TITLE:
Topology as a Test of ΛCDM: Evidence for a Near-One-Dimensional Cosmic Web from Join Distributions and Percolation
AUTHORS:
Stuart Alan Kauffman, Stuart Marongwe
KEYWORDS:
Cosmic Web Topology, Join Distributions, Percolation Analysis, Fractal Dimension, Dimensional Attractors, ΛCDM Discrepancy, Branching Process, Box-Counting Dimension, Matter-Void Symmetry, Scale-Free Scaling
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.12 No.4,
October
14,
2026
ABSTRACT: Standard analyses of large-scale cosmic structure rely primarily on two-point correlation functions
ξ(
r
)
and power spectra
P(
k
)
. Distinct networks can share identical two-point statistics while differing fundamentally in graph-theoretic properties. Here, we analyze the topology of the cosmic web using join distributions
P(
k
)
, which count independent connections (joins of order
k
) within the percolating filament graph and provide a direct, non-metric probe of effective dimensional organization
D
eff
. We apply join analysis to observational galaxy surveys spanning a broad range of redshifts
0.1≤z≤5.0
. Across five statistically independent sky regions (each 5003 Mpc3, ~106 galaxies), the observed
P(
k
)
are statistically uniform (
χ
2
/ν
<1.1
) and quantitatively fit by a Galton-Watson branching process with offspring probability generating function
f(
s
)=(
1−p
)+p
s
m
, mean offspring
m=1.054
, yielding
D
eff
=
log
2
m≈1.054
. In contrast, the LCDM model predicts and
N
-body simulations exhibit a broad
P(
k
)∝
k
−α
(
1.5≤α≤2.0
) with substantial high-order tails (
k=5 - 8
) from hierarchical halo mergers. These high-order joins are strongly suppressed (
>25σ
discrepancy (
χ
2
>1700
) that cannot be resolved by parameter tuning (
Ω
m
,
σ
8
) or baryonic feedback. Three further independent empirical probes reinforce this conclusion: i) Box-counting analyses across redshift slices spanning ~12 billion years yield effective dimension
D
eff
=−
lim
ϵ→0
logN(
ϵ
)/
logϵ
and density
ρ
converging gradually toward 1.0 from above,
D
eff
(
z
)≈1+0.02
(
1+z
)
0.1
. LCDM simulations do not exhibit comparable convergence. ii) Observational data show matter and voids percolate at the same threshold
ρ
c
≈0.20
ρ
¯
(within 2% - 3%), whereas LCDM generically exhibits separated thresholds
ρ
c
matter
≈0.22
ρ
¯
,
ρ
c
void
≈0.15
ρ
¯
. iii) Finally, matter and voids display identical scale-free power-law behavior
N(
>R
)∝
R
−γ
with
γ≈2.89
(
D=3−γ≈0.11
for void filling factor) in the scaling regime 1 R h−1, indicating phase symmetry consistent with critical phenomena.