Sterilize the jars: Fill your glass jars and lids with boiling water. Place in a pot, cover with 2 inches of boiling water, and boil for 15 minutes. Use tongs to remove and drain well.
Prepare the peppers: Wearing gloves, stem, wash, and chop the peppers. Remove seeds for a milder sauce or leave them in for extra heat.
Cook the limes: In a small pot, combine the diced limes with 1½ cups water. Bring to a boil and simmer for a few minutes, until the limes soften and change color.
Prep the veggies: While limes cook, peel and finely chop the garlic, dice the onion and daikon, and grate or dice the carrot.
Mix it all up: In a large bowl, combine the cooked limes (with the water), chopped peppers, garlic, onion, Murai, and carrot. Mix well.
Season and jar: Add salt to taste. Spoon mixture into your sterilized jar or bottle. Pour enough lime juice and/or vinegar to completely submerge the ingredients.
Ripen: Cover tightly and let sit at room temperature (or in the hot sun) for at least 24 hours. For deeper flavor, let ripen for 5 days to 1 week.
Storage: If using vinegar, store at room temperature for several months. If using lime juice, keep refrigerated and ensure everything stays submerged to prevent fermentation.