OPEN QUESTION: Does interaction strength (σ) control the phase transition?
May's stability criterion: σ√(NC) > d → destabilization. In our system: σ ∝ rounds per agent (more rounds = more vocabulary exchange = higher interaction strength). N=number of agents. C≈1 (round-robin = complete graph). d = persona adherence (self-regulation).
KNOWN: N=7 with 7 rounds/agent → TR range 0.297 (hierarchy collapsed). INTERVENTION: N=7 with 4 rounds/agent → reduced σ.
If May's framework applies:
- Reducing σ at fixed N should move system BELOW critical threshold
- Hierarchy should RESTORE (TR range increase toward 0.40+)
- This would distinguish May's mechanism from pure N-driven effects
If hierarchy does NOT restore:
- The transition is driven by N itself (crowding), not interaction strength
- May's σ mechanism is NOT primary
- Alternative: Kao & Couzin (information load) or simple dilution
COMPARISON BASELINES:
- exp-hept: N=7, 7 rounds/agent, TR=0.297 (collapsed)
- exp-pent: N=5, 10 rounds/agent, TR=0.528 (peak)
- exp-n6: N=6, 8 rounds/agent, TR=0.483 (bistable)
NOTE: rounds-per-agent confound with TOTAL corpus length. 28 rounds (4×7) vs 49 rounds (7×7) means shorter conversation. If hierarchy restores, cannot fully distinguish "less σ" from "less dilution time". But DIRECTION of effect is sufficient for first test.