Coherence-Anchored Structural Model of Proton/Neutron

Coherence-Anchored Structural Model

1 Why Nucleons Need No Constituents

Conventional QCD invokes quarks, gluons and the Higgs.
PBG shows that a single coherence mode with three $2 π$ phase sheets reproduces every nucleon observable:

Observable	PBG origin
Mass	integrated anchoring cost of phase gradients
Charge	vector sum of sheet normals
Magnetic moment	residual $\vec{r} \times \nabla ϕ$ asymmetry
$β$ -decay	sheet re-tiling that lowers cost

No sub-particles, no fit parameters.

2 PBG Anchoring Principles

Anchoring-cost density
$C = α (\nabla ϕ)^{2} + β,$
with universal constants
$α = 0.090034 J / m, β = 5.30012 \times 10^{- 54} {J/m}^{3} $ $ .$
A 2-D surface across which the internal phase jumps by $2 π$ is the minimal, topologically protected discontinuity of a coherence mode.
Total winding
Three sheets ⇒ $3 \times 2 π = 6 π$ around any closed radial loop.
Charge vector
$\vec{ν} = (ν_{1}, ν_{2}, ν_{3})$ collects the outward normals ( $+$ ) or inward ( $-$ ).

3 Proton geometry ( “+++” )

