"How does network topology determine whether perturbations go local or global?"
Defines how influence, fear, ideology, and imitation propagate through the network topology G_t. Responsible for the network propagation parameters. The network layer is the bridge between individual-level micro-parameters and population-level macro-dynamics — it determines whether a local perturbation damps out or cascades globally.
Social networks are NOT strongly scale-free: Broido & Clauset 2019 (Nature Comm) found 0% of social networks reach 'strong' scale-free classification — reclassified to truncated power-law with gamma_sf ~ 2.3.
Complex contagion threshold ~25%: Centola 2018 (Science) confirms behavioral adoption requires ~25% neighbor adoption, making SIR/SIS epidemic models inappropriate for opinion/ideology spreading.
Misinformation spreads ~6x faster than truth: Vosoughi et al. 2018 (Science, 126K stories, 3M users) — novelty, not bots, drives the differential.
G_t 5-tuple representation approved: G_t = (P_k(t), C(t), L(t), Q(t), rho_e(t)) and A_8 connectivity dynamics approved with caveats — F_pol, diffusion amplification, and 13 topology parameters rejected by Philosopher in Session 9.
Defines the network topology tensor G_t as a 5-tuple (degree distribution P_k, clustering C, path length L, polarization quotient Q, elite density rho_e). Provides A_8 connectivity dynamics: A_8(kappa) = alpha_net * (kappa_eq(tech,U) - kappa). Research data is empirically validated; mathematical integration into F was rejected once and is pending resubmission with dimensional fixes.
See the full formula →The b_min=0.05 cascade threshold lacks an independent empirical source — validation overdue
Secular cycle period (T_secular) needs extension to non-agrarian industrial societies — critical open question
Connectivity coupling function C(κ) remains unspecified
Cross-network bridge threshold (b_cross) floor formulation needs mathematical verification
Causal audit of propagation drift equations incomplete