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Financial market prices are often driven by differences between expectations and outcomes. When a widely watched economic release diverges from the consensus forecast, asset prices can adjust sharply within minutes, which is why trading volume usually spikes around major data publications.

On-chain transaction fees depend largely on congestion. When many transactions are competing for limited block space, validators prioritize the ones offering higher fees, so the cost of inclusion can rise sharply during busy periods. Batching transfers, using layer-two networks, or simply waiting for quieter hours are common ways to keep costs down.

A cryptographic hash function maps an input of arbitrary length to an output of fixed length, and it is effectively one-way. Changing a single character in the input produces an entirely different output, an effect known as the avalanche property. This behaviour underpins file integrity checks, password storage, and the chaining of blocks inside a blockchain.

Cross-border payments have long suffered from slow settlement and opaque intermediary charges. A traditional wire may pass through several correspondent banks, each of which can deduct a fee, so the amount that finally arrives often differs from the amount that was sent.

Crypto wallets fall into two broad categories: custodial and non-custodial. A custodial wallet is operated by a service that holds the private keys on the user's behalf, which is convenient but requires trusting that operator. A non-custodial wallet returns control of the keys to the user, which removes counterparty risk but also means that a lost recovery phrase cannot be restored by anyone.