why it is written "And I will remember … My covenant with Yaakov …" yet concerning Yitzchak no "remembering" is written, because his ashes are [already] heaped [there].

Since Yitzchak's "ashes" (the merit of the Akeidah) are perpetually present before Hashem, the Torah needs no separate "remembering" for him. Zachor — "remember [what Amalek did]" — corresponds to Yitzchak's midah of din, by which Amalek is judged.

ויתכן עוד כי לא מפורש בו זכירה כי מפסולת שלו יצא עמלק ולכן בפרשת זכור נזכר עמלק לרעה.

And it may further be said that "remembering" is not stated explicitly regarding him because Amalek came from his "refuse (pesoles)," and therefore in Parshas Zachor, Amalek is remembered for ill.

Amalek emerged from the "waste" of Yitzchak's line (through Esav), so the "remembering" connected to Yitzchak is the negative one — remembering Amalek in order to wipe him out.

ופרשת פרה הוא בית יעקב אש ששורף הפסולת כי מטתו של יעקב שלימה:

And Parshas Parah is "the house of Yaakov" — a fire that burns away the refuse — for the "bed" of Yaakov was complete (sheleimah).

Parah, with its burning and purifying ashes, corresponds to Yaakov, whose offspring were entirely righteous ("his bed was whole," with no pesoles among them). Yaakov's midah of emes is the fire that consumes all impurity.

Summary: Hashem governs the world measure-for-measure, "with the devoted one showing devotion." Tzaddikim are the vessels of chesed and rachamim, while the wicked become channels of harm. The three Avos embody the three midos — Avraham (chesed), Yitzchak (din), and Yaakov (emes) — and the special parshiyos of this season align with them: Shekalim with Avraham's generosity, Zachor with Yitzchak's din that judges Amalek (born of Esav's "refuse"), and Parah with Yaakov, whose wholeness is the purifying fire that burns away all impurity.