Trust Decay

Borrowed from physics, the half-life defines the time required for a signal's weight to reduce to 50% of its original value. A citation half-life of 90 days means a link from 3 months ago carries half the authority of one posted today. This parameter is domain-specific: financial fraud signals may have a half-life of hours, while academic citations may span years.

The most common mathematical implementation uses an exponential decay function: W(t) = W₀ * e^(-λt), where λ is the decay constant. This ensures a smooth, continuous reduction in weight rather than abrupt drops. The decay rate λ is inversely proportional to the half-life: λ = ln(2) / t₁/₂. Exponential decay is memoryless, meaning the rate of decay is constant regardless of the signal's age.

Not all systems require smooth exponential curves. Linear decay reduces weight at a constant rate until it reaches zero at a cutoff point. Step decay applies discrete drops at predefined intervals—for example, reducing weight by 25% every 30 days. These simpler models are computationally cheaper and easier to audit but introduce discontinuities that can be exploited if the interval boundaries are known.

A sophisticated trust system applies heterogeneous decay rates based on signal type. A verified security audit may decay slowly over 365 days, while a social media sentiment spike decays within 48 hours. This requires a decay rate registry mapping each signal class to its empirically derived half-life. Misalignment—applying a slow decay to a volatile signal—is a common source of score inflation.

Decay functions encode a deliberate recency bias—the assumption that newer information is more predictive. Over-aggressive decay creates instability, where scores oscillate wildly with each new data point. Under-aggressive decay produces trust inertia, where a once-authoritative entity retains high scores despite current malpractice. Calibration requires A/B testing decay parameters against a ground-truth dataset of known trustworthy and untrustworthy entities.

Some signals are designated as decay-resistant or decay-proof. A cryptographic identity verification or a permanently recorded legal judgment may retain full weight indefinitely. These anchors prevent a malicious actor from simply waiting out a decay window to reset their trust score. The anchor ratio—the proportion of non-decaying to decaying signals—must be carefully balanced to maintain responsiveness while preventing reset attacks.