1. Beyond Centralized Datastores
In a conventional client-server architecture (e.g., PostgreSQL or cloud databases), state validity is dictated by a single organization holding administrative credentials. If the root administrator is compromised, or the hosting server suffers a failure, the entire system is vulnerable.
A public blockchain distributes copies of the full state machine to thousands of independent physical nodes globally. Each node executes identical rules to independently verify every state transition.
You do not trust what a remote server reports; your local node re-executes cryptographic proofs to verify truth.
2. State Machine Transitions
Mathematically, a blockchain can be defined as a formal state machine: S_{t+1} = apply(S_t, Block_t). If a proposed block contains even a single invalid signature or an attempted double-spend, every honest node rejects the entire block.