Deterministic tracing follows explicit ledger relationships; probabilistic tracing estimates relationships from patterns and contextual evidence.
Deterministic examples
A Bitcoin input spending a named output, a direct address transfer, or a bridge message naming a destination creates an explicit relationship in the recorded data.
Probabilistic examples
Amount matching, timing, change-output heuristics, behavioral similarity, and wallet clustering support conclusions with varying confidence.
Attribution is another layer
Even an explicit transaction edge does not automatically establish the legal identity of the address owner. Off-chain evidence may be necessary.
Why wording matters
Privacy content should say “can be associated” or explain the evidence rather than turn every analytic estimate into certainty.
How to read the evidence
Tracing conclusions should identify their evidence and confidence. An explicit spend, transfer, event, or message is stronger than a match based only on time or amount. Address attribution is another step beyond proving a transaction relationship. When several weaker signals agree, an association can become persuasive without becoming mathematically certain. This distinction prevents both exaggerated privacy promises and exaggerated claims about what a public ledger alone proves.