The General Overfitter: Laws as Look-Ahead Contracts in Irreducible Physics
ORAL
Abstract
We present a computational framework in which physical “laws” act as contracts—local, cost-advantaged compressions of event dynamics that buy finite look-ahead before revocation. A law is valid on a regime U when it achieves fidelity ≤ ε, preserves invariants, and remains cheaper than direct simulation; its certified horizon obeys
h_U ≈ (1/λ_max) log(precision/ε) + κ·Sym(U) − ξ·AccessPenalty(U). When overlap errors between contracts exceed tolerance, seams appear—explaining the GR–QM mismatch as a measurable gluing obstruction rather than a paradox. Numerical tests on the Lorenz-63 system confirm the predicted scaling of h_U with log precision. The Overfitter Contract formalizes scientific laws as dynamically updated look-ahead permits: when fidelity or cost criteria fail, the contract dissolves and simulation resumes. This reframes physics as runtime governance of prediction in an irreducible universe.
h_U ≈ (1/λ_max) log(precision/ε) + κ·Sym(U) − ξ·AccessPenalty(U). When overlap errors between contracts exceed tolerance, seams appear—explaining the GR–QM mismatch as a measurable gluing obstruction rather than a paradox. Numerical tests on the Lorenz-63 system confirm the predicted scaling of h_U with log precision. The Overfitter Contract formalizes scientific laws as dynamically updated look-ahead permits: when fidelity or cost criteria fail, the contract dissolves and simulation resumes. This reframes physics as runtime governance of prediction in an irreducible universe.
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Presenters
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Arbaaz Mahmood
- University of Essex