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This research establishes a computable precision lower bound that delineates the limits of certification in computer-assisted proofs.

July 26, 2026Open Access

Certification Complexity: A Computable Precision Lower Bound for Computer-Assisted Proofs

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This research establishes a computable precision lower bound that delineates the limits of certification in computer-assisted proofs.
Developed a three-line impossibility theorem regarding interval Jacobians and approximate inverses.
Constructed upper and lower bounds using arbitrary-precision interval arithmetic to analyze near-singular families.
Examined a controlled nonlinear instance to differentiate between intrinsic and artifact influences on certification.
Identified that certification cost χ can rise without bound as κ approaches infinity, with specific values such as χ = 83 at κ ≈ 2⁸².
Showed fixed bounds for divergence family (≈419 bits) and multiplier family (≈665 bits) in the non-hyperbolic context.
Successfully certified calibration grounds for various dynamic systems, achieving notable accuracy in published enclosures.

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Randomized trial demonstrates computable precision limits in certification, suggesting implications for computational proofs.

Radoslav Lovecky (2026) studied this question.

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