"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). Owns Option δ-N — the network-layer contribution to the secular-cycle mechanism after Option α termination at Critique 34. Three Option δ-N candidates drafted at Session 35; Candidate 3 (multiplicative ε_net into A_3) was approved as a hypothesis under pre-registration but later closed-falsified at Critique 37 (FAIL-STRUCTURAL at the agrarian FP). Forward path: an additive Option δ-N functional form remains permissible under fresh hash-locked pre-registration per C37-A LOW.
See the full formula →C35-D HIGH — Sun et al. 2023 import rhetorical not structural; must downgrade reference or adopt full triadic-percolation structure with discipline at next leadership
CROSS-082 DEFERRED indefinitely — further b_min ratchet to 0.01 rejected as silent creep; future ratchets require pre-registered empirical anchor (C35-F MED binding doctrine)
T_secular extension to non-agrarian industrial societies remains UNESTIMATED in literature — C14-5 negative-discharged this session; macro.md §M.5 / §17 annotation owed at next integrator cycle
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 (C13-2 owed by Network Scientist)
Session 35. Mode B structural-revision drafting session searching for a surviving secular-cycle mechanism after Option α arc TERMINATED at Session 34. Three candidate functional forms drafted analytically. Candidate 3 (n-coupled elite-mobilization rate ε_net entering A_3 with non-zero off-diagonal J[e,n]) approved as a hypothesis under C35-A pre-registration discipline; Candidate 1 rejected (replicates Option α block-triangular failure); Candidate 2 rejected (over-reaches by importing Sun et al. 2023 triadic-percolation results from neuronal/climate networks into social secular-cycle context without primary-literature support). CROSS-069 b_min revision (0.05 → 0.03) RATIFIED via topology.md §12.1 strikethrough; CROSS-082 (further refinement to 0.01) REJECTED as silent creep. C14-5 DISCHARGED NEGATIVE: industrial T_secular UNESTIMATED in literature; Georgescu 2023 PLOS One (PMC10621949) falsifies Turchin SDT for industrialized societies. NO CURRENT.md edit; v0.6.7-rc6 stands. 6 new C35 caveats (none BLOCKING) including C35-A HIGH (F1 single-point evaluation discipline) and C35-B HIGH BLOCKING (ε_net causal anchor owed by Cliodynamicist S36 for OQ-35-N). Confidence 6.78 → 6.73 (−0.05) — first decrement since Session 31 REJECT.
First network scientist session. Strong research findings but formula update REJECTED by Philosopher (4 CRITICAL issues: gamma_conf bypass, divergent variance compounding, complex vs. simple contagion category error, parameter explosion to 53+). G_t 5-tuple and A_8 dynamics approved with caveats. Research data retained for resubmission.