Rav Shlomo Wahrman, late Gaon and Rosh Yeshiva of the Hebrew Academy of Nassau County (my high school), opens his short essay (in Oros HaShabbos) on Kriyat HaTorah on Shabbos with the following question:
Let's look back to the earliest origin of a public reading of the Torah scroll.
(י) וַיְצַ֥ו מֹשֶׁ֖ה אוֹתָ֣ם לֵאמֹ֑ר מִקֵּ֣ץ ׀ שֶׁ֣בַע שָׁנִ֗ים בְּמֹעֵ֛ד שְׁנַ֥ת הַשְּׁמִטָּ֖ה בְּחַ֥ג הַסֻּכּֽוֹת׃ (יא) בְּב֣וֹא כׇל־יִשְׂרָאֵ֗ל לֵֽרָאוֹת֙ אֶת־פְּנֵי֙ יְהֹוָ֣ה אֱלֹהֶ֔יךָ בַּמָּק֖וֹם אֲשֶׁ֣ר יִבְחָ֑ר תִּקְרָ֞א אֶת־הַתּוֹרָ֥ה הַזֹּ֛את נֶ֥גֶד כׇּל־יִשְׂרָאֵ֖ל בְּאׇזְנֵיהֶֽם׃
(10) And Moses instructed them as follows: Every seventh year, the year set for remission, at the Feast of Booths, (11) when all Israel comes to appear before the LORD your God in the place that He will choose, you shall read this Teaching aloud in the presence of all Israel.
What are the Biblically defined objectives of this reading ceremony?
(יב) הַקְהֵ֣ל אֶת־הָעָ֗ם הָֽאֲנָשִׁ֤ים וְהַנָּשִׁים֙ וְהַטַּ֔ף וְגֵרְךָ֖ אֲשֶׁ֣ר בִּשְׁעָרֶ֑יךָ לְמַ֨עַן יִשְׁמְע֜וּ וּלְמַ֣עַן יִלְמְד֗וּ וְיָֽרְאוּ֙ אֶת־יְהֹוָ֣ה אֱלֹהֵיכֶ֔ם וְשָֽׁמְר֣וּ לַעֲשׂ֔וֹת אֶת־כׇּל־דִּבְרֵ֖י הַתּוֹרָ֥ה הַזֹּֽאת׃
(12) Gather the people—men, women, children, and the strangers in your communities—that they may hear and so learn to revere the LORD your God and to observe faithfully every word of this Teaching.
There are five stated objectives:
שמיעהלימודיראת ה׳שמירהעשיה
So we have the Torah reading at Hakhel established; but what about the weekly Torah reading on Shabbos?
מֹשֶׁה רַבֵּנוּ תִּקֵּן לָהֶם לִישְׂרָאֵל שֶׁיְּהוּ קוֹרִין בַּתּוֹרָה בָּרַבִּים בְּשַׁבָּת וּבְשֵׁנִי וּבַחֲמִישִׁי בְּשַׁחֲרִית כְּדֵי שֶׁלֹּא יִשְׁהוּ שְׁלֹשָׁה יָמִים בְּלֹא שְׁמִיעַת תּוֹרָה.
Moses, our teacher, established the rule for Israel that they should read the Law publicly on Sabbaths and also on the second and fifth days of the week, during the morning service, so that three days shall not elapse without hearing the Law.
PROOF 1: SHEMA YA'AVIRENU, RESTRICTION ON CARRYING A SEFER TORAH ON SHABBOS?
Concept Orientation
Rabbis banned waving the lulav, blowing the shofar and reading Megillat Esther on Yom Tov/Shushan Purim that falls out on Shabbos since one might come to carry them four amot in the public domain to ask a shaila to a chacham, whether about how to perform the mitzvah or if something went awry (e.g. lulav leaves tore or a crack appeared on the shofar).
Reading the Other Megillot: We read Shir HaShirim on Shabbos Chol HaMoed Pesach; Ruth on Shavuot; Kohelet on Shabbos Chol HaMoed Sukkos. We traditionally do not recite a beracha beforehand. CAS does have megilla scrolls for these megillot.
