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June 3, 2026Open Access

Scalar Fragility Loci and Observable Horizons in Single-Ratio Spectral Sensitivity

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Authors

HSHiroyuki Shioiri

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Overview

Randomized trial examines spectral sensitivity impacts on observability, suggesting thresholds for measurement design.

Key Points

  • This paper investigates how inverse spectral reconstruction fails through the concepts of genuine collapse and apparent flattening.
  • Analyzed the spectral family S(ω) = Aω^α + B using scale-independent ratio observables.
  • Derived the Jacobian of the ratio map with respect to (α, ρ) and related it to the Fisher information matrix.
  • Developed criteria for optimal probe-frequency selection based on the fragility locus.
  • Identified that information loss occurs primarily through apparent flattening, with no genuine-collapse locus at finite parameter values.
  • Determined that singular value decays as O(ρ^−1) off the fragility locus and accelerates to O(ρ^−2) on it.
  • Demonstrated that reducing observational noise expands the observable horizon without altering the fragility locus.

Cite This Study

Hiroyuki Shioiri (2026) studied this question.

synapsesocial.com/papers/6a1fc530dee9eb8c0dce6918https://doi.org/10.5281/zenodo.20497137
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Genuine Collapse, Apparent Flattening, and Observable Horizons in Inverse Spectral Reconstruction2026
  2. 2Multi-Ratio Identifiability and Local Completeness in Dynamical-Decoupling Spectroscopy2026
  3. 3Inverse Geometry and Identifiability of Protocol Ratios in Dynamical-Decoupling Spectroscopy2026
  4. 4Sensitivity Hierarchy and Observable Horizons in Reduced Reheating Geometry2026
  5. 5Unified Collapse Geometry of Reduced Observation Maps: Dual-Limit Structure Across Reheating Reconstruction and Dynamical-Decoupling Spectroscopya2026