The taproot annex is an optional field in the witness structure of segwit v1 (taproot) inputs that currently has no defined purpose. If an annex is present, any taproot and tapscript signatures must commit to its value.
As of the implementation and activation of taproot, the annex was reserved for future upgrades. Transactions containing an annex were not relayed or mined by default by Bitcoin Core. There have been several ideas for using the annex, as well as at least one attempt to define an extensible data structure for the field.
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