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How is wallet balance from unspent transactions in cryptography terms?

There is already a good almost complete answer here (but missing the cryptography explanation):
How is a wallet’s balance computed?

  1. Is a bitcoin wallets balance calculated on the client computer app? eg. Leger Live

  2. How is bitcoin wallet balance calculated cryptographically?

  • Does Ledger Live app check/compare each transaction+hash & transaction+signature hash like mempool nodes do?

  • Or does it only look at the unspent output addresses and check if they are children of wallet public key? If so how does it do this in cryptography terms?

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Crypto Market Analysis: October 18, 2021
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CryptoCurrencyAUDChange 1hChange 24hChange 7d
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Tether1.330 0.78 % 0.80 % 0.83 %
Cardano2.820 1.86 % 1.82 % 3.24 %
XRP1.440 2.37 % 1.48 % 5.19 %
--- --- --- ---
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USD Coin1.330 1.56 % 1.31 % 1.56 %
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