Within the framework of the axiomatic system of the stability ladder, this paper reduces the existence of neural coding to a geometric necessity arising from thetension between information conservation and local synaptic update. The core argument shows that if a neural system requires the discriminability of external stimuli (the effective information conservation axiom L0), and if its synaptic plasticityoperates only locally (the local update axiom L1), then a structure of quasi-stableclusters separated by a strictly positive information-geometric barrier must emergein the state space; this barrier is precisely the coding gap (the spectral stability axiom L2). Without such a gap, neural representations of different perceptual modeswould undergo irreversible mixing under noise and plastic perturbations, leadingto exponential decay of the decoding mutual information and thus violating information conservation. By constructing a coarse-grained topology of the neuralstate space without presupposing attractor basins or energy landscapes, this paperproves the positivity of the coding gap. On this basis, the storage capacity limit ofHopfield networks, the information bottleneck principle, and Barlow’s efficient coding hypothesis are reformulated respectively as the phase transition of gap closure,the variational realisation of gap maximisation, and the redundancy-minimisationexpression of gap geometry. This framework provides an ontological necessity argument for neural coding and offers a unified geometric foundation for explainingperceptual mixing phenomena in pathological conditions such as schizophrenia,epilepsy, and Alzheimer’s disease.