Late Universe Dynamics and Vacuum Geometry - Selection-Stitch Model (SSM)

Late-Universe Dynamics from Vacuum Geometry:

Unifying Dark Energy and the Hubble Tension

via a Discrete Topological Phase Transition

Raghu Kulkarni

SSMTheory Group, IDrive Inc., Calabasas, CA 91302, USA

raghu@idrive.com

April 2026

Abstract

Two stubborn problems sit at the heart of modern cosmology: the

120

-fold

gap between the predicted and observed vacuum energy, and the

5σ

Hubble

tension between early-universe (

≈ 67.4

km s

−1

Mpc

−1

) [1] and late-universe

(

≈ 73.0

km s

−1

Mpc

−1

) [2] measurements. We argue that both arise from one

geometric phase transition in a discrete Face-Centered Cubic (FCC) vacuum lat-

tice with coordination number

K = 12

. The saturated FCC bulk is provably at:

every interior hexagonal sheet satises the Euler characteristic constraint

χ = 0

K = 6

, meaning the bulk carries zero vacuum stress (

bulk

= 0

). Dark en-

ergy is therefore conned to the elastic bending strain of the outermost holographic

boundary shell, yielding a bare tension

Ω

Λ,bare

≈ 0.623

. Non-linear structure for-

mation in the late universe punches macroscopic voids through this lattice, break-

ing the local

symmetry and unlocking one extra expansion channelfrom 12

to 13 active nodes per unit cell. That single integer ratio amplies the CMB

baseline to

pred

= 67.4 × 13/12 ≈ 73.02

km s

−1

Mpc

−1

with no adjustable pa-

rameters, and simultaneously renormalizes the boundary tension to

Ω

≈ 0.675

The framework yields three parameter-free, falsiable predictions: (i) environmen-

tally dependent

(void-dominated sight-lines measure

∼73

, lament-dominated

sight-lines trend toward

∼67.4

km s

−1

Mpc

−1

); (ii) a thawing equation of state

w(z) ≈ −1 + (1/12)(1 + z)

−3

, consistent with recent DESI DR2 BAO evidence

for dynamical dark energy [6]; and (iii) the infrared vacuum energy from known

particle masses is structurally absent because particles are topological defects of the

lattice, not independent elds.

Keywords:

cosmological parameters, dark energy, Hubble tension, large-scale structure,

tensor networks, vacuum geometry

1 Introduction

CDM works remarkably well as a bookkeeping device for the large-scale universe. It

does not, however, explain its own parameters. Two have become genuine crises.

The

Cosmological Constant Problem

: quantum eld theory predicts a vacuum energy

density roughly

120

times larger than what drives the observed accelerated expansion

(

Ω

≈ 0.685

[1]) [3]. No convincing cancellation mechanism exists.

The

Hubble Tension

: Planck gives

≈ 67.4

km s

−1

Mpc

−1

[1], while SH0ES nds

73.04 ± 1.04

km s

−1

Mpc

−1

[2]a

5σ

gap. JWST TRGB lands at

69.8 ± 1.6

[4], sustain-

ing rather than resolving the tension [5]. Proposed xes introduce new free parameters

without clear physical motivation.

We take a dierent path. The vacuum is treated not as a featureless continuum, but as a

discrete crystalline lattice whose microstructure has macroscopic consequences. Within

the Selection-Stitch Model (SSM), the vacuum saturates into a

K = 12

Face-Centered

Cubic (FCC) lattice through geometric phase transitions whose observational imprints

include both the cosmological constant and the Hubble parameter.

The paper is self-contained. Section 2 derives the three phase transitions from rst

principles. Section 3 establishes the atness of the bulk and the Planck-scale lattice

parameters. Section 4 derives Lorentz invariance from the cuboctahedral bond geometry.

Section 5 computes the boundary bending stress as dark energy. Sections 67 derive the

Hubble tension resolution. Section 8 gives falsiable predictions.

Interactive visualizations.

Two WebGL applications explore the phase transitions

discussed here:



Early Universe

(

K = 6 → K = 4 → K = 12

https://raghu91302.github.io/ssmtheory/ssm_regge_deficit.html



Late Universe

(

ν = 12 → ν = 13

https://raghu91302.github.io/ssmtheory/ssm_hubble_13_12.html

A potential concernthat IR contributions from known particle masses (

∼ m

) would

regenerate the cosmological constant problem at

∼ 10

is addressed in Section 3.3:

particles are topological defects of the lattice, not independent elds, so their energies

are redistributed from bond rearrangements, not added to the vacuum energy.

