Structural Indeterminacy in Thermodynamic, Chiral, and Informational Contexts. A Unified Operational Framework Anchored in the I-G Corpus

This paper presents an operational framework extending the I-G (Gradient Indeterminacy) inequality to three distinct biological regimes: thermal homeostasis, chiral maintenance, and informational fidelity. In each regime, the conjugate-pair inequality $\Delta \cdot \dot{E} \geq \mathcal{C}(\Omega)$ admits two operational formulations---a gradient-field formulation in analogy with classical irreversible thermodynamics, and a margin-cost formulation foregrounding the homeostatic function. The three regimes are shown to share a common structural floor at the Landauer scale $k_B T \ln 2$, with experimental anchors in single-bit erasure, Maxwell's demonrealizations, and the thermodynamic uncertainty relation. We argue that this constitutes structural unification across the three regimes rather than three independent extensions of a common formalism, and we develop falsifiable predictions including cross-regime couplings whose experimental test discriminates between the two readings. The framework provides a structural language for biological multi-regime homeostasis at the cellular and organismal scales.