The All-or-Nothing Potential as Instantiation of the Z/2Z Bundle: A Formal Derivation of Neuronal Threshold Quantisation

The action potential of excitable cells exhibits three quantitative features that the Hodgkin-Huxley model describes but does not derive as necessary properties: the discrete threshold V_threshold, the standardised amplitude of approximately 100 mV, and the absolute refractory period. This paper proposes that these three features are necessary consequences of the Z/2Z bundle structure governing the G→X→Q→N cycle — the same structure shown to govern topoisomerase quantisation in DNA (ΔLk = ±1, ±2) and spin quantisation in quantum mechanics (s_z = ±ℏ/2). Within this framework, the resting potential is the G pole (flat connection), depolarisation is operator X (Hopf bifurcation, integer residue condition), the action potential peak is Q (concentrated curvature), and the refractory period is N (return to G). Three verifiable predictions are generated, each testable against existing electrophysiological datasets without new experiments: universality of V_threshold within neuron classes as a structurally necessary property; maximum stimulation frequency 1/τ_refractory as the neuronal analogue of the telomeric instability threshold P3; and afterhyperpolarisation amplitude as a linear function of action potential amplitude through the return parameter ε of N. The connection between the refractory period as temporal quantisation and the Page-Wootters mechanism of emergent time is discussed.