Paradigm Comparison: Standard Model vs. Selection-Stitch Model (SSM)

Paradigm Comparison: Standard Model vs. Selection-Stitch Model (SSM)

SSMTheory Group Updated: March 22, 2026

New entries from Triadic Orthogonal Calculus (TOC) marked with

τ

Parameter Standard Paradigm Selection-Stitch Model (SSM) SSM Reference

Foundations

Spacetime Foundation Continuous, innitely divisible smooth

manifold

Discrete, saturated FCC (

K=12

) tensor network built from

entanglement bonds

Geometric Phase Transitions

10.5281/zenodo.18727238

Speed of Light (

c

) Fundamental, unexplained empirical

constant

Geometric renormalization:

c = 4v

lattice

(structure tensor

eigenvalue

S

µν

= 4δ

µν

)

SSM Foundations 10.5281/zenodo.18752809

Gravitational

Constant (

G

N

)

Empirical constant; gravity resists

quantization

Derived from boundary entanglement entropy via

Ryu-Takayanagi:

G

N

=

2

3

L

2

/(4 ln 2) ≈ 0.997 l

2

P

SSM Foundations 10.5281/zenodo.18856833

The Planck Scale (

l

P

) Arbitrary mathematical UV cuto Physical lattice spacing:

L = 2

√

6 ln 2 l

P

≈ 1.84 l

P

SSM Foundations 10.5281/zenodo.18856833

Lorentz Invariance Assumed as continuous spacetime

symmetry

Exact, inherited from isometric holographic projection of

continuous 2D boundary via four

{111}

planes

Lorentz from Holography

10.5281/zenodo.18856415

τ

Triadic

Orthogonal

Calculus

No analogue Vacuum triad

τ = (4, 4, 4)

: unique decomposition of

K=12

shell

into 3 orthogonal 4-bond sheets. All derived:

|τ |=12

,

dim(τ )=3

,

τ

i

=4

,

|τ |+1=13

.

Matter as Entanglement Defect

10.5281/zenodo.18933667

Quantum Mechanics

Complex Wave

Mechanics (

i

)

Axiomatic; complex Hilbert space

assumed

Emergent;

i

maps between translational (

u

) and rotational (

θ

)

Cosserat modes:

ψ = u + iθ

Complex Structure from Cosserat

10.5281/zenodo.18645619

Schrödinger Equation Postulated as fundamental Derived from chiral Cosserat Lagrangian via Larmor frame

→

Klein-Gordon

→

non-relativistic limit

Schrödinger from Cosserat

10.5281/zenodo.18919140

Quantum

Decoherence

Ad-hoc thresholds (Diósi-Penrose with

free

R

0

)

Two-step structural threshold: soft 11.8

µ

g, hard 20.5

µ

g, ratio

=

√

3

SSM Foundations 10.5281/zenodo.18752809

Quantum Error

Correction

Surface codes, color codes on ad-hoc

lattices

[[192, 130, 3]]

CSS code native to FCC: 67% rate, weight-12

stabilizers

QEC on FCC Lattice 10.5281/zenodo.19078942

Particle Physics & Coupling Constants (TOC-derived)

τ

Proton-Electron

Mass Ratio (

m

p

/m

e

)

Unexplained empirical input

(1836.153)

(|τ |+1)|τ |

2

− dim(τ )|τ | = 13 × 144 − 36 = 1836

(0.008%)

Matter as Entanglement Defect

10.5281/zenodo.18933667

τ

Weinberg Angle

(

sin

2

θ

W

)

Empirical coupling ratio (

≈ 0.231

)

dim(τ )/(|τ |+1) = 3/13 = 0.2308

(0.19%)

Matter as Entanglement Defect

10.5281/zenodo.18933667

Fine Structure

Constant (

α

−1

)

Empirically measured (

≈ 137.036

)

2 × 4 × 17 + 1 = 137

from topological, algebraic, and resonant

dilution

Topological Origin of

α

10.5281/zenodo.18637451

τ

Tau Lepton Mass Empirical input (3477.15

m

e

)

2|τ | · |τ |

2

= 24 × 144 = 3456 m

e

(0.6%)

Entanglement Harmonics

10.5281/zenodo.18254503

τ

Kaon Mass (

K

0

) QCD-derived (973.8

m

e

)

|τ |

3

/2 + |τ |

2

− dim |τ | = 972 m

e

(0.2%)

Entanglement Harmonics

10.5281/zenodo.18254503

Parameter Standard Paradigm SSM SSM Reference

τ

Muon Mass Empirical input (206.7

m

e

)

|τ |

3

/(2τ

i

) − |τ | = 204 m

e

(1.3%)

Entanglement Harmonics

10.5281/zenodo.18254503

τ

Higgs Boson Mass Empirical input (125.25 GeV)

|τ |

5

m

e

= 248,832 m

e

≈ 127.15

GeV

(1.5%)

