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RE: Why is median_history_price no longer the median of feed price? My investigation.

It is. But by design, if STEEM market cap is too low, SBD will jump off the 1$ peg. See https://steem.com/wp-content/uploads/2018/10/steem-whitepaper.pdf . quoting in section about sustainable debt ratios:

A rapid change in the value of STEEM can dramatically change the debt-to-ownership ratio. The blockchain
prevents the debt-to-ownership ratio from getting too high by reducing the amount of STEEM awarded
through SBD conversions if the debt level were to exceed 10%. If the amount of SBD debt ever exceeds
10% of the total STEEM market cap, the blockchain will automatically reduce the amount of STEEM
generated through conversions to a maximum of 10% of the market cap. This ensures that the blockchain
will never have higher than a 10% debt-to-ownership ratio.

Note that conversions still reduce the SBD supply, which in turn affect the debt ratio.