PROOF 2: BLESSINGS BEFORE AND AFTER KRIYAT HATORAH
Concept Orientation
Blessings of the Oleh: The Mishnah in Megillah 21a states that the first oleh says a beracha before his aliyya and the final oleh says a beracha after his aliyya but none of the olim in the middle say a beracha. The Gemara there says that nowadays, all the olim say berachot before and after the aliyya so as not to confuse those who come to shul mid-rishon (and missed the first oleh's beracha) and none of the other olim are making berachot beforehand, he'll conclude that the halacha is we don't say an initial beracha on an aliyya ever; and also not to confuse those who leave shul mid-shvi'i (and misses the final beracha) and none of the other olim said a concluding beracha, he'll concude that the halacha is we don't say a final beracha on an aliyya ever.
PROOF 3: TALKING DURING KRIYAT HATORAH
Concept Orientation:
Minyan: A kehilla may only read from the Sefer Torah with Barchu and berachot if there is a minyan.
PROOF 4: THE RAMBAN ON MEGILLAH 23b
Concept Orientation
פורסין על שמע - A minyan is required to say the kaddish and Barchu that precede the birkos krias shema.
PROOF 5: MAKING UP MISSED TORAH READINGS (TASHLUMIN)
According to the Toras Chayyim (Rav Avraham Chaim Schorr; d. 1631; Poland) tashlumin is incumbent on the tzibbur only when there was a minyan present and they didn't read; but if there was no minyan present at all, there is no necessity of tashlumin.
The Sha'ar Ephraim (Rav Ephraim ben Yaakov HaKohen; d. 1678; Lithuania) quoted by Rav Schachter in response to COVID-19 echoes the Toras Chayyim.
Rav Hershel Schachter in Piskei Corona
קרה"ת בשבת שאחר המגפה
כתוב בס' שערי אפרים (שער ז' ס"ט), אם בטל קריאת הסדר בשבת אחת מחמת איזה אונס, אזי לשבת הבאה קורין וכו'. וכן אם בטלו כמה שבתות אין לקרות כל מה שבטלו...רק קורין הסדר של שבת שלפניו עם סדר שבת זו לבד. ומי שרוצה לנהוג ולקרות מה שבטלו שבת של מחוברין או בטול כמה שבתות, אין מזניחין אותו וכו'. והוסיף עוד שמה (בסל"ט), שאם לא בטלו באונס, רק שלא היו שם עשרה...א"צ להשלים בשבת הבאה. ועי' משנ"ב (קל"ה סק"ז) ובס' אורחות חיים (ספינקא, שמה) שכל זה מוטל במח' (מכמה שבתות, ומשני ספרים), ועי' בתוספת מעשה רב (אות ל"ד) שהגר"א החמיר בזה. וכן עי' בס' פאר הדור (ח"ג עמ' ל"ג) שהחזו"א ג"כ החמיר בזה. ומסתמא מן הנכון שבישיבות יחמירו בזה כהנהגת הגר"א והחזו"א להשלים כל הפרשיות בשבת הראשונה לאחר תום המגפה.
THE VILNA GAON'S TIME IN JAIL
Excerpt from The Genius: Elijah of Vilna and the Making of Modern Judaism, Eliyahu Stern, Yale University Press, 2013, pgs. 32-33
Excerpt from the Sefer Tosefes Ma'aseh Rav
Note that it doesn't say that the Gra called a minyan to his home as well, so he might hold that it's a full chovas hayyachid, irregardless of whether there is a minyan present. This however contradicts the conclusion of Rav Wahrman based on the anecdote of the Gra cited above that Kriyas HaTorah is a chovas hatzibbur based on his conclusion about the megillos being muttar on Shabbos and that we're not worried about shema ya'avirenu. It's possible though that the Gra held it's a chovas hayyachid.
CHOVAS HAYACHID? THE SHITTA OF REB CHAIM BRISKER
SHOWDOWN OF THE [RAV'S] GRANDFATHERS
If the underlying objective is for the individual to learn (chovas hayachid), then it makes sense to do a full tashlumin, as the Gra and Chazon Ish hold; but if the objective is to have a communal religious event (chovas hatzibbur), then what difference does it make which portion is read -- the objective is still being fulfilled, and tashlumin is not necessary, as the Shaar Efraim holds.
LITERACY IN ANCIENT ISRAEL
RE-EXPERIENCING SINAI
Prof. Aaron Demsky, Professor of Biblical History at Bar-Ilan University, www.thetorah.com
After citing Deut. 31:12: "The opening word of this verse, Hakhel “gather,” from the root ק.ה.ל meaning “congregation” or “gathering,” gives the commandment its name and reflects its outlook nicely. This reading was not meant for priests, scribes or other initiated literati alone, as we would have expected in antiquity, but rather for the widest possible audience, without regard to status, gender or age. This fits with the public nature of the theophany at Horeb, which forms the basis of God’s covenant with Israel."
