Toward a Kinetic Limit on a Supplied Schrödinger Fibre: Conditions for Generator Suppression

A free kinetic limit is one possible ingredient of a reconstruction of spatial geometry, but its identification with part of a supplied Heisenberg representation does not reconstruct that geometry. We give a sufficient condition for nonnegative modulation energies to leave a kinetic Mosco limit unchanged: the kinetic forms must converge in a specified Hilbert-space comparison, and each finite-energy limit vector must admit one kinetic recovery sequence on which the modulation energy vanishes. An explicit discrete moment estimate keeps the energy normalisation visible. Neither this moment condition nor kinetic convergence is derived here from a Born–Infeld envelope. On any supplied Schrödinger fibre with nonzero central character, the resulting form is the free kinetic form, not the full harmonic-oscillator form, and cannot distinguish the fibre's central character. Separately, a supplied relative position-moment bound gives an elementwise kinetic lower bound; its admissible class is a cone and need not be a linear form domain. These results do not discharge the geometric lifting hypothesis or establish bridge non-obstruction. Interpretive outlook: the result specifies tests for a proposed discrete-to-continuum construction; a representation carrier, compatible recovery and the passage from a kinetic form to spatial geometry remain inputs to be constructed, rather than consequences of the formal identity.