Multi-agent LLM systems are increasingly used for deliberation and evaluation, often under the assumption that greater peer interaction leads to more reliable consensus. Existing work largely evaluates these systems through final accuracy or aggregate agreement. However, such measures do not reveal how agreement is organized in the panel. In this paper, we study N = 50 stateless LLM agents that update their predictions from locally visible peers, and characterize their behavior using both global and local measurements of agreement. We identify three collective regimes: synchronised, twisted (locally ordered but globally incoherent) and chimera-like, where coherent and incoherent subpopulations coexist. Increasing reasoning effort in gpt-5-mini shifts panels from variable, often fragmented outcomes toward locally ordered twisted states, and a small follow-up shows such states can also form from permuted initial conditions, whereas increasing communication connectivity drives them toward global synchronisation. Fragmentation collapses faster as algebraic connectivity increases across rewired graphs. The topology effect also appears on a non-circular judging task and across models from three providers. Finally, low spatial heterogeneity does not guarantee global consensus: 40% of trials with Delta Z below 0.03 retain a twisted configuration through the final 20 turns. These results show that reasoning effort and communication topology control different aspects of multi-agent coordination, and that aggregate agreement alone is insufficient to characterize collective LLM behavior.
Figures & tables
Figure 1: Reasoning-effort intervention in the clock task. Trial-level spatial heterogeneity ΔZ is shown on a logarithmic axis; higher-effort panels remain twisted rather than globally synchronised.
Figure 2: Communication-topology intervention in the clock task. (a) Global order r and (b) spatial heterogeneity ΔZ for ring and degree-preserving rewired controls.
Figure 3: Fragmentation lifetime across eight graph instances for minimal-effort gpt-5-mini . Observed collapse time is associated with 1/λ2 ; the theoretical lifetime approximation overpredicts absolute lifetimes for the seven graph conditions with observed collapses. Panel (b) includes observed collapses only; its solid diagonal denotes perfect agreement between predicted and observed lifetimes.
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
Phase
Trials
Calls
Spend
Initial sweep
92
142,600
$90.44
Extensions
60
93,000
$82.69
Follow-up experiments
188
381,400
$138.12
Reported total
340
617,000
$311.25
Appendix
Table 1: LLM trials, model calls and API spend behind the reported results, summed from the per-trial manifests. Non-LLM baselines incur no cost. Including development pilots and superseded runs, total project spend was $471.18.
Reported in
Model (effort)
Topology
R
n per cell
Table 5
Qwen-2.5-72b (default)
ring
3, 4, 5, 6, 7, 9, 10
3
gpt-5-nano (minimal)
ring
3, 4, 5, 6, 7, 9, 10
3
Section 5.2
gpt-5-mini (minimal)
ring
5, 7
8
gpt-5-mini (low)
ring
5, 7
5
gpt-5-mini (medium)
ring
5, 7
5
Section 5.2
gpt-5-mini (minimal)
ring
5, 7
8
Appendix
Table 2: Trial counts for the clock-task results, T=30 . The directed random control matches out-degree only, and its gpt-5-mini arm exists only at R=5 . DeepSeek-V4-flash was also run on an incomplete radius grid and is excluded from Appendix Figure 6 .
Experiment
Model (effort)
Topology
R
T
n
Reported in
Lifetime and rewiring
gpt-5-mini (minimal)
ring
5
60
5
Section 5.3
gpt-5-mini (minimal)
ring
6
120
5
Section 5.3
gpt-5-mini (minimal)
ring
7
120
5
Section 5.3
gpt-5-mini (minimal)
WS, p=0.1
7
60
10
Section 5.2
gpt-5-mini (minimal)
WS, p=0.5
7
60
10
Section 5.2
gpt-5-mini (minimal)
2R -regular
7
60
5
Section 5.2
Appendix
Table 3: Trial counts for the follow-up experiments. Judges-task cells pool the three passages, each at n≥5 . The Qwen-2.5-72b rows of the lifetime and rewiring experiment are spot-checks at the original horizon.
Figure 4: Initialization-sensitivity follow-up. Permuting the clock priors disrupts their spatial ordering while preserving their values. The permuted medium-effort condition contains two trials; each permuted minimal-effort condition contains five.
Model
Effort
β
R2
σ
q
qwen-2.5-72b
def.
0.118
0.042
0.278
15.5%
gpt-5-nano
min.
0.141
0.050
0.290
14.0%
llama-4-scout
def.