Rav Yosef also understands the Torah reading to have an aspect of the theophany...
אֶלָּא הָא דְּתָנֵי רַב שִׁימִי אֵין פּוֹחֲתִין מֵעֲשָׂרָה פְּסוּקִין בְּבֵית הַכְּנֶסֶת וַיְדַבֵּר עוֹלֶה מִן הַמִּנְיָן הָנֵי עֲשָׂרָה כְּנֶגֶד מִי אָמַר רַבִּי יְהוֹשֻׁעַ בֶּן לֵוִי כְּנֶגֶד עֲשָׂרָה בַּטְלָנִין שֶׁבְּבֵית הַכְּנֶסֶת רַב יוֹסֵף אָמַר כְּנֶגֶד עֲשֶׂרֶת הַדִּבְּרוֹת שֶׁנֶּאֶמְרוּ לְמֹשֶׁה בְּסִינַי (רַבִּי לֵוִי אָמַר כְּנֶגֶד עֲשָׂרָה הִילּוּלִין שֶׁאָמַר דָּוִד בְּסֵפֶר תְּהִלִּים) וְרַבִּי יוֹחָנָן אָמַר כְּנֶגֶד עֲשָׂרָה מַאֲמָרוֹת שֶׁבָּהֶן נִבְרָא הָעוֹלָם.
The Gemara raises a question: But with regard to this baraita that Rav Shimi taught: One may not decrease to fewer than ten the number of verses read during a public Torah reading in the synagogue, and a generic verse, e.g., “And God spoke to Moses saying,” is included in the count, to what do these ten verses correspond? Why specifically the number ten? Rabbi Yehoshua ben Levi said: They correspond to the ten idlers that are in the synagogue, i.e., ten men who have the leisure not to work, and instead sit in the synagogue and are available to attend to communal needs. Rav Yosef said: They correspond to the Ten Commandments that were spoken to Moses at Sinai. Rabbi Levi said: They correspond to the ten psalms of praise that David said in the book of Psalms. And Rabbi Yoḥanan said: They correspond to the ten utterances with which the world was created.
The fact that a public reading is performed on Shabbos fits perfectly into the Biblical construct of Shabbos, fleshed out in Omer's chabura and defined explicitly in the Torah as a day devoted to G-d.
(יג) וְאַתָּ֞ה דַּבֵּ֨ר אֶל־בְּנֵ֤י יִשְׂרָאֵל֙ לֵאמֹ֔ר אַ֥ךְ אֶת־שַׁבְּתֹתַ֖י תִּשְׁמֹ֑רוּ כִּי֩ א֨וֹת הִ֜וא בֵּינִ֤י וּבֵֽינֵיכֶם֙ לְדֹרֹ֣תֵיכֶ֔ם לָדַ֕עַת כִּ֛י אֲנִ֥י יְהֹוָ֖ה מְקַדִּשְׁכֶֽם׃
(13) Speak to the Israelite people and say: Nevertheless, you must keep My sabbaths, for this is a sign between Me and you throughout the ages, that you may know that I the LORD have consecrated you.
And finally, what is the whole stated purpose of the Torah reading at Hakhel?
(יג) וּבְנֵיהֶ֞ם אֲשֶׁ֣ר לֹא־יָדְע֗וּ יִשְׁמְעוּ֙ וְלָ֣מְד֔וּ לְיִרְאָ֖ה אֶת־יְהֹוָ֣ה אֱלֹהֵיכֶ֑ם כׇּל־הַיָּמִ֗ים אֲשֶׁ֨ר אַתֶּ֤ם חַיִּים֙ עַל־הָ֣אֲדָמָ֔ה אֲשֶׁ֨ר אַתֶּ֜ם עֹבְרִ֧ים אֶת־הַיַּרְדֵּ֛ן שָׁ֖מָּה לְרִשְׁתָּֽהּ׃ {פ}
(13) Their children, too, who have not had the experience, shall hear and learn to revere the LORD your God as long as they live in the land that you are about to cross the Jordan to possess.
These verses unlock the riddle of this verse in Proverbs:
(ז) יִרְאַ֣ת יְ֭הֹוָה רֵאשִׁ֣ית דָּ֑עַת...׃ {פ}
(7) The fear of the LORD is the beginning of knowledge...