UI Mechanism Based Nobel Filter Criteria: UIO Unifies All Nobel Discoveries (2020–) via Force–Energy–Geometry–Curvature

Abstract

We establish the universality of the Unified Invariant (UI) Optimization Theoryas a unifying mathematical framework for Nobel Prize-winning mechanisms awardedduring 2020-2026.The UI framework is governed by the fundamental invariant identityf (Tη(x∗, y)) ≥ f (x∗), ∀y.characterized by four interdependent principles:(i) Invariant Identity: ............ f (Tη(x∗, y)) ≥ f (x∗), ∀y.(ii) Force as equilibrium: ....... ∇f (x∗) = 0,(iii) Energy as potential: ....... Φ(y) = f (y) − f (x∗) ≥ 0,(iv) Geometry as mapping: .... Tη(x, y) = x + η(y, x),We demonstrate that seminal Nobel contributions—including Auction Theory(2020), Natural Experiments and Causal Inference (2021), Financial Intermediation andBank Stability (2022), Gender Gap and Labor Dynamics (2023), Institutional GrowthTheory (2024), and Physics of Neural Networks and Generative Intelligence (2024)—areall canonical realizations of this single invariant identity. Each laureate’s mechanismcorresponds to a specific configuration of the Force-Energy-Geometry-Curvature tetrad.This paper provides the first rigorous usefulness proof for UI Optimization Theory,showing it functions as a Universal Nobel Filter. It unifies previously disjoint Nobeldiscoveries under one invariant optimization law and provides a predictive criterion forfuture Nobel-class mechanisms.