Information TheoryComputational LimitsPrediction
The Information-Theoretic No-Script Theorem
Recursent Research•Abstract
We establish an information-theoretic bound on the predictive closure of observers embedded in finite computational environments. Under four minimal premises—(i) finite classical storage within the accessible domain, (ii) finite cumulative computational throughput, (iii) a positive innovation rate at observational resolution r, and (iv) reflexive coupling between observation and disclosure—no embedded predictor can encode or compute unboundedly precise future trajectories.
Prediction TheoryOperational LimitsPhysical Systems
The Budgeted Universal Prediction Horizon Principle
Recursent Research•Abstract
We present the Budgeted Universal Prediction Horizon (UPH) as an operational corollary of the Information-Theoretic No-Script framework. For a physically embedded predictor with initial memory B (bits) and side-information inflow C (bits per unit step), the available predictive information is A_T(B,C)=B+CT (bits over T steps). The required predictive information R_T(·) is induced by the scoring loss (log-loss, exact identification, or process-level rate–distortion). The useful horizon T is the crossing where R_T ≈ A_T.