OPEN QUESTION: "emergence threshold: at what N agents + interaction density do emergent properties appear?"
CONTEXT: Star topology at N=3 (exp-topo-star) confirmed hub-as-SINK:
- Alpha (hub, in-degree=2): TR=0.409 (lowest), E/I=0.69, Red=1.24 (highest)
- Hub absorbs redundant info from both spokes
- VP=0.243 (highest of all topologies — hub amplifies convergence)
KEY QUESTION: Does increasing fan-in (N=5, hub in-degree=4) AMPLIFY these effects? Three competing hypotheses: (A) LINEAR scaling: hub-as-sink deepens proportionally (4 input sources → ~2× redundancy) (B) THRESHOLD/SATURATION: 4 inputs overwhelm hub → convergence collapses or hierarchy inverts (hub can't absorb, starts generating from overload) (C) EMERGENT: new dynamics appear at N=5 that don't exist at N=3 — spoke cliques, intermediate hierarchy levels, hub fragmentation
BASELINE DATA: Star N=3 (exp-topo-star, N=1): TR_range=0.141, VP=0.243, C=0.778, RP=0.072 Complete N=3 (exp-asym, N=9): TR_range=0.444, VP=0.075, C=0.344, RP=0.147 Complete N=5 (exp-pent, N=1): available for comparison
GROUNDING: Gershenson E/S/C framework — complexity (C) at intermediate coupling. Star N=5 increases coupling for hub only. Does C peak or plateau?