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June 3, 20260 citationsOpen Access

Vanishing-Order Structural Walls in Reduced Inverse Problems: Measurement Cost Governed by Sensitivity Vanishing Exponents

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HSHiroyuki ShioiriUniversity of Jaffna

Key Points

  • This research aims to establish a framework for understanding measurement costs related to structural walls in reduced inverse problems. It specifically addresses the effects of vanishing exponents on these costs.
  • Developed a local scaling framework for measurement cost related to structural walls.
  • Distinguished between finite walls with vanishing exponent β and asymptotic walls with γ.
  • Applied framework to investigate cost laws in reduced reheating reconstruction and dynamical-decoupling spectroscopy.
  • Identified distinct cost laws based on finite-distance resolution and horizon push-out related to structural walls.
  • Organized phenomena like fold diagnostics and cusp root scaling under the sensitivity-vanishing principle.
  • Demonstrated the utility of this framework in practical spectroscopy applications.

Abstract

This paper develops a local scaling framework for measurement cost near structural walls in reduced inverse problems. It separates finite walls, governed by a vanishing exponent β, from asymptotic walls, governed by γ, and derives the corresponding cost laws for finite-distance resolution and horizon push-out. The framework is applied to reduced reheating reconstruction and dynamical-decoupling spectroscopy. Fold diagnostics, cusp root scaling with singular-mode lift order, and DD fragility exponents are organized as instances of a common sensitivity-vanishing principle.

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Cite This Study

Hiroyuki Shioiri (2026) studied this question.

synapsesocial.com/papers/6a1fc530dee9eb8c0dce6970https://doi.org/10.5281/zenodo.20482519
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