Resolution of the Neutron Star Radius and
Mass Anomalies via Geometric Vacuum
Saturation
Raghu Kulkarni
1,2,∗
1
Independent Researcher
2
CEO, IDrive Inc.
raghu@idrive.com
February 23, 2026
Abstract
Current observations of Neutron Stars present a conflict between Gravitational
Wave data (GW170817), which favors a compact “soft” Equation of State (R ≈
11.5 − 12.0 km), and X-ray Pulse Profiling (NICER), which reports systematically
larger radii (R ≈ 13 km). We propose that this “Radius Tension” is not a nuclear
physics contradiction, but a macroscopic geometric signature of the vacuum lat-
tice being compressed to its absolute 1/
√
3L kinematic exclusion limit (the metric
wall). Unlike black holes, where gravity completely overcomes the material and
shunts this stress orthogonally, neutron stars are supported by immense quantum
degeneracy pressure. This allows the star to physically support the maximum the-
oretical volumetric saturation strain of the K = 12 unit cell (ξ = 13/12 ≈ 1.0833).
This zero-parameter geometric boost accurately predicts the observed radius of PSR
J0030+0451 (12.0 km ×1.0833 ≈ 13.0 km) and the maximum mass saturation limit
of PSR J0952-0607 (2.17M
⊙
× 1.0833 ≈ 2.35M
⊙
), effectively resolving the tension
without invoking exotic matter.
1 Introduction
The study of supranuclear matter is currently deadlocked by two conflicting observational
datasets. On one hand, tidal deformability measurements from gravitational wave events
(e.g., GW170817) favor a “soft” Equation of State (EOS), predicting a standard neutron
star radius of R ≈ 11.5 − 12.0 km [1]. On the other hand, direct X-ray hotspot mapping
by the NICER mission consistently returns larger values, such as 13.02
+1.24
−1.06
km for PSR
J0030+0451 [2].
Concurrently, the discovery of the “Black Widow” pulsar (PSR J0952-0607) with a
mass of 2.35±0.17M
⊙
challenges the standard Tolman-Oppenheimer-Volkoff (TOV) limit
of ≈ 2.17M
⊙
for soft EOS models [3].
1
We propose that these are not separate anomalies. They are the structural conse-
quences of the Selection-Stitch Model (SSM) [4], which posits that under extreme gravi-
tational curvature, the K = 12 Face-Centered Cubic vacuum lattice is compressed against
an absolute 1/
√
3L kinematic exclusion limit. This mechanism has previously been iden-
tified in the remnant horizon of GW250114 [5], where the lack of material support forced
the geometric strain into a dampened orthogonal area inflation.
2 The Geometric Radius Boost
In the SSM, extreme nucleon density compresses the bulk of the star until the local
vacuum nodes strike the 1/
√
3L metric wall. At this absolute limit, the K = 12 unit cell
reaches its maximum theoretical volumetric saturation strain. Because the K = 12 unit
cell consists of 12 boundary nodes surrounding 1 central void, the maximum kinematic
strain ratio before total geometric failure is exactly ξ = 13/12.
Unlike a black hole event horizon—which is a vacuum boundary compressed by over-
whelming gravity that forces this strain orthogonally—a neutron star possesses a material
surface supported by immense quantum degeneracy pressure. This outward material pres-
sure fights against the gravitational compression, allowing the star to physically support
the full radial expansion of this topological strain. We therefore apply the unconstrained
Lattice Expansion Factor (ξ = 13/12) directly to the linear dimension of the star:
R
SSM
= R
EOS
×
13
12
≈ R
EOS
× 1.0833 (1)
Applying this to the baseline prediction of standard soft Equations of State (R
EOS
≈
12.0 km):
R
pred
≈ 12.0 km × 1.0833 = 13.0 km (2)
This prediction matches the central value of the NICER measurement for PSR J0030+0451
(13.02 km) with high precision [2], effectively bridging the gap between GW (bulk) and
X-ray (surface) data.
3 The Saturation Mass Limit
The stability of the star is defined by the maximum load the lattice can support before
local structural failure at the metric wall. Pushing the core to the absolute 1/
√
3L satu-
ration limit creates a macroscopic geometric resistance, increasing the effective stability
threshold by the exact same volumetric strain ratio (13/12):
M
SSM
max
≈ M
T OV
max
×
13
12
≈ M
T OV
max
× 1.0833 (3)
For a standard soft EOS limit of 2.17M
⊙
:
M
SSM
max
≈ 2.17M
⊙
× 1.0833 = 2.35M
⊙
(4)
This value perfectly matches the mass of the heaviest known neutron star, PSR J0952-
0607 (2.35M
⊙
) [3], suggesting that this object represents the literal “Lattice Saturation”
point of the macroscopic universe.
2
4 Conclusion
The SSM provides a unified geometric resolution to the Neutron Star Radius Tension and
the Hyper-massive Mass anomaly. The star represents a macroscopic volume of spacetime
driven to its absolute 1/
√
3L geometric saturation limit. Supported by internal degeneracy
pressure, this maximum vacuum strain (13/12) flawlessly explains why neutron stars
appear physically larger and structurally stronger than standard nuclear physics alone
predicts.
References
[1] B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration),
“GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspi-
ral,” Phys. Rev. Lett. 119, 161101 (2017).
[2] M. C. Miller et al., “PSR J0030+0451 Mass and Radius from NICER Data and
Implications for the Properties of Neutron Star Matter,” Astrophys. J. Lett. 887,
L24 (2019).
[3] R. W. Romani et al., “PSR J0952-0607: The Fastest and Heaviest Known Galactic
Neutron Star,” Astrophys. J. Lett. 934, L18 (2022).
[4] R. Kulkarni, “Constructive Verification of K=12 Lattice Saturation: Exploring Kine-
matic Consistency in the Selection-Stitch Model,” Preprint available at Zenodo:
https://doi.org/10.5281/zenodo.18294925 (2026).
[5] R. Kulkarni, “Geometric Horizon Inflation: A Universal Prediction for Binary Black
Hole Mergers,” Preprint available at Zenodo: https://doi.org/10.5281/zenodo.
18411594 (2026).
3
