In Bava Metzia 59a, Rav Yehuda recommends ensuring you have a ready supply of grain in your house, for discord is found only when grain is lacking. His prooftext is Tehillim 147:14, “He makes your borders (גְּבוּלֵךְ) peace; He satiates you with cream of wheat (חֵלֶב חִטִּים).” I’d add: “your borders” is equivalent to “your house”, as we see from the chametz / se’or prohibition, though on Pesach, we eliminate much of the house’s grain, if it’s leavened. Also, I wonder if there’s a Biblical parallelism or resonance in the verse. Biblical גְּבוּל regularly means border, and only means mixing / kneading post-Biblically (e.g. גַּבֵּיל לְתוֹרָא גַּבֵּיל לְתוֹרֵי in Bava Metzia 69a, mixing fodder for an ox, mix fodder for oxen, or Pesachim 34a, אַבָּא שָׁאוּל גַּבָּל שֶׁל בֵּית רַבִּי הָיָה, Abba Shaul was the dough kneader of Rabbi Yehuda HaNasi’s house). Still, the chains of gold of Shemot 28:14 are מִגְבָּלֹת, twisted / braided, so the root might carry this kneading meaning in Biblical Hebrew as well. Compare also גבב, to give a rounded shape, connecting kneading and border.
Chametz vs. Se’or
On Pesach, there are prohibitions concerning eating / owning two different substances. One is שְׂאֹר, leaven / sourdough, and the other is חָמֵץ, bread which has been leavened. Hebrew שְׂאֹר is Aramaic חֲמִיר, while חָמֵץ is חֲמִיעַ – see Onkelos’ translation of Shemot 13:71. Indeed, חֲמִיעַ is a cognate of חָמֵץ, since Hebrew ע often corresponds to Aramaic צ. I am not sure that this is carried out consistently in the Talmud, but this may be because scribes weren’t so sure of the difference. Searches for חמירא yield results but not חמיעא. Thus, in Pesachim 4a, Rav Nachman bar Yitzchak is asked whether it’s upon the landlord to search, דַּחֲמִירָא דִּידֵיהּ הוּא, for it’s his chametz. In Pesachim 5b, Rava instructed the residents of Mechoza בַּעִירוּ חֲמִירָא דִבְנֵי חֵילָא מִבָּתַּיְיכוּ, “remove the chametz of the soldiers from your house”. There’s a similar usage by Rava on 30a: Rava says that when they were in Rav Nachman’s house, when the seventh day of Pesach passed, he would say to buy חֲמִירָא of the (gentile) soldiers. Maybe some occurrences can indeed be interpreted as sourdough, since Jews require sourdough to make their own bread, and it’s faster and more certain than creating their own starter.
From a strictly textual perspective, the prohibition of ownership is stated almost entirely regarding sourdough, while the prohibition of eating is stated by leavened bread. Indeed, sourdough is not really edible. Thus, in Shemot 12:15, we are commanded to eat matzot, that is unleavened bread; indeed, on the first day – taken as the 14th of Nissan, prior to the onset of Pesach, we should remove (תַּשְׁבִּ֥יתוּ) sourdough (שְׂאֹ֖ר) from your houses, for anyone who eats leavened bread (חָמֵ֗ץ) shall be cut off. Shemot 12:19 states that for seven days, שְׂאֹר should not be found in your houses, because (כִּ֣י) whoever eats leavened bread (מַחְמֶ֗צֶת) shall be cut off. The next verse states that you shouldn’t eat anything leavened (כׇּל־מַחְמֶ֖צֶת) but only eat matza in your dwellings. In Shemot 13:7, one should eat matza for seven days, because leavened bread (חָמֵ֗ץ) shall not be seen and leaven (שְׂאֹ֖ר) shall not be seen in all your borders (בְּכׇל־גְּבֻלֶֽךָ). Note that this is the single instance where being seen (taken as ownership) refers to both substances. In Devarim 16:3, one should not eat any leavened bread (חָמֵ֔ץ) with the paschal offering. In the next verse, sourdough (שְׂאֹ֛ר) should not be seen in all your borders (בְּכָל־גְּבֻלְךָ֖).
Why shouldn’t we possess שְׂאֹר? Possibly, we could regard it as a gezeira, a decree to prevent something else, operating on a Biblical rather than Rabbinic level. Don’t own leaven, because you might use it to make chametz and you are not to eat chametz. Similarly, a king shouldn’t collect horses, because it might cause us to return to Egypt.
