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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
tinycore has WAY more functionality than OP is looking for. floppinux crams a stripped out but modern kernel and busybox onto a single floppy. tbh it's still a lot of bloat for what OP wants.
There is vi within busybox, heavily stripped down version, which you may further configure for size https://github.com/insane-adding-machines/busybox/blob/master/editors/vi.c
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