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June 3, 20260 citationsOpen Access

Residual Discrimination Mapping in Fixed-Gap Casimir Cavities: Distance-Scaling Fingerprints of Systematic and Yukawa-Type Residuals

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MFMassimiliano Falleri

Key Points

  • The research aims to establish a framework for analyzing residual deviations in Casimir cavity experiments, focusing on distance-dependent characteristics.
  • Defined residual asymmetry to identify deviations in fixed-gap measurements.
  • Constructed residual discrimination maps over a gap range of 50–300 nm.
  • Utilized a local fingerprint separability score for diagnostic classification of residual mechanisms.
  • Identified roughness-induced and Yukawa-type scaling residuals produce distinguishable signatures.
  • The 150–250 nm gap range was highlighted as most informative for Yukawa template discrimination.
  • Introduced multiple diagnostic gap zones to improve experimental outcome interpretations.

Abstract

This paper introduces residual discrimination mapping as an operational framework for interpreting residual deviations in fixed-gap Casimir cavity measurements. Building on the fixed-gap differential asymmetry metric A₍A,B₎(d), the work defines the residual asymmetry R₍A,B₎(d) = Aᵐᵉᵃˢ₍A,B₎(d) − Aᴸⁱᶠˢʰⁱᵗᶻ₍A,B₎(d) and treats it not as a single anomaly threshold, but as a distance-dependent diagnostic fingerprint. The framework classifies residual mechanisms into known systematic effects, geometric and spacer-related effects, material-state contributions, and candidate non-Lifshitz residuals. As an illustrative case study, the Au/doped-Si comparison is used to construct residual discrimination maps over the 50–300 nm gap range. Roughness-induced residuals, patch-potential residuals, and Yukawa-type scaling templates are shown to produce distinguishable multi-gap signatures. The paper further introduces a local fingerprint separability score Sᵢⱼ(d), a window-averaged separability measure Davg,ij, four diagnostic gap zones, and a residual interpretation workflow for classifying future experimental outcomes. The analysis identifies the 150–250 nm window as the most informative region for discriminating Yukawa 100–200 nm templates from systematic backgrounds under the illustrative assumptions used. The contribution is methodological and predictive. No experimental anomaly is claimed. The Yukawa curves are scaling templates, not claims of observed or allowed parameter values. Supplementary code and numerical data are included to reproduce the residual discrimination map, the optimal gap-window analysis, and the window-averaged fingerprint separability scores.

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Cite This Study

Massimiliano Falleri (2026) studied this question.

synapsesocial.com/papers/6a1fc76ddee9eb8c0dce850dhttps://doi.org/10.5281/zenodo.20491675
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