Network-Layer Axiom Restatements (N1-N3)

Canonical definition

Network-Layer Axiom Restatements (N1, N2, N3). Three derivative restatements of canonical Axioms 5, 7, and 8, introduced in Appendix A.5.7 to specify the network layer of the three-layer formalism in the same way M1 through M5b specify the fast layer and B1 through B3 specify the slow layer. N1 Observability as Inter-Individual Channel (from Axiom 7 and the Observability Gradient): the exogenous input $m{obs}^{i}(t)$ at the population scale is a realised signal produced by the valuations and behaviours of other Individuals, weighted by the observability-gradient edge weight $\lambda{ij}$. N2 Evidence as Coupling-Mediated Input (from Axioms 5 and 8): coupling-mediated Evidence entering Individual $i$ is a function of the emitted Evidence propositions $Et^{j}$ of other Individuals $j$, weighted by the interpersonal coupling strength $\kappa{ij}$. N3 Non-Commutativity Propagation (from the From-Wang-to-Mechanism derivation): intrapersonal non-commutativity of measurement contexts entails interpersonal coupling as a derived consequence, making path-dependence of Belief trajectories the expected regime at the network scale and the Hilbert-space formalism of Quantum Epistemology the natural language for the network-layer Belief Register.