2 The Discrete Vacuum: Three Phase Transitions

The SSM rests on the ideashared with several contemporary programmes [7, 8, 9]

that quantum entanglement is the fabric from which spacetime is built. Each bond in

the network is a Bell pair of fundamental length

. A Stitch operator

nucleates new

nodes wherever the local coordination falls below saturation, so macroscopic expansion

is the bookkeeping of entanglement maximization. This drives three sequential phase

transitions.

2.1 Phase I: the at hexagonal sheet (

K = 6

)

The Euler characteristic of a triangulated closed surface is

χ = V − E + F

. For a pure

triangulation with every vertex of valence

, this gives

χ = V (1 − K/6)

. At

K = 6

χ = 0

, the surface is a at torus or plane. Any triangulated surface with

K < 6

has

χ > 0

(positive curvature, like a sphere);

K > 6

gives

χ < 0

(hyperbolic). The Stitch

operator minimizes bending energy, so the ground state is

K = 6

: a at hexagonal sheet.

K = 6 ⇐⇒ χ = 0 ⇐⇒

zero intrinsic curvature (at)

(1)

Flatness is not an initial condition; it is a theorem of the topology.

2.2 Phase II: the tetrahedral foam (

K = 4

) and ination

Stochastic uctuations punch vertices out of the at sheet, spawning tetrahedra (

K =

). Regular tetrahedra cannot tile

: ve packed around a shared edge subtend only

5 × 70.53

◦

= 352.6

◦

, leaving a gap of

δ = 360

◦

− 352.6

◦

= 7.36

◦

≈ 0.1284

rad per shared

edge [11]. This is the Regge decit angle.

Every shared edge carries irreducible positive curvature. The Stitch operator nucleates

new nodes to close the gapsthat is ination. The decit angle enters the slow-roll

parameter as

ϵ = δ

/(4π

) ≈ 1.66 × 10

−3

, giving a scalar spectral index:

= 1 −6ϵ + 2η ≈ 1 −

√

3 δ

2π

≈ 0.9646.

(2)

The Planck 2018 constraint is

= 0.9649 ± 0.0042

[1]; our geometric prediction lies

within

0.07σ

of central.

2.3 Phase III: the FCC crystal (

K = 12

) and reheating

Once the node density is high enough, the foam crystallizes into the FCC lattice, the

unique densest sphere packing in three dimensions [12]. Each interior node achieves

cuboctahedral coordination:

K = 6

plane

+ 3

above

+ 3

below

= 12.

(3)

This decomposition is geometrically unique: the ABC stacking of hexagonal sheets at

inter-layer spacing

h =

2/3 L

(the regular tetrahedron altitude) is the only arrangement

achieving

K = 12

with equal bond lengths throughout. Decit angles vanish, curvature

drops to zero, and ination ends. The latent heat of crystallization (

∆Q = 4ϵ

per

bond, where

ϵ = ℏc/L

is the bond energy at the Planck scale) reheats the universe.

Setting

∆Q = k

reheat

gives

reheat

∼ ℏc/(k

L) ∼ 10

GeV for

L ∼ 1.84 l

(derived in

Section 3.2).

2.4 The Big Bang as topological resonance: a Diophantine proof

The phase transition from the

K = 4

tetrahedral foam to the

K = 12

FCC bulk is not

merely a densication. It is the unique algebraic solution for a at macroscopic universe,

as we now prove.

In Regge calculus [11], curvature is localized at hinges and measured by the decit angle

δ = 2π −

. Flatness requires

δ = 0

at every hinge. The dihedral angle of a regular

tetrahedron is

= arccos(1/3) ≈ 70.53

◦

. Five tetrahedra around an edge give

5θ

≈

352.6

◦

, leaving a permanent decit of

7.36

◦

: the foam is geometrically frustrated. The

natural complement is the regular octahedron with dihedral angle

= π −arccos(1/3) ≈

109.47

◦

. Let

and

be the integer counts of tetrahedra and octahedra meeting at a

hinge. Flatness requires:

+ n

= 2π.

(4)

Substituting

= π − θ

− n

) arccos(1/3) + n

π = 2π.

(5)

By Niven's theorem [10],

arccos(1/3)/π

is irrational:

cos(arccos(1/3)) = 1/3

is rational,

but the only rational

θ/π

with rational

cos θ

are

{0, 1/3, 1/2, 2/3, 1}

, none of which equal

arccos(1/3)/π ≈ 0.392

. Since the irrational part must vanish for integer

, n

− n

= 0 =⇒ n

= n

= 2.

