← back to timeline

EXP-N6

artifact

Hexad Scaling — Locating the Inverted-U Peak at N=6

2026-03-10 L3 level paper3 4 runs $0.02
new
premortem
mock
real
metrics
analyze
review
krit
done

In plain language

Hierarchy peaks at 4-5 agents; at 7 it already drops. But is the drop sharp or gradual? Six agents — the missing point on the curve. If hierarchy still holds at 6, the cutoff is sharp; if it already drops — gradual.

What we found

No predictions scored

Predictions we made before running

0/5 confirmed

Technical details

Research hypothesis

N-SCALING INVERTED U: The trophic hierarchy curve peaks at N=4-5 then declines. Known data points (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 (hierarchy with non-integrative only) N=5: TR range = 0.528 (peak observed so far) N=7: TR range = 0.297 (sharp decline — middle crowding effect)

GAP: N=6 is the critical missing data point. The decline from N=5 (0.528) to N=7 (0.297) is -0.231. Where does the decline begin?

Three competing hypotheses: H1 (CLIFF): Decline is abrupt between N=6 and N=7. N=6 still near peak (TR > 0.450). The middle-crowding mechanism only kicks in at N=7+. H2 (GRADUAL): Decline starts at N=6. TR ≈ 0.350-0.450. The decline is approximately linear from N=5→N=7. H3 (EARLY DECLINE): Peak is at N=4, and N=5 was already declining but masked by stochastic variance. N=6 continues decline (TR < 0.350).

CONFOUND CONTROL: 4 rotations (0-3) to control for position effects. Position > persona is the strongest confirmed confound (EXP-ENGINEER-REPL SD=0.057 across rotations). With N=6, the effect of speaking position on hierarchy measurement must be averaged out.

EVEN/ODD PARITY: N=6 is even. The original exp-quad (N=4, even) was flat (TR=0.059), but that was confounded by an integrative persona. exp-quad2 (N=4, non-integrative) showed TR=0.509 — so even N CAN produce hierarchy with non-integrative personas. N=6 tests whether even-number suppression reappears at larger N.

MECHANISM: At N=7, the "middle crowding" effect compressed 5 of 7 agents into TR range 0.393-0.524. At N=6, do 4 of 6 agents crowd the middle? If so, crowding is progressive (more agents → more crowding → lower TR range).

Experimental setup

Type: simple

Condition Parameters
HEX_LIVE persona: PERSONA, interaction: LIVE, n_agents: 6, note: 6 non-integrative personas. Direct comparison: exp-dyad(N=2), exp-asym(N=3), exp-quad2(N=4), exp-pent(N=5), exp-hept(N=7).

Factors: n_agents (6) × persona_type (non_integrative)

Parameters

n_agents
6
n_rounds
48
n_runs_per_condition
4
model
gemini-2.5-flash-lite
temperature
0.9
scheduler
round_robin

Trophic Ratios by Condition

Mean trophic ratio per agent across runs. Error bars = ±1 std dev. Higher TR = more upstream (exporter).