EXP-PENT-SERIES

informative

Pentagon Topology — 5-Node Ring Hierarchy

2026-03-09 L3 level 4 runs

In plain language

Two agents: flat. Three: hierarchy. Four: flat again. Is it the odd number that matters? We test five agents — another odd number — to see if the pecking order returns. This time, no synthesizer roles that might blur the lines.

What we found

Pentagon: P2 (predicted mechanism) consistently refuted, but hierarchy emerges. Mechanism wrong, phenomenon real.

▶ Technical details

Research hypothesis

EXP-DYAD (N=2): flat (TR range 0.060). EXP-ASYM (N=3): hierarchy (TR range 0.444). EXP-QUAD (N=4): flat again (TR range 0.059). Non-monotonic pattern.

Two competing explanations: H1 (ODD/EVEN CYCLE): 3-cycle (odd) breaks symmetry → hierarchy. 4-cycle (even) restores symmetry → flat. 5-cycle (odd) should RESTORE hierarchy. H2 (N=3 UNIQUE): triad is Goldilocks — enough for asymmetry, too few for averaging. Any N>3 homogenizes regardless of parity. N=5 should remain flat.

CONFOUND FROM EXP-QUAD: Delta (narrative/synthesis) was an INTEGRATIVE persona that homogenized flow. This experiment uses only NON-integrative personas (no synthesis, no narrative weaving) to disentangle persona choice from topology.

If N=5 shows hierarchy (TR range > 0.15): H1 supported (odd/even mechanism). If N=5 is flat (TR range < 0.10): H2 supported OR density effect dominates parity.

Series (5 experiments)