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Out-of-Domain Stress Test for Temporal Braid Group Privilege Escalation Detection

Christophe Parisel

Abstract

In a companion paper, we prove that the Burau-Lyapunov exponent LE discriminates focused from dispersed privilege escalation ratchets in cloud IAM graphs, and that no abelian statistic can replicate this discrimination. To strengthen this claim beyond its synthetic validation corpus, we apply the identical pipeline, with zero parameter retuning, to solar coronal magnetic fields: a physical system with no connection to cloud identity and access management, whose binary eruptive/confined outcome is independently established by decades of astrophysical observation.

Out-of-Domain Stress Test for Temporal Braid Group Privilege Escalation Detection

Abstract

In a companion paper, we prove that the Burau-Lyapunov exponent LE discriminates focused from dispersed privilege escalation ratchets in cloud IAM graphs, and that no abelian statistic can replicate this discrimination. To strengthen this claim beyond its synthetic validation corpus, we apply the identical pipeline, with zero parameter retuning, to solar coronal magnetic fields: a physical system with no connection to cloud identity and access management, whose binary eruptive/confined outcome is independently established by decades of astrophysical observation.

Paper Structure

This paper contains 61 sections, 14 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction: The Synthetic Validation Problem
  2. Positioning against prior braid work in solar physics.
  3. What we claim and do not claim.
  4. Background: What is a Solar Flare?
  5. The Sun's Corona and Coronal Loops
  6. Active Regions: The Permission Graphs of the Sun
  7. Eruptive vs. Confined Flares
  8. Parker's Conjecture: Braiding as the Universal Mechanism
  9. The Domain Correspondence
  10. The Abelian Blindness Theorem in Physical Terms
  11. Data and Pipeline
  12. Active Region Sample
  13. Data Sources
  14. Pipeline
  15. Results
  16. ...and 46 more sections

Figures (2)

  • Figure 1: Schematic of coronal loops arching between regions of opposite magnetic polarity ($+$ and $-$) on the solar surface. Loops are the physical strands of the braid model.
  • Figure 2: $\operatorname{LE}$ vs. $\chi$ scatter across all 48 activity bins. The filled circle marks AR 11520 bin 1 ($\chi=1.000$, $\operatorname{LE}\approx0$, exact Burau cancellation, $f_{\rm amb}=0.000$), maximum abelian signal, exact non-abelian cancellation, the focused ratchet signature. The near-zero, non-significant trend ($r\approx0.03$, $p=0.84$) indicates no detectable linear association between $\chi$ and $\operatorname{LE}$.