# Review and verification summary

## Reviewed version

Title: Protective Switching and Sharp Observation Margins in a Two-Node Ordinal-Sum System
Author: Brian Theory
Release: Research preprint, 8 November 2026
Source SHA-256: 3b326efa74180f7a5e1a57290eaebebd6d582c7b4b1bf70a3b377d5e6613bb38
PDF SHA-256: 270ce1f38483750d163b8bfb74293a1ca7ccb6aef3e99ef4811e19b35e273491

## Mathematical review outcome

A fresh internal adversarial AI review read the complete final source and the complete change record. It found no fatal issue, major issue, or required minor correction within the stated two-node model. Earlier favorable review was not used as a substitute for reading the final source.

The review checked the critical-basin proof, greedy comparison, fairness versus uniform infimum, exchange ordering and admissibility, initial-region restrictions, energy and margin transfer, recurring tail estimate, fixed-parameter logarithmic expansion, and exact rational obstruction. Independent symbolic/rational calculations reproduced the key identities and the printed counterexample without importing the supplied audit implementation.

The cited nilpotent-parabolic theorem, constrained linear-switching comparison, and monotone repeated-control comparison were checked within their stated scope. The text distinguishes inherited local theory from this model's schedule and margin conclusions. This was not an exhaustive novelty search or historical-priority certification.

## Reproducibility and production

- The packaged targeted verification script passes 111 assertions.
- The second packaged check independently reproduces key symbolic identities and printed rational constants.
- Both scripts were executed successfully from this package directory.
- The final nine-page PDF was compiled with installed MiKTeX using package installation disabled.
- The final second-pass log has no undefined references, actual LaTeX warnings, or overfull/underfull boxes.
- Every rendered page was visually inspected. No clipping, overlap, missing formula glyphs, or unreadable content was found.
- Printed and PDF-metadata bylines both read Brian Theory.

## Limits

This is an internally AI-reviewed research preprint, not external human peer review or formal proof verification. Historical priority and journal suitability remain unverified. Parameter/state hypotheses and nonuniform-limit qualifications in the manuscript are essential. Observation margins do not imply robustness to process disturbances. No claim is made that the sufficient global parameter range is maximal.