It has already sat the month being "put up"
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I hate to sound like the preserving police, but, yes, I would absolutely throw away the jar. I am overly cautious in these situations and because eggplant and garlic are both low acid (high pH) foods, the potential for botulism is increased when too much air remains in the jar. The recipe is very specific about liquid covering the food and removing air bubbles. Pitch the jar and try again. Work deliberately, tamping down the eggplant as the jar is filled, then run a chopstick or plastic knife (metal could chip the glass) around the perimeter of the jar and through the food, to remove all air bubbles. Top off with additional liquid and carefully wipe the rim of the jar before capping. Check the jars every day or so.
They barely need effort, in fact.
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