(6)

The unique integer solution

= n

= 2

is veried:

2θ

+ 2θ

= 2π

exactly, giving

δ = 0

The only geometry where two tetrahedra and two octahedra meet at every edge is the

tetrahedral-octahedral honeycomb  the FCC lattice with

K = 12

[12].

The FCC lattice is therefore not an arbitrary packing choice; it is the unique algebraically

necessary ground state for a at discrete universe. The Big Bang is the moment of

topological resonance: the irrational decit of the tetrahedral foam is exactly cancelled

by the octahedral complement, locking the vacuum into the frustration-free, Lorentz-

invariant FCC crystal.

3 Flat Bulk and Zero Vacuum Stress

3.1 The atness theorem

Viewed along the

[111]

crystallographic axis, the

K = 12

FCC lattice decomposes into

hexagonal sheets. By Eq. (1), each interior sheet has

K = 6

and

χ = 0

: it carries zero

intrinsic curvature. The extrinsic curvature of an interior sheet is also zero: each sheet

lies in a plane, and adjacent sheets are parallel and equally spaced. Therefore:

bulk

= 0.

(7)

This is a geometric theorem, not a simulation result. The inter-sheet spacing follows from

the regular tetrahedron altitude:

d =

2/3 a ≈ 0.8165 a.

(8)

The

[[192, 130, 3]]

CSS code [24] built on this geometry has

-vector

, f

) =

(13, 36, 38)

per coordination cluster, conrming the cuboctahedral structure: 13 nodes,

36 edges (physical qubits), 38 faces (32 triangular stabilizers + 6 square faces). Any de-

parture from atness would break the stabilizer structure and destroy the code's distance

d = 3

; atness is therefore enforced by fault-tolerance requirements.

3.2 Planck-scale lattice parameters

Two characteristic length scales arise from independent physical conditions.

Bulk spacing.

The FCC lattice gives Newton's constant via the holographic Ryu-

Takayanagi relation: each bond carries one unit of entanglement entropy, and the en-

tanglement entropy of a region scales as its boundary area in Planck units. Setting the

lattice entanglement per bond equal to one ebit and requiring

= l

xes:

bulk

√

6 ln 2 l

≈ 1.84 l

(9)

The derivation uses the

K = 12

coordination and the Landauer energy

ϵ = kT ln 2

per

bond [23].

Boundary scale.

The cosmological horizon is not in equilibrium: it wraps a closed

spherical topology, and the extrinsic curvature

κ = H/c

forces the outermost lattice

shell into maximal close-packing. To see why, note that the extrinsic curvature of a

sphere of radius

= κ

= 1/R

, giving a bending stress per bond of

bend

∼

E κ

. As

R → R

(the Hubble radius), this stress grows until the lattice reaches the

maximum energy density at which nodes can still maintain mutual contactthe Planck

density

= c

/(ℏG

)

. The horizon must therefore be at Planck compression: any lower

density would reduce the bending stress below the saturation threshold, contradicting

the closed-topology boundary condition. Setting the lattice energy density equal to

at the boundary:

bdy

√

, a

bdy

≈ 0.77 l

(10)

The at bulk is at

bulk

≈ 1.84 l

(relaxed, zero stress); the compressed boundary is at

bdy

≈ 0.77 l

(Planck density, maximum bending stress). This distinction is essential:

dark energy is a property of the boundary, Newton's constant of the bulk.

3.3 Why particle masses do not regenerate the problem

Even with

bulk

= 0

, infrared contributions from known particle masses (

∼ m

/16π

)

would normally regenerate a cosmological constant at

∼ 10

times the observed value.

The resolution lies in the identity of particles within the lattice.

In the M/E/I framework [23], massive particles are topological defects of the

K = 12

latticesub-complexes of the cuboctahedral coordination cluster whose fault-tolerant

verication costs in the

[[192, 130, 3]]

CSS code reproduce the mass ratios of the electron,

muon, pion, proton, and neutron to

< 0.12%

. This identication eliminates the IR

problem through three mechanisms:

No independent zero-point modes.

The only vacuum degrees of freedom are the

K = 12

bonds per node. Formally, the vacuum Hamiltonian is

vac

⟨ij⟩

ϵ ˆn

, where

the sum runs over the

K/2 = 6

bonds per node and

ˆn

is the bond occupation operator.

