OPEN QUESTION: "emergence threshold: at what N agents + interaction density do emergent properties appear?"
Known scaling curve (all non-integrative personas, round-robin): N=2: TR range 0.060 (flat, no hierarchy) N=3: TR range 0.444 (hierarchy emerges) N=4: TR range 0.509 (confirmed non-integrative only) N=5: TR range 0.528 (5 non-integrative personas)
Pattern: massive jump N=2→3, then diminishing returns (0.444 → 0.509 → 0.528). Growth from N=3→5 = +0.084. This looks like logarithmic or asymptotic saturation.
N=7 provides the CRITICAL 5th data point to distinguish: A) LOGARITHMIC: TR continues growing slowly (≈0.54-0.56) B) ASYMPTOTIC: TR saturates at ~0.53 (growth < 0.02 from N=5) C) PEAK + DECLINE: too many agents → averaging effect → TR decreases
At N=7, each agent speaks 7 times (49 rounds). Less per-agent data than N=5 (10 each) or N=3 (12 each). If hierarchy persists despite sparser individual data, the mechanism is robust.
Two new personas (Zeta, Eta) extend the cognitive axis without introducing integrative/synthesis roles (lesson from exp-quad confound).