Humility Balance Equation (HBE): A Calibration Mechanism for Epistemic Confidence in Self-Auditing AI Systems

This release consolidates the canonical Humility Balance Equation (HBE v1.0) with the public structural clarifications introduced in Version 1.1, alongside a non-normative interpretive companion translating the framework into control theory, dynamical systems, and machine learning-adjacent terminology.

No modifications have been made to the underlying equation or theoretical structure. The additional materials serve to clarify parameter roles, invariants, system boundaries, and interpretive constraints, with particular emphasis on preserving the framework’s non-optimization and endogenous reflexivity principles. These documents are intended to support technical understanding while reducing the risk of premature reduction to reward shaping, loss functions, or training objectives.

The ML/Systems companion provides an accessible mapping of the HBE formalism into state-space, feedback control, and stability analysis perspectives. It is explicitly interpretive and does not prescribe implementation strategies, optimization targets, or numerical parameter values.

This work forms part of the Recursive Equilibrium mathematical framework, which unifies RBE, HBE, MAF, and TSC into a single stability formalism

This version therefore functions as a consolidation and clarification release, improving accessibility and reproducibility without altering the canonical theory.

Archival PDF versions of all materials have been included to ensure long-term reference stability and citation consistency.