This note attempts to formalize a verification bound underlying weak subjectivity in proof-of-stake systems.
It introduces the concept of an observation horizon: the maximum duration for which an offline verifier can uniquely determine canonical history using protocol verification alone.
Under the standard long-range adversary model, the paper argues that proof-of-stake systems with signature-based finality and finite slashability admit a bounded observation horizon. Beyond this interval, multiple protocol-valid histories may become indistinguishable to an offline observer.
The intent is not to propose protocol changes, but to clarify the security parameter that weak subjectivity operationally addresses.
The full note is attached below. Comments and feedback are very welcome.
Observation_Horizon_Time_Bounded_Offline_Verifiability_in_Proof_of_Stake_Systems.pdf (222.5 KB)