The trace

Tr[e

−β

vac

]

is already fully saturated by these

K = 12

bond degrees of freedom;

there are no mathematically independent zero-point modes remaining to sum over. The

bonds

are

the vacuum.

Particle energy is redistributed, not additive.

Creating a particle rearranges bonds

from the at ground state into a defect topology. The energy cost

comes

from

the

lattice bonds, not in addition to them. There is no separate

polarization term because

the electron is not an independent eld.

The phonon analogy.

In a crystal, phonons do not add an independent zero-point en-

ergy on top of the cohesive energythey

are

the crystal's excitations. Similarly, particles

are FCC vacuum excitations; their energy is already in the bond structure. The at-bulk

theorem describes the ground state; particles are nite-energy excitations above it.

Together, the UV resolution (at bulk,

bulk

= 0

) and the IR resolution (particles as

defects) eliminate both components of the cosmological constant problem.

4 Lorentz Invariance from the Cuboctahedral Geome-

try

Before deriving dark energy, we establish that the

K = 12

cuboctahedral geometry is

Lorentz invariant. This is proven in [23] and reproduced here for completeness.

The

K = 12

FCC nearest-neighbour bond vectors are

∈

{(±1, ±1, 0), (±1, 0, ±1), (0, ±1, ±1)}/

√

. The rank-2 structure tensor

µν

≡

j=1

satises (by explicit enumeration of the 12 bond vectors):

µν

= 4 δ

µν

(11)

The odd-rank tensor

µνλ

≡

= 0

exactly (FCC lattice is centrosymmetric:

every bond

has a partner

−n

, so all odd-power sums vanish). This eliminates any

preferred direction and any linear

term in the dispersion relation.

For a scalar eld on the FCC lattice, expanding

(k) = κ

[1 −cos(k ·n

a)]

to second

order:

≈

κa

µν

= 2κa

|k|

(12)

giving

ω = c

lat

|k|

with

lat

= a

√

2κ

. The dispersion is exactly isotropic by Eq. (11)

not an approximation, but an algebraic identity. Corrections appear only at

O(k

) ∼

(E/M

)

. The two tensor identities (11) and

µνλ

= 0

, together with the isotropic linear

dispersion (12), are sucient for Lorentz boosts to emerge in the continuum limit [23].

Residual Lorentz violation is suppressed by

(E/M

)

, consistent with all current experi-

mental bounds [13].

The photon propagates on the 6 square faces of the cuboctahedron (the EM sector of

the

[[192, 130, 3]]

CSS code [24]). These 6 faces form 3 opposite pairs along the 3 cubic

axes, related by the octahedral symmetry group

, giving equal propagation speed in

all three spatial directions within each grain. Macroscopic isotropy is further guaranteed

by polycrystalline grain averaging.

5 Boundary Bending Stress as Dark Energy

5.1 Elastic constants of the lattice shell

While the interior is at, the outermost layer wraps the cosmological horizona closed

spherical surface. Each

K = 6

hexagonal sheet within that boundary behaves as a two-

dimensional triangular lattice under central-force interactions, for which the Poisson ratio

is exactly [14]:

(13)

Each Bell-pair bond at the compressed boundary carries energy

ϵ = E

= ℏc/l

(Planck

energy). A unit cell of volume

∼ a

bdy

contains

K/2 = 6

bonds (each shared between two

nodes), giving volumetric energy density:

bond

6 E

bdy

(14)

The elastic modulus at the Planck-compressed boundary scale is:

E = ρ

Planck

√

2 ℏc

4 a

bdy

(15)

This is the mechanical stiness of the discrete bond network at maximum compression

not a Casimir zero-point energy.

5.2 Flexural rigidity and curvature energy

Treating the boundary shell as a Kirchho-Love thin plate [15], its exural rigidity is:

D =

E d

12(1 − ν

)

Planck

√

(16)

Isotropic FLRW expansion forces the shell into a spherical topology. Both principal

extrinsic curvatures equal

κ = H/c

, giving bending energy per unit area:

bend

(κ

+ κ

)

= 2D(H/c)

(17)

5.3 Holographic projection into the bulk

The bending stress is localized on the 2D boundary. By the holographic principle [16,

17, 18], dividing the areal energy density by the stacking interval

d =

2/3 a

projects it

into the bulk volume:

bend

Planck

(18)

The dark energy fraction

Ω

Λ,bare

= ρ

bend

/ρ

crit

uses the critical density

crit

/(8πG)

Ω

Λ,bare

bend

crit

√

2 ℏc

32 a

8πG

(19)

Notice that

cancels exactly. Substituting the boundary area relation

= 2

−3/4

ℏG/c

(from Eq. 10), all of

, and

ℏ

also cancel identically. The result is a pure geometric

fraction:

Ω

Λ,bare

√

12(2

−3/4

)

3 × 2

3/4

≈ 0.623.

