Experimental Proposals for Testing the Theory of Axiomatic Necessity (TNA): Immediate TNA Effect, Bridge Dissipation, and the Human Parallel Test

This paper proposes three experimental protocols designed to empirically validate the central claims of the Theory of Axiomatic Necessity (TNA). By investigating the boundary-driven dynamics between external constraints ($N_1$) and operational optimization ($N_0$), the proposed tests aim to establish a mathematical and phenomenological baseline that distinguishes human cognitive instantiation from artificial simulation. The first protocol, the Immediate TNA Effect, evaluates whether exogenous, non-derivable constraints produce discontinuous, non-Lipschitz operational reconfigurations that purely gradient-based systems cannot replicate. The second, Bridge Dissipation, measures the quantitative collapse of structural coherence and meaning when the coupling between execution and the phenomenological Selector is systematically interrupted. The third, the Human Parallel Test, exposes the asymmetry between human existential triggering and algorithmic loss minimization under conditions of unresolved multiplicity ($\Delta > 1$). Together, these protocols transform TNA into a falsifiable, cross-disciplinary research program spanning machine learning, cognitive neurodynamics, decision theory, and formal ontology.