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The aim is to provide a corrected proof of the inequality related to structural inertia in Information-Dynamic Theory.

March 16, 2026Open Access

Theorem M ≤ κ for Structural Inertia in Information-Dynamic Theory

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The aim is to provide a corrected proof of the inequality related to structural inertia in Information-Dynamic Theory.
Corrected proof of the inequality M(ω) ≤ κ.
Clarification of the equality condition.
Replaced earlier references with a direct spectral bound argument.
Confirmed that structural inertia is always bounded by the condition number.
Established a formal verification of the inequality.

Abstract

This note provides a corrected and formally verified proof of the inequality M(ω) ≤ κ for the structural inertia functional in Information-Dynamic Theory (IDT).The proof clarifies the equality condition and replaces the earlierCauchy–Schwarz reference with a direct spectral bound argument. The result establishes that structural inertia is always boundedby the condition number of the generalized eigenvalue problem Hv = λGv.

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Aleksei Sadovnikov (Sat,) studied this question.

www.synapsesocial.com/papers/69b79ea18166e15b153ac412 — DOI: https://doi.org/10.5281/zenodo.19014309

Theorem M ≤ κ for Structural Inertia in Information-Dynamic Theory

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