The Tenson Limit Equation: Structural Incompleteness in Energy–Information Field Theories

In preceding work, energy–information dynamics were formulated in terms of minimal dis- crete units (Tenson particles) and their collective continuum description (the Tenson field). A natural expectation in such constructions is that an appropriate limiting procedure yields a closed and complete field equation. The present paper demonstrates that this expectation fails in a systematic and structural manner. We show that, in the limit of infinite resolution or infinite degrees of freedom, the Tenson field does not admit exact closure. Instead, a residual term emerges that cannot be eliminated without destroying the structural consistency of the theory. This residual contribution is neither a perturbative correction nor an artefact of approximation, but a necessary feature of the energy– information framework. We formulate this result as the Tenson limit equation, which explicitly exhibits the persis- tence of a non-vanishing residual in the continuum limit. The implications of this structural incompleteness for stability, observability, and subsequent quantization are briefly discussed, while detailed dynamical and thermodynamic analyses are deferred to future work.