Entanglement Harmonics

10.5281/zenodo.18254503

τ

Natural UV Cuto Articial regularization required in

QFT

λ

max

= |τ | + τ

i

= 16

: strict upper band edge of FCC Laplacian Entanglement Harmonics

10.5281/zenodo.18254503

Fermion Doubling Requires Wilson terms to evade

Nielsen-Ninomiya

Evaded geometrically: non-bipartite FCC topology lifts all 15

doublers to

E ∼ 5/a

Fermion Chirality on FCC

10.5281/zenodo.18410364

Color Connement QCD ux tube dynamics 4 entanglement bonds through non-bipartite (triangular) faces;

topological protection

Matter as Entanglement Defect

10.5281/zenodo.18933667

τ

Three Colors SU(3) gauge symmetry (assumed)

dim(τ ) = 3

: three degenerate antisymmetric eigenvalues (spread

< 10

−9

)

Matter as Entanglement Defect

10.5281/zenodo.18933667

τ

Three Generations No explanation for 3 families

dim(τ ) = 3

: one generation per orthogonal sheet Micropolar Neutrinos 10.5281/zenodo.18503146

Fractional Charges Assigned (

+2/3

,

−1/3

)

O

h

∩ T

d

symmetry breaking:

1+3

entanglement asymmetry Matter as Entanglement Defect

10.5281/zenodo.18933667

Neutrino Sector (TOC-derived)

τ

Neutrino Mass (

m

3

) Empirical (

≲ 0.05

eV)

m

e

× Φ

3

×

p

π/4 = 0.0503

eV,

Φ = 1/[(|τ |+1)τ

2

i

] = 1/208

(exact)

Micropolar Neutrinos 10.5281/zenodo.18503146

τ

Atmospheric Angle

(

θ

23

)

Empirical (

49

◦

± 1.5

◦

)

θ

23

= 45

◦

from XY-sheet bisection

(

2σ

)

Micropolar Neutrinos 10.5281/zenodo.18503146

τ

Solar Angle

(

sin

2

θ

12

)

Empirical (

0.307 ± 0.013

)

sin

2

θ

12

= (1 − 3 sin

2

θ

13

)/(3(1 − sin

2

θ

13

)) = 0.319

(

1σ

)

Micropolar Neutrinos 10.5281/zenodo.18503146

τ

Reactor Angle

(

sin

2

θ

13

)

Empirical (

0.022 ± 0.001

)

sin

2

θ

13

= 1 − (τ

i

+1) arccos(τ

i

/|τ |)/(2π) = 0.020

(

2σ

)

Micropolar Neutrinos 10.5281/zenodo.18503146

τ

Mass Hierarchy TBD (JUNO) Normal (

m

3

≫ m

2

> m

1

): dimensional quenching

3 → 2 → 1

across sheets

Micropolar Neutrinos 10.5281/zenodo.18503146

τ

Neutrino Nature TBD (LEGEND) Dirac: curl on

C

3

faces forces single chirality;

ψ

ν

=

¯

ψ

ν

Micropolar Neutrinos 10.5281/zenodo.18503146

τ

CP Phase (

δ

CP

)

∼ −π/2

(T2K hint)

δ

CP

= −π/2

: orthogonal 3D twist against 2D boundary Micropolar Neutrinos 10.5281/zenodo.18503146

Dark Sector (TOC-derived)

Dark Matter Undiscovered particle (WIMPs,

axions)

Torsional entanglement disruption:

S

tors

= |τ | − τ

i

= 8

channels.

No particle needed.

Matter as Entanglement Defect

10.5281/zenodo.18933667

τ

DM/Baryon Ratio

(

Ω

DM

/Ω

b

)

Fitted to CMB (

≈ 5.36

)

9840/1836 = 5.3595

from torsional cascade

(0.09%)

Matter as Entanglement Defect

10.5281/zenodo.18933667

DM is Dark No explanation within

Λ

CDM Torsional modes (

|τ |−τ

i

= 8

) don't couple to EM sector Matter as Entanglement Defect

10.5281/zenodo.18933667

MOND Acceleration

(

a

0

)

Empirical (

1.2 × 10

−10

m/s

2

)

a

0

= cH

0

/(2π) ≈ 1.1 × 10

−10

m/s

2

from lattice horizon coupling DM as Lattice Torsion

10.5281/zenodo.18285444

τ

Dark Energy

(

Ω

Λ

) Cosmological constant;

10

120

vacuum

catastrophe

Spectral TOC Theorem:

Ω

Λ

= τ

i

|τ |/(2 dim(τ )|τ |)

+ Regge

correction

= 0.687

(0.3%)

Spectral Cosmic Energy

10.5281/zenodo.19158986

Parameter Standard Paradigm SSM SSM Reference

τ

DE physical

origin

Unknown Cosserat-inert Laplacian modes (

E

g

+T

2u

+A

1g

): vacuum

entanglement that matter cannot convert

Spectral Cosmic Energy

10.5281/zenodo.19158986

10

120

CC Suppression No known mechanism

Λ

bulk

= 0

(at sheets); holographic boundary scaling

(l

P

/R

H

)

