The Avos: whole years containing all time

במדרש יודע ה' ימי תמימים כשם שהם תמימים כך שנותיהם תמימים כו' כי כל מעשה האבות הוא הכנה לכל בני ישראל ולפי שהם כוללים כל בנ"י נקראו תמימים.

In the Midrash: "Hashem knows the days of the wholehearted" (Tehillim 37:18) — just as they are wholehearted (temimim), so their years are whole — for all the deeds of the Avos are a preparation for all of Bnei Yisrael, and because they include all of Bnei Yisrael they are called "temimim" (whole/complete).

The Avos are called "whole" because they contain within themselves the totality of Bnei Yisrael; their every act paves the way for all their descendants.

וכמו שהם תמימים כן שנותיהם כוללין כל הזמנים ונק' תמימים.

And just as they are whole, so their years include all the times and are called "whole."

Because the Avos are all-inclusive, their lifespans too encompass all of time and are termed "complete."

ושנותיהם הם קיום כל הזמנים.

And their years are the sustaining of all the times.

The years of the Avos are the very foundation that upholds and gives existence to all eras of history.

ולכן כתיב יודע ה' ימי תמימים כמו שהמועדות נקראו מועדי ה'.

Therefore it is written, "Hashem knows the days of the temimim," just as the festivals are called "the appointed times of Hashem" (Vayikra 23:4).

The days of the Avos carry a special divine quality, comparable to the moadim — fixed times charged with Hashem's revelation.

והאבות בכל ימיהם הי' נגלה אותה ההארה שמתגלה במועדים.

And the Avos, in all their days, had revealed that same illumination which is revealed on the festivals.

The special light that shines on Yom Tov was present in the Avos every single day of their lives.

ואותו המועד שהוא בזכות אותו הצדיק הי' בכל ימיו מתגלה הארה זו כמו כן.

And that particular festival which is in the merit of a given tzaddik — in all his days that same illumination was likewise revealed.

Each festival draws on the merit of a particular Av; for that tzaddik, the light of "his" festival shone throughout all his days.

וזה ג"כ רמז המדרש באסתר שמלכה על קכ"ז מדינות שכמו שתיקנה שרה בזמן קכ"ז שנים.

And this is also the hint of the Midrash regarding Esther, who ruled over 127 provinces — that just as Sarah established things in the span of her 127 years…

The Midrash links Esther's 127 provinces to Sarah's 127 years: Sarah's complete years laid a spiritual foundation that Esther inherited.

כך בבחי' המקום האירה לקכ"ז מדינות כי בחי' עולם שנה נפש ענין א' הוא:

…so in the dimension of "place" (makom) she illuminated 127 provinces — for the aspects of "world, year, soul" (olam, shanah, nefesh) are one matter.

What Sarah accomplished in the dimension of time (her 127 years) translated into Esther's reach in the dimension of space (127 provinces), since the three dimensions of world (space), year (time), and soul are ultimately a single unified reality.

Summary: The Avos are called "temimim" (whole) because they contain all of Bnei Yisrael and all of time; the special illumination of the festivals shone in them every day of their lives. This unity of dimensions explains the link between Sarah's 127 complete years (time) and Esther's rule over 127 provinces (space), for "olam, shanah, nefesh" — space, time, and soul — are one.