OPEN QUESTION: "cyclicity confound: sparse but highly cyclic networks may still prevent hierarchy. need to pre-screen BOTH density AND cycle fraction."
CONTEXT: All prior experiments use COMPLETE topology — every agent reads every other agent's contributions. Hierarchy (trophic structure) emerges reliably (exp-asym N=9, TR_range=0.444). But is hierarchy an artifact of complete visibility, or does it form even in restricted topologies?
DIRECTED CYCLE: A reads only C, B reads only A, C reads only B. Each agent has in-degree=1, out-degree=1 (uniform, no hubs). Information propagates transitively: A→B→C→A.
HYPOTHESIS: Cycle topology REDUCES hierarchy (TR_range) relative to complete topology because: 1. No agent can accumulate DIRECT positional advantage over all others 2. Influence is mediated — A affects C only through B 3. Uniform degree distribution prevents hub-formation
BUT hierarchy may persist partially because transitive influence creates temporal advantage: early vocabulary innovations propagate around the cycle, and the originator is always 1 step ahead.
BASELINE DATA: Complete topology (exp-asym PERSONA_LIVE, N=9): TR_range = 0.444 ± 0.15 Full decay complete (exp-forget, N=1): TR_range = 0.015
This is the FIRST of 4 designed topologies (cycle/star/chain/complete) for the TC analysis program. Cycle first because it directly tests cyclicity confound.