This is a little different from what’s going on with 4 and 7, but numbers 1-10 all have special readings when you’re referring to the 1st-10th day of the month, like the 6th of May for example. 一日 becomes ついたち when you’re talking about the 1st day of the month, when in other contexts, いちにち is a perfectly valid reading for 一日. Meanwhile, the 11th of the month,十一日 (more commonly written 11日) is read as じゅういちにち, never じゅうついたち. いちにち is also correct for 一日 when it means simply “one day”. Honestly, there’s no end to special readings for numbers.
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Evidence is 証拠, 証明 is when you’re proving something. As another user said, its typically going to be with a する as 証明する in some conjugation. You often use 証拠 to 証明 something
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Thanks, appreciate the answers 
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@pembo @Redglare @izzyfizz96 @Vanilla
Thanks a lot everyone! I think I’ll find it A LOT easier to remember it as just ‘proof’ now, especially by keeping in mind it can be used to say, “to prove something”.
I had been struggling with it for a long time. My brain just thought of it as ‘evidence’ and I couldn’t seem to remember it as ‘proof’ at all, but this really helped 
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I visited a Catholic church during my trip to Japan, and it had a sign outside the door saying 土足でどうぞ. That means I enter with my shoes on, right?
Encountered signs throughout my trip with a dozen different variations in wording for shoes on and shoes off, but this was the first and only time I encountered this particular one.
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Lots of likes, but no actual response yet, so…
Yes! come in with your dirt feet/ outdoor shoes still on.
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I’m curious to know if there’s a reason why 北国 uses kun’yomi, but 南国 is in on’yomi? Or it just is?
Also, 焼き芋 mainly means baked sweet potato, right?
If I wanted to mean the white potatoes, would I say something like 焼きじゃが芋 instead…?
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Yep! A way you can check this out too regarding food stuff is by typing them into a google image search. I got this with 焼き芋
And I got this with 焼きジャガイモ
Although I’m not sure about the 南国 and 北国… I’ll leave that to a native, but it might also just be a case of きたぐに is easier to say than ほくごく
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and this is why I am not the one to answer the question 
In my head I know く and つ get turned into っ but it didn’t register. Oh well
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If a “white potato” is what I think it is, they just write baked potato in katakana
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Ah, got it, thanks! Forgot about the google images trick 
Of course, how did I forget that it also should be in katakana 
Thanks (again) everyone!
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ほっこく and きたぐに are two words sharing the same kanji. Fwiw idk if I’ve run into きたぐに before, but here’s some JP definitions:
From: 北国(ホッコク)とは？ 意味や使い方 - コトバンク
Idk why you’d use one or the other, in any given situation tho
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