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The phrase "a ledger that" is correct and usable in written English.
It can be used when referring to a specific type of ledger that has certain characteristics or functions.
Example: "We need to review a ledger that tracks all our financial transactions for the year."
Alternatives: "a record that" or "a document that".
Exact(18)
This item is a ledger that was reused as a scrapbook portfolio for 1960s items.
They register the names of the refugees in a ledger that was once an electric company's complaint book.
A public blockchain, like the one bitcoin uses, is a ledger that keeps time-stamped records of every transaction.
In testimony before the Senate, Mr. Singson produced a ledger that listed the names of recipients of payoffs.
"How long am I good for?" I asked the clerk as I signed the bottom row of a ledger that was cartoonishly huge.
Bitcoins, in contrast, are kept on a ledger that is maintained and updated by any user of Bitcoin who wants to help.
Similar(42)
A blockchain is a continuous ledger that keeps a permanent record of all transactions in chronological order.
Blockchain technology is a decentralized ledger that allows a shared set of computing systems to agree that a transaction between multiple parties is authentic.
The underlying technology Bitcoin uses is blockchain, which is defined as: "a decentralized ledger that keeps a record of all transactions that take place across a peer-to-peer network.
A blockchain is a digital ledger that records transactions or other data over time.
Blockchain is a digital ledger that provides a secure and public way of making and recording transactions, agreements and contracts; its best-known use is bitcoin, the virtual currency.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com