OPEN QUESTION: "degree distribution operationalization: need SPECIFIC threshold — density < X% → F₀_excess > Y AND degree heterogeneity > Z → hierarchy. without this, mechanism = unfalsifiable."
CONTEXT: Cycle topology (exp-topo-cycle, N=1) KILLED hierarchy (TR 0.071 vs 0.444 baseline). Cycle = uniform degree (in=1, out=1 for all). Complete = uniform but higher (in=2, out=2). Both uniform degree topologies produce different hierarchy levels.
KEY QUESTION: Does ASYMMETRIC degree create hierarchy? Star topology introduces a HUB with higher in-degree than spokes.
- Hub (Alpha): reads Beta AND Gamma (in-degree=2)
- Spoke Beta: reads only Alpha (in-degree=1)
- Spoke Gamma: reads only Alpha (in-degree=1)
If hub becomes source → degree heterogeneity CAUSES hierarchy. If hub doesn't → hierarchy in complete topology is NOT from degree alone.
PREDICTIONS grounded in:
- Cycle result: uniform degree → flat (TR=0.071)
- Complete baseline: uniform-but-high degree → hierarchy (TR=0.444)
- Theory: hub has informational advantage (sees 2 streams), spokes are isolated from each other (convergence must transit through hub)
BASELINE DATA: Complete topology (exp-asym PERSONA_LIVE, N=9): TR_range = 0.444 ± 0.15 Cycle topology (exp-topo-cycle, N=1): TR_range = 0.071 Full decay complete (exp-forget, N=1): TR_range = 0.015
SECOND in designed-topology series: cycle (done) → star (this) → chain → complete (baseline).