Abstract
Large-scale structure formation is currently modeled via gravitational instability within a continuous
ΛCDM background. However, recent observations from JWST (early massive galaxies) and modern void
catalogs (BOSS) indicate that structure formation proceeds faster and more efficiently than gravitational
dynamics predicts. We propose a solution based on the **Selection-Stitch Model (SSM)**. By treating
baryonic matter as volumetric defects within a Face-Centered Cubic (FCC) vacuum lattice, we derive a
specific repulsive potential U
lat
arising from the energy cost of coordination mismatch (∆K). We constrain
the coupling constant α ≈ 9J directly from the lattice binding energy derived in prior SSM work on
the proton mass, eliminating free parameters. Using a calibrated N-Body simulation (N = 20, 000), we
demonstrate that this mechanism clears voids to < 2% density and accelerates halo formation by ∼ 30%,
offering a consistent geometric resolution to the ”Impossible Early Galaxy” problem.
INTRODUCTION
The standard model of cosmology, ΛCDM, posits that the ”Cosmic Web” emerged solely from
the gravitational collapse of initial density fluctuations [1]. While successful on large scales, this
paradigm faces tension on small scales. Two specific anomalies have become prominent:
1. **The Void Phenomenon:** Cosmic voids are observed to be emptier and sharper than
predicted by dark matter simulations. Surveys like BOSS and DES reveal ”super-voids”
that are significantly under-dense compared to ΛCDM expectations [2].
2. **The Early Galaxy Problem:** JWST has detected massive, fully formed galaxies at red-
shifts z > 10. Standard gravitational assembly requires more time to form such structures
[3].
These tensions suggest a secondary, non-gravitational mechanism assists gravity. We propose
**Geodesic Sorting**: a repulsive force arising from the thermodynamic relaxation of the vacuum
lattice itself.
THEORETICAL FRAMEWORK: THE BARYONIC DEFECT
Vacuum Topology
In the established SSM framework [4], the vacuum ground state is a Face-Centered Cubic (FCC)
lattice (K = 12). Cosmic Voids correspond to regions of topological strain where the coordination
number shifts to K = 13 (the ”Exposed” phase).
2
Derivation of the Lattice Force
To couple matter to this topology, we treat baryonic mass not as a passive tracer, but as a
**volumetric defect** in the lattice structure. This framework was established in our derivation
of the proton mass, where mass is defined as the displacement of lattice nodes [5]. Following
this logic, the total binding energy of a fundamental super-cell is proportional to its aggregate
coordination (N = 108). The potential energy U
lat
of a defect is the ”marginal cost” of disrupting
this local order. We approximate this as the total super-cell energy distributed over the local node
connectivity (N = 12):
α ≈
108
12
J = 9J (1)
where J is the stabilizer gap energy. This derivation connects the macro-scale lattice force directly
to the micro-scale binding energy, removing α as an arbitrary tunable parameter.
The resulting force acts to minimize the lattice energy by driving defects (matter) out of high-
energy K = 13 regions (voids) and into low-energy K = 12 regions (walls):
F
lattice
= −∇U
lat
≈ −9J∇K (2)
METHODOLOGY
Simulation Setup
We performed a particle-mesh N-Body simulation using a 100
3
Mpc box with **N
p
= 20, 000**
test masses to capture medium-scale filament morphology.
• **Dynamics:** The total force is
F
total
=
F
grav
+
F
lattice
.
• **Time Calibration:** We map simulation time steps to redshift z using the standard linear
growth factor D(t) ∝ a(t), calibrating T = 0 to z = 100 and the final step to z = 0.
Control vs. SSM
We ran two epochs: 1. **Control (ΛCDM):** α = 0. Pure Newtonian gravity. 2. **SSM:**
α = 9J (normalized units). Gravity + Geodesic Sorting.
3
RESULTS
Morphology and Void Clearing
As shown in Figure 1, the SSM run produces significantly sharper filaments. We quantified this
by calculating the mean radial density ρ(r) within 10 Mpc of void centers.
• **Control:** Voids retain ≈ 15% of the mean cosmic density (¯ρ).
• **SSM:** Voids are cleared to < 2% of ¯ρ.
FIG. 1: Geodesic Sorting. Left: Standard gravity produces diffuse structures (N = 20, 000).
Right: SSM lattice repulsion (derived from α ≈ 9J) actively clears voids and sharpens filaments,
creating distinct ”walls” absent in the control run. (Code available [6]).
Crucially, the SSM density profile (”bucket-shaped”) aligns with the deep void profiles observed
in the BOSS DR12 catalog [2], whereas the Control run produces ”V-shaped” profiles that are
shallower than observed data.
Acceleration of Structure Formation
We tracked the clustering rate by measuring the redshift z
50
at which 50% of particles collapse
into halos.
• **Control:** z
50
≈ 10.
4
• **SSM:** z
50
≈ 15.
**Implication:** The SSM accelerates structure formation by approximately 30%. This shift pro-
vides the necessary time window to explain the mature galaxies observed by JWST at z > 10,
which are currently challenging to explain via gravitational collapse alone.
CONCLUSION
We have integrated the ”Baryonic Defect” hypothesis into the Selection-Stitch Model to derive a
specific lattice force without free parameters. By constraining α ≈ 9J from geometric principles, we
show that vacuum thermodynamics actively sorts matter. This mechanism simultaneously resolves
the ”Void Phenomenon” and the ”Early Galaxy Problem,” demonstrating that the Hubble Tension,
Black Hole stability, and Cosmic Web morphology may all stem from the same underlying K = 12
vacuum geometry.
∗
raghu@idrive.com
[1] V. Springel et al., Nature 435, 629 (2005). https://doi.org/10.1038/nature03597
[2] S. Nadathur et al., *Monthly Notices of the Royal Astronomical Society* 490, 3 (2019). https://doi.
org/10.1093/mnras/stz2825
[3] I. Labb´e et al., Nature 616, 266 (2023). https://doi.org/10.1038/s41586-023-05786-2
[4] R. Kulkarni, ”The Selection-Stitch Model (SSM): Resolving the Hubble Tension,” Zenodo (2026). https:
//doi.org/10.5281/zenodo.18463515
[5] R. Kulkarni, ”Geometric Origin of the Proton Mass via Lattice Dislocation Energy,” Zenodo (2026).
https://doi.org/10.5281/zenodo.18253326
[6] R. Kulkarni, GitHub: ssmtheory (2026). https://github.com/raghu91302/ssmtheory/blob/main/
cosmic_simulation_filament.py
5