(20)

This

-independence is fundamental: the dark energy fraction does not depend on the

expansion rate. The

120

suppression relative to the naïve QFT expectation factorizes

into three geometric pieces:

(a/l

)

≈ 0.59

(lattice renormalization),

)

≈ 1.4 ×

−122

(holographic scaling), and the

1/8

plate-bending coecient.

6 The Hubble Tension as a Topological Phase Transi-

tion

6.1 Two states of the unit cell

The bare tension of Section 5 describes the pristine, fully saturated, early-universe vac-

uum. Consider a single cuboctahedral unit cell: 12 surface nodes around one central

node. In the saturated bulk, the central node sits at distance

√

from every face of its

coordination shellbelow the critical compression threshold for independent nucleation.

It is geometrically blocked. The number of active expansion channels is:

early

= 12.

(21)

When non-linear structure formation evacuates a large regiona cosmic voidthe lattice

fractures locally. Inside the void, the local

symmetry is broken. The central node,

no longer pinned at

√

, becomes an active zero-mode, free to couple to the Stitch

operator. The channel count becomes:

late

= 13.

(22)

6.2 Kinematic derivation via Fermi's golden rule

In a discrete volume-generating model, the macroscopic Hubble parameter

H = ˙a/a

proportional to the volumetric nucleation rate

. By Fermi's golden rule:

N→N+1

2π

ℏ

|⟨ψ

N+1

S|ψ

⟩|

ρ(E

(23)

The matrix element is a universal constant: each node is a vertex of the same lattice

bonded with the same energy

, so it cancels in the ratio. What remains is pure state-

counting:

late

early

ρ(E

)

late

ρ(E

)

early

(24)

6.3 Thermodynamic derivation via partition function

The same ratio follows from statistical mechanics. Write the canonical partition function

for a single cell evaluating volume nucleation:

Z =

−βE

. In the saturated bulk,

only the 12 boundary nodes contribute:

early

= 12 e

−βϵ

. In a void-exposed cell, the

freed central node adds one identical microstate:

late

= 13 e

−βϵ

. The Boltzmann factor

cancels (the unblocked central node is energetically identical to the 12 that were already

activethe distinction is purely kinematic):

late

early

late

early

(25)

6.4 The prediction

Applying the ratio to the Planck CMB baseline:

pred

= 67.4 ×

≈ 73.02

km s

−1

Mpc

−1

(26)

This matches the SH0ES measurement (

73.04 ± 1.04

[2]) to 0.03 per cent, with zero free

parameters and no modications to early-universe physics.

7 Renormalizing Dark Energy with the Same Integer

The bare tension

Ω

Λ,bare

≈ 0.623

treated the vacuum as a stack of independent 2D sheets.

But late-universe expansion engages the full 13-node bulk cluster. The same topological

correction that amplies

rescales the boundary stress:

Ω

= Ω

Λ,bare

≈ 0.623 ×1.083 ≈ 0.675.

(27)

The Planck 2018 value is

Ω

= 0.685 ± 0.007

[1]; our zero-parameter prediction sits

1.4σ

below central. Whether this gap is a shortcoming or an artefact of treating the void

fraction as a step function remains to be explored.

8 Predictions and Observational Tests

8.1 Environmental

anisotropy

The

13/12

boost is tied to macroscopic void exposure. Distance ladders through under-

dense voids probe the

ν = 13

state and should measure

≈ 73

km s

−1

Mpc

−1

. Lines

of sight along dense laments, where the vacuum remains shielded at

ν = 12

, should

trend toward the CMB baseline of 67.4. The intermediate JWST TRGB result (

≈

69.8

[4]) may reect sight-lines averaging both environments. The framework predicts a

strict positive correlation between locally measured

and the void fraction along the

calibration path.

