Why a formulaic greeting on ליל ראש השנה?

Question

On Rosh Hashana night, it is customary to greet one another with "לשנה טובה תכתב (ותחתם)‏" (Rama 582:9, MB). People (in my experience) and machzorim (Rosh Hashana prayer books) treat this as formulaic, with no variation from the specified text. (Specific customs vary, with, e.g., some adding "לאלתר לחיים טובים ולשלום", but whatever custom people may have, they stick to it, rather than saying wholly different things like the suggestions below.) It's so formulaic that some people (purposely) don't even decline the verbs for number and gender.

• Is it correct to treat the greeting as an immutable formula, the way people and machzorim do? (E.g., is that how we should read the Rama?) Sources, please.

And if it's correct (or correct according to some sources), then:

• Why is there such a formulaic greeting? Why not use whatever other wording we may think of, like "לשנה טובה ומתוקה תכתב ותחתם" or "תכתב בספר החיים" or "תכתב ותחתם לשנה טובה"?

Answer 1

This most common formula is based on the Mateh Efraim. However there are other formulas in the Mishna Berura, Chayai Adam, and other seforim. The main thing is to wish your fellow congregants and friends with a full heart.

Answer 2

Is it correct to treat the greeting as an immutable formula, the way people and machzorim do? (E.g., is that how we should read the Rama?) Sources, please.

Well, the Kitzur Shulchan Aruch in סימן קכט - הלכות ראש השנה says:

סעיף ח' לְאַחַר גְּמָר תְּפִלַּת מַעֲרִיב בְּלֵיל רִאשׁוֹן, נוֹהֲגִין לוֹמַר כָּל אֶחָד לַחֲבֵרוֹ, לְשָׁנָה טוֹבָה תִּכָּתֵב וְתֵחָתֵם. וְלִנְקֵבָה. אוֹמְרִים, תִּכָּתְבִי וְתֵחָתֵמִי. אֲבָל בַּיּוֹם, אֵין אוֹמְרִים, לְפִי שֶׁכְּבָר נִגְמְרָה הַכְּתִיבָה קֹדֶם חֲצוֹת הַיּוֹם, וּבְלֵיל שֵׁנִי, יֵשׁ נוֹהֲגִין לְאָמְרוֹ, כִּי לִפְעָמִים נִדּוֹנִין בְּיוֹם שֵׁנִי (תקפב). ‏

So clearly there seems to be something ommited from machzorim who don't provide conjucated versions.

And if it's correct (or correct according to some sources), then:

As we see, it isn't.

Why is there such a formulaic greeting? Why not use whatever other wording we may think of, like "לשנה טובה ומתוקה תכתב ותחתם" or "תכתב בספר החיים" or "תכתב ותחתם לשנה טובה"?

It's easiest to wish everybody the same thing. Otherwsie people may get insulted that you wished them less than you did to the other guy. or you may get insulted when one fellow wishes you less than the other one did.

Similarly, in communities, the Shabbat greeting is uniform, be it Gut Shabbos or Shabbat Shalom or whatever. People may get upset if one guy gets a "Sweet and mellow Shabbat to you" and they got a simple "Shabbat Shalom".