This is clearer for the prohibition of owning חָמֵ֗ץ itself, lest one eat it. There’s even an analogous Rabbinic directive (כעין דאורייתא תקון). If nullifying your chametz is effective, why bother removing chametz from your possession? Rava explains (Pesachim 6b) that it’s a decree lest you find a tasty loaf on Pesach and want it, thereby coming to own it.
Tashbitu and Gevul
As above, Shemot 12:15 commands removal of שְׂאֹ֖ר from our houses on the first day, because whoever eats חָמֵ֗ץ from the first to seventh day shall be cut off. The gemara (Pesachim 5a) grapples with the act of removal on the first day of Pesach, when the prohibition of owning already has begun. Therefore, this first occurrence of יוֹם הָרִאשׁ֔וֹן in the verse refers to the day prior to Pesach.
A controversial alternative might be that תַּשְׁבִּ֥יתוּ could mean “to cause to rest”, rather than to remove. You can cause sourdough to rest by not putting it in the משארת, the kneading bowl2. The Biblical degree aspect of the injunction is then clearer. From the first day and on (not the prior day), don’t knead along with leaven, because you are not supposed to eat leavened bread.
This could also be why sourdough shouldn’t be seen / found within your houses. That doesn’t necessarily mean that you shouldn’t own it, but that it won’t be seen / found in use, in your kneading bowls in your houses. However, what of Shemot 13:7 and Devarim 16:4, that sourdough shouldn’t be seen in all your borders? This clearly indicates ownership as the problem! To this, we can invoke the word sense of G-B-L known from post-Biblical Hebrew, to say that leaven shouldn’t be seen in any of your kneadings, בְּכָל־גְּבֻלְךָ֖, because that would produce chametz, which shouldn’t be eaten. Where Shemot 13:7 mentions both seeing chametz and se’or, this might indicate that we shouldn’t encounter chametz or se’or, the former by introducing the latter into our kneadings.
Every year, I see people uncomfortable with the idea of nullifying chametz after a good-faith effort to dispose of it, or that chametz crumbs under a kezayit / which you cannot access3 aren’t so problematic. That’s part of why I suggest the above ideas, providing a literalist contrast to Chazal’s understanding of the prohibition. It is הֵם אָמְרוּ וְהֵם אָמְרוּ – we are Pharisees, and trust in Chazal should encompass the full breadth of what they say works.
Artscroll’s translation of the kol chamira recitation renders כל חמירא וחמיעא דאיכא ברשותי as “all chametz or leaven that is in my possession”, but that’s reversed.
See Shemot 12:34, about how the Israelites took the not-yet chametz dough as well as מִשְׁאֲרֹתָ֛ם.
or indeed selling it and locking it away such that we don’t encounter it, as a legitimate cultural development rooted in Tosefta and perhaps parallel to an Elephantine Pesach, in how we practice and experience the prohibition. But, this would require elaboration of an entire other article.
גבול technically means "territory" in Tanach, with border as a secondary, though intimately related, meaning. But I like your take, too.
Do you have a source for your take on תשביתו? That might answer a difficulty with the passuk and still fit with the Gemara, in a way. A literal translation of the passuk might be "Seven days unleavened bread shall ye eat, but on the first day ye shall put sourdough to rest; for any eater of leavened bread, [and] cut off that person will be from Yisrael, from the first day until the seventh day." Most switch the order of the last two phrases so it reads "any eater of leavened bread from the first day until the seventh day, that person will be cut off" but maybe "for any...Yisrael" is parenthetic, explaining why sourdough is forbidden, and the main verse is "Seven days unleavened bread shall ye eat, but on the first day ye shall put sourdough to rest...from the first day until the seventh day." Now you have two "first days" and you can have one be the day before, and say אך divides and translate "Seven days unleavened bread shall ye eat, and for part of the first day ye shall put sourdough to rest...from the first day until the seventh day." Don't know if that fits the Gemara, though.
No source for tashbitu, other than a grammatical analysis (of causitive) and general meaning of $-B-T, like in tishbot, בחריש ובקציר תשבות. About gevul and border vs. territory, yes, someone was telling me that the other day.
Maybe it can be aligned with the gemara, but I'd suspect it would be a big kvetch. The way I envision it is that the rest begins on the first day, when you aren't using it, so the repetition need not be about the prior day.