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Temporal Decay and Half-Lives

Evidence about capability gets stale. A Python project from a long time ago is weaker evidence of current Python competence than a project from last month. The decay model encodes this.

The decay function

Bukti uses exponential half-life decay, the same functional form as radioactive decay. The weight of a VOI observed age_months ago is multiplied by:

decay(age_months, half_life_months) = 0.5 ^ (age_months / half_life_months)

At age = 0, the multiplier is 1.0 (full weight). At age = half_life, the multiplier is 0.5. At age = 2 × half_life, it is 0.25. The function asymptotically approaches zero but never reaches it.

There is no floor in the posterior

A naive scoring approach might floor the decay multiplier so that very old evidence still contributes a non-trivial amount. Bukti's posterior math does not impose such a floor. A floor is a UI-layer approximation that introduces systematic bias: it would mean that ten-year-old self-reports never fully decayed, keeping marginal evidence alive indefinitely.

The Arthur 1998 meta-analysis (53 studies, 189 effect sizes) found a mean Cohen d of −1.4 at >365 days of non-use for cognitive tasks. On a proportion-retained scale, this corresponds to retention of roughly 25–30% — more optimistic than a fixed floor over short-term retention, but for artificial cognitive tasks at 5–10 years of non-use the meta-analytic trend supports near-zero retention.

If the UI should communicate "this person may still have some residual capability," that is a display decision, not a scoring decision. The posterior math does not impose a floor.

Half-lives by cluster

Half-lives are tunable parameters per capability cluster, grounded in:

  • Arthur, Bennett, Stanush & McNelly (1998), "Factors That Influence Skill Decay and Retention," Human Performance 11(1) (53 studies, 189 effect sizes)
  • Wang, Berger & Burdick (2013) replication extending to cognitive-procedural skills
  • Driskell et al. (1992) on cognitive overlearning

The directional structure across clusters:

  • Foundational, overlearned skills (e.g. quantitative reasoning) retain longest.
  • Closed-loop physical / manual-kinesthetic skills retain longer than open-loop cognitive ones (Arthur 1998).
  • Mixed cognitive domains (e.g. pedagogy) sit in the middle.
  • Tool-heavy cognitive-procedural domains (software engineering, applied ML) decay faster as ecosystems turn over.
  • Regulation-dependent knowledge (medical, legal) decays with rule changes.
  • Pure cognitive recall (natural-language proficiency without active practice) decays fastest among knowledge-work skills.

Specific half-life values are tunable parameters held in private config and will be revised against pilot outcome data.

Practical examples

A software-engineering behavioral artifact observed at one half-life ago has a decay multiplier of 0.5. After two half-lives, it has a multiplier of 0.25. It still contributes to the posterior — it is not zeroed out — but its contribution is substantially smaller than a recent equivalent VOI.

A foundational quantitative skill decays on the same exponential curve, but with a much longer half-life: foundational skills decay, slowly.