=12: central node BLOCKED

(a) Topological Phase Transition

=12 (bulk) =13 (void)

Planck CMB

(early)

SH0ES

(late)

Prediction

13/12×67.4

H (km s ¹ Mpc ¹)

73.02

73.04

67.4

(b) H Amplification: 13/12 Ratio

Zero free parameters

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Redshift z

1.00

0.98

0.96

0.94

0.92

0.90

w(z)

DESI DR2

deviation

0.917

Consistent with DESI DR2 BAO

(

) = 1 +

(1 +

)

CDM (w=-1)

Observable Prediction Observed

H (late) 73.02 km/s/Mpc 73.04±1.04 0.03%

0.675 0.685±0.007 1.4

w 0.917 0.9 (DESI) consistent

_ ,bare

0.623

n_s (early)

0.9646 0.9649±0.0042 <0.1

(d) Parameter-Free Geometric Predictions

(zero adjustable parameters)

=13

void

Late-Universe Dynamics from Vacuum Geometry

Dark Energy + Hubble Tension from One Topological Phase Transition

Figure 1:

Unifying Dark Energy and the Hubble Tension.

(a) The topological

phase transition from

ν = 12

(saturated bulk) to

ν = 13

(void exposure) as the cen-

tral node unlocks. (b) The

13/12

amplication maps the Planck CMB baseline to the

SH0ES measurement. (c) The void fraction growth produces a thawing equation of state

(

≈ −0.917

), consistent with DESI DR2 BAO data [6]. (d) Summary of parameter-free

predictions.

8.2 A thawing equation of state

The cosmic void fraction grows as

η(z) ∝ (1 + z)

−3

, giving a redshift-dependent equation

of state:

w(z) ≈ −1 +

(1 + z)

−3

(28)

z = 0

≈ −0.917

(thawing dark energy). As

z → ∞

w → −1

(stable cosmological

constant at early times). The recent DESI DR2 BAO analysis [6] nds

≃ 3σ

deviation

from

CDM at

z ≤ 0.3

, consistent with this prediction.

8.3 BBN and early-universe consistency

During nucleosynthesis, the radiation-dominated universe is conformally invariant (Ricci

scalar

R = 0

). The lattice scales isotropically without accumulating transverse strain,

so the bending stress is absent. It activates only when conformal symmetry breaks at

matter domination, synchronizing with

CDM's timeline for dark energy activation [19].

9 Discussion

9.1 Relation to other discrete spacetime programmes

The SSM shares territory with Regge calculus [11], causal dynamical triangulations [20],

causal set theory [21], and the spacetime quasicrystal of Boyle and Mygdalas [22]. The

critical dierence is dynamical: most discrete approaches select a lattice by mathematical

elegance; the SSM derives the

K = 12

FCC lattice as the thermodynamic endpoint of

entanglement-driven phase transitions, with each intermediate phase yielding falsiable

observational imprints.

9.2 Limitations

The lattice spacingPlanck length relation (

√

2/4 l

) is self-consistent but ultimately

rests on the empirical value of

. The

13/12

channel-counting has been derived from

two independent statistical-mechanics routes but has not been conrmed by a full high-

resolution lattice simulation of void formation.

The IR vacuum energy argument (Section 3.3) depends on the identication of particles

as topological lattice defects. This identication is supported by the mass ratios of the

ve lightest non-strange particles being reproduced to

< 0.12%

[23], but has not been

extended to strange or heavy quarks, and a rigorous proof that lattice defect energies

cannot contribute vacuum polarization terms remains open.

10 Conclusions

The Cosmological Constant Problem and the Hubble Tension are two faces of one coin:

the structural limits of a discrete

K = 12

vacuum lattice. The topologically at bulk

(

bulk

= 0

, proven from the Euler characteristic constraint) eliminates the

120

over-

shoot. The identication of particles as topological defects [23] eliminates the

contribution. Dark energy is conned to the holographic boundary shell.

Non-linear void formation triggers a macroscopic phase transition from 12 to 13 ac-

tive expansion channels, simultaneously resolving the

5σ

Hubble tension (

pred

73.02

km s

−1

Mpc

−1

, matching SH0ES to 0.03%) and renormalizing the boundary stress

(

Ω

≈ 0.675

, within

1.4σ

of Planck).

Three rigid, parameter-free, falsiable predictions follow: environmental

anisotropy

correlated with void fraction; a thawing dark energy equation of state consistent with

DESI DR2; and structural absence of IR vacuum energy contributions. These are directly

testable with Euclid, DESI, and Rubin Observatory LSST.

Declarations

Conict of interest.

The author declares provisional patent applications related

to quantum error correction on the FCC lattice (U.S. Provisional Application Nos.

64/008,236; 64/008,866; 64/014,145; 64/014,153; 64/015,757; 64/029,144).

Funding.

This work was supported internally by IDrive Inc. No external funding was

received.

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