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The membrane pump theory (MPT) attributes the resting membrane potential of neurons to ionic diffusion driven by transmembrane concentration gradients, maintained by the Na,K-ATPase. Despite decades of dominance, this model harbours fundamental thermodynamic, kinetic, and geometric inconsistencies that have remained unaddressed in mainstream biophysics. We present a systematic quantitative critique across five independent axes: (1)~the electrostatic force exceeds the diffusive force by $\sim$300-fold under physiological conditions; (2)~the peri-axonal space contains 10--100$\times$ fewer ions than required by channel-based models; (3)~the Na,K-ATPase carries an energy deficit of $\sim$26\% per cycle and operates 5000$\times$ too slowly to compensate measured leak fluxes; (4)~the Nernst and Goldman--Hodgkin--Katz equations are applied outside their domain of validity; and (5)~cell geometry invalidates plane-membrane approximations. In contrast, direct experimental evidence (Tamagawa experiment) demonstrates that a potential of $\approx -40$\,mV arises from fixed negative charges alone, without any ionic gradient. We formalise this result within a Poisson--Boltzmann/Grahame electrostatic framework, supplemented by Ling's ion adsorption model and Manoj's murburn concept, and obtain $\Delta\psi \approx -65$ to $-85$\,mV from first principles. Four specific experimental predictions distinguish the model from MPT.