2

≈ 10

−122

Unifying DE & Hubble Tension

10.5281/zenodo.18753874

Hubble Tension

5σ

discrepancy; no consensus Void-induced topological shift

ν

:

12 → 13

;

H

pred

0

= 67.4 × 13/12 ≈ 73.02

(0.03%)

Unifying DE & Hubble Tension

10.5281/zenodo.18753874

DE Equation of State

w = −1

(cosmological constant) Thawing:

w(z) ≈ −1 + (1/12)(1 + z)

−3

;

w

0

≈ −0.917

(consistent

with DESI)

Unifying DE & Hubble Tension

10.5281/zenodo.18753874

Cosmology & Early Universe

Cosmic Flatness

(

Ω

k

= 0

)

Fine-tuned initial condition Euler characteristic:

χ = V (1 − K/6) → 0

at

K=6

ground state Geometric Phase Transitions

10.5281/zenodo.18727238

Spectral Index (

n

s

) Fitted from slow-roll inaton

n

s

= 1 −

√

3 δ/(2π) = 0.9646

from Regge decit

(0.03%)

Geometric Phase Transitions

10.5281/zenodo.18727238

The Big Bang Simultaneous expansion from

singularity

Localized crystallization wave (

K=4 → K=12

) at

v

3D

= c

,

v

front

= ce

3

≈ 20c

The 1.37 Gyr Big Bang

10.5281/zenodo.18843626

CMB Hemispherical

Asymmetry

Unexplained (

A ≈ 0.07

)

A = e

−3

≈ 0.049

; within

0.8σ

of Planck (

0.066 ± 0.021

) CMB Asymmetry 10.5281/zenodo.18807053

CMB Large-Angle

Anomalies

Unexplained Geometric suppression

g(ℓ) = −2/(3ℓ)

; quadrupole ratio

C

SSM

2

/C

iso

2

= 7/9

CMB Large-Angle 10.5281/zenodo.18822137

Black Holes, Neutron Stars & Gravitational Waves

BH Singularities GR predicts innite density Cannot form; radial compression halted by

1/

√

3 L

metric wall BH Merger Dynamics 10.5281/zenodo.18411594

Neutron Star Radius NICER exceeds GW soft-EOS

R

obs

= R

EOS

× 13/12

: compressed core activates void as 13th

entity

NS Radius 10.5281/zenodo.18434917

Primordial BH

Lifetime

τ ∝ M

3

(Hawking)

τ ∝ M

2

(geometric evaporation); resolves gamma-ray constraints PBH Evaporation 10.5281/zenodo.18463661

τ

TOC Master Scorecard: All from

τ = (4, 4, 4)

, Zero Free Parameters

Observable TOC Expression Predicted Observed Match

m

p

/m

e

(|τ |+1)|τ |

2

− dim |τ |

1836 1836.15 0.008%

Ω

DM

/Ω

b

|τ |[(|τ |+1)(|τ |−τ

i

)

2

−|τ |]/1836

5.3595 5.364 0.09%

sin

2

θ

W

dim(τ )/(|τ |+1) 3/13 = 0.2308

0.2312 0.19%

Ω

Λ

(τ

i

|τ | + dim ·S

tors

· f)/(2 dim |τ |)

0.687 0.6847 0.3%

∆m

2

31

[m

e

Φ

3

p

π/4]

2

2.53 × 10

−3

2.51 × 10

−3

0.8%

M

τ

2|τ | · |τ |

2

3456

m

e

3477

m

e

0.6%

M

K

0

|τ |

3

/2 + |τ |

2

− dim |τ |

972

m

e

974

m

e

0.2%

M

µ

|τ |

3

/(2τ

i

) − |τ |

204

m

e

207

m

e

1.3%

H

0

(late)

67.4 × (|τ |+1)/|τ |

73.02 73.04 0.03%

n

s

1 −

√

3 δ/(2π)

0.9646 0.9649 0.03%

θ

23

XY-sheet bisection

45

◦

49

◦

2σ

sin

2

θ

12

Body-diagonal

→

sheet projection 0.319 0.307

1σ

sin

2

θ

13

Regge decit:

1 − (τ

i

+1) arccos(τ

i

/|τ |)/(2π)

0.020 0.022

2σ

N

colors

dim(τ )

3 3 exact

N

generations

dim(τ )

3 3 exact

Key SSM/TOC Constants:

K = 12

,

τ = (4, 4, 4)

,

|τ | = 12

,

dim(τ ) = 3

,

τ

i

= 4

,

S

tors

= 8

,

|τ |+1 = 13

,

|τ |

2

= 144

,

δ ≈ 0.128

rad,

L ≈ 1.84 l

P

.

Interactive 3D Visualizations:

Phase Timeline + CMB:

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

Entanglement Defect:

https://raghu91302.github.io/ssmtheory/ssm_

entanglement_defect.html

Hubble 13/12:

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

Quark Structure:

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

Big Bang Wavefront:

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

Neutron Star 13/12:

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