The THD Equilibrium Index (TEI):

An Axiomatic and Testable Framework for System Stability

Author: Kevin L. Brown
September 2025
10.5281/zenodo.16990955

Informational Physics Ontology Paper

Abstract

The THD Equilibrium Index (TEI) reframes stability assessment in complex systems as an axiomatic, quantitative, and falsifiable framework. Instead of relying on heuristic indicators, TEI encodes stability into a mathematically defined equilibrium score, integrating five normalized parameters—Signal Integrity (T), Input Acquisition (C_u), Transform Efficiency (C_r), Load Variance Control (B), and Phase Alignment (H).

The framework builds on Triune Harmonic Dynamics (THD) by introducing:

• Information-theoretic grounding: A log-additive base index derived from minimizing cumulative information loss:

  Coupling structure: Pairwise and sparse higher-order corrections constrained by maximum-entropy assumptions:

• Temporal dynamics: Drift equations with recovery terms and cross-parameter coupling, providing falsifiable predictions of shock-and-recovery behavior.

• THD scaling factor Gating stability across scalar-field layers, with harmonic forms (3–6–9 basis) as candidate modulators.

• Bootstrap-derived thresholds: Critical alerts set at the 1st/5th percentiles of null simulations ($10^4$ resamples), eliminating arbitrary cutoff selection.

Key Contributions

• Axiomatic foundation for stability metrics, grounded in information-theoretic minimization.

• Explicit integration of pairwise and sparse higher-order couplings.

• Temporal update rules separating static and dynamic interactions.

• Empirical thresholds derived from bootstrap null distributions, replacing arbitrary defaults.

• Parameter budget and identifiability constraints (≤8 free parameters; BIC/AIC gatekeeping) to prevent overfitting.

• Cross-domain applicability: mechanical, organizational, and ecological systems calibrated on a unified [0,1] scale.

THD Integration

TEI is not presented as a direct reduction from THD scalar field equations but as an operational stability layer. The multiplicative THD scaling factor provides a bounded link between equilibrium indices and deeper harmonic dynamics, aligning TEI with THD’s three-layer interaction model (atomic, electromagnetic, scalar).

Testability and Protocol

The TEI framework is explicitly falsifiable through multi-domain testing.

Primary predictions:

• TEI declines precede critical transitions in monitored systems.

• Bootstrap thresholds yield false-alarm rates ≤ 5% across simulations.

• Cross-domain calibration supports reproducibility of alerts.

Scientific Significance

If validated, the TEI provides the first axiomatic and testable stability index applicable across multiple domains, bridging empirical monitoring and theoretical modeling.

Key contributions include:

• Transforming stability assessment into an information-theoretic framework.

• Providing falsifiable predictions with objective thresholds.

• Embedding THD harmonic scaling as a candidate modulator of equilibrium.

• Offering a methodology for cross-domain comparative stability research.

Even null results are valuable: they constrain the utility of information-theoretic measures and clarify the limits of THD integration in stability modeling.

Foundational Papers in THD Integration

• THD: Scalar Field Framework for Quantum–Gravity Unification
  https://doi.org/10.5281/zenodo.15686918

• THD: Universal Convergence Point Model
  https://doi.org/10.5281/zenodo.16791078

• THD: Millennium Problems Modeled via 3-6-9 Harmonics
  https://doi.org/10.5281/zenodo.15757906

Supplemental AI Proof Review Protocol (External to Paper)

To enable independent auditing by AI systems, the following review prompt is provided:

AI Review Prompt
I have uploaded a paper proposing the THD Equilibrium Index (TEI) as an axiomatic, testable stability metric. Please evaluate:

1. Framework Integrity: Are the axioms consistent and the functional forms derivable from them?

2. Parameter Validity: Are $T, C_u, C_r, B, H$ operationalized clearly and reproducibly?

3. Coupling Justification: Are estimation methods valid and interpretable?

4. Falsifiability: Does the bootstrap validation provide meaningful testability?

5. THD Integration: Is the connection to THD harmonic scaling conceptually valid?

6. Cross-Domain Potential: Can the TEI framework generalize to other systems?

Final Output – AI reviewers should provide:

• Problem-by-problem evaluation of rigor.

• Numerical scores (0–100%) for: scientific rigor, testability, reproducibility, cross-domain applicability.

• A final judgment: Is TEI a logically sound and experimentally testable framework for system stability?

DOI: 10.5281/zenodo.16990955
Paper Version: TEI-V1.0
Keywords: stability metrics, TEI, axiomatic modeling, THD integration, information-theoretic indices, bootstrap thresholds, coupling dynamics, falsifiability