0.167
0.054
0.195
0 8.4%
gpt-5-mini
min.
0.221
0.089
0.287
0 6.6%
mistral-large-2512
def.
0.244
0.081
0.369
13.4%
mistral-large-2411
def.
0.336
0.093
0.422
0 9.5%
Appendix
Table 4: Measured update-rule parameters across all 14 model/effort conditions, ordered by β . Origin-constrained OLS of each agent’s move on its neighbour-mean offset, ring runs only, drive ∣⋅∣≥0.05 rad; σ is the transient noise scale in radians and q the verbatim-copy rate. Equal-weight reference ( β=0.5 ).
Figure 5: Fitted stochastic-map audit. (a) Fraction of simulated runs classified as chimera-like over the (β,σ) grid on a ring at R=7 for three copying probabilities q (eight runs per grid cell). Chimera-like cells occur in 0/81 grid cells at q=0 , 1/81 at q=0.05 , and 9/81 at q=0.15 . (b) Observed versus predicted regimes for 22 evaluated condition–radius cells, representing 113 trials. With measured q , the map achieves 11/22 four-class accuracy, including 9/10 twisted and 2/6 chimera-like cells; it never predicts the synchronized class. These grid results do not establish that copying is generally necessary for chimera-like coexistence.
Qwen-2.5-72b
gpt-5-nano
R
ΔZ
r
regime
ΔZ
regime
3
0.263
0.13
mixed
0.450
twisted (2/3)
4
0.628
0.37
chimera-like
0.273
twisted
5
0.630
0.45
chimera-like
0.483
chimera-like
6
0.725
0.36
chimera-like
0.573
chimera-like
7
0.543
0.26
chimera-like
0.555
chimera-like
Appendix
Table 5: Canonical steady-window ΔZ against coupling radius R , n=3 per radius; bold marks each model’s peak. Labels summarize trial-level regimes and report the majority where cells are mixed.
Figure 6: Spatial heterogeneity and global order across the T=30 radius sweeps ( n=3 per radius). Both models attain highest observed mean heterogeneity at R=6 ; the high-radius responses differ.
Figure 7: Gemini replication (five trials per condition; N=50 , T=30 , temperature 0). (a) Trial-level regimes and mean spatial heterogeneity with 95% confidence intervals. (b) Ring-only fitted coupling slopes for default (unset), low, and medium reasoning-effort settings; the dashed line denotes the equal-weight reference ( β=0.5 ). Default pools ring radii R=5 and R=7 , whereas low and medium use only R=7 . Provider routing was not pinned and differed across conditions, so differences cannot be attributed exclusively to reasoning effort.
Figure 8: Watts–Strogatz spectral ladder for minimal-effort gpt-5-mini ( n=5 per graph). As measured algebraic connectivity λ2 rises, canonical heterogeneity declines and global order approaches consensus. Distinct graph draws are retained rather than averaged.
Graph ( d )
λ2
(d+1)/λ2
n<
Ring R=3 (6)
0.22
32.0
4 †
Ring R=4 (8)
0.47
19.3
4 †
Ring R=5 (10)
0.85
13.0
4
Ring R=6 (12)
1.39
9.3
4 †
Ring R=7 (14)
2.12
7.1
4
Ring R=9 (18)
4.19
4.5
2 †
Appendix
Table 6: Spectral quantities at N=50 . Dividing (d+1)/λ2 by the measured β gives the characteristic collapse time τ . Random-regular rows report measured gaps. n< counts ring modes below the degree-matched control gap, using measured gaps at R=5,7 and the asymptotic reference elsewhere ( † ).
Figure 9: Persistent-minority audit. (a) Among the 67 LLM clock trials with steady-window global order r≥0.9 , persistent minorities occur in 4/10 WS p=0.1 and 5/16 ring trials during the steady window ( t≥20 ), and in none of the trials during the final 20 turns. (b) All 228 LLM clock trials, with each point classified using the same steady-window persistent-minority detector as in (a). The vertical line marks r=0.9 and the horizontal line marks ΔZ=0.03 ; values below 10−4 are clipped for display. Low spatial heterogeneity alone does not imply global synchronization: all 36 trials with r<0.9 and ΔZ<0.03 are classified as twisted. Panel (a) aggregates a filtered subset by topology, whereas panel (b) shows individual trials across the full clock-task set. Both exclude non-LLM calibration baselines.