Information Erasure Inside Action Quanta

Quantum states are operationally indistinguishable within finite-support Heisenberg cells. By coupling these de Gosson ``blobs'' into conjugate pairs of action quanta, we show that Landauer information erasure exhausts the available time and energy, causing the classical continuum to collapse into discrete configurations. Numerical results show that at low action, eigenstates are dense, but as action increases, they become sparse---consistent with the experimental difficulty in isolating pure states---stabilizing into the classical expectations of the correspondence principle. This model establishes an information-action constraint where finite capacity forces least action coarse-graining and the emergence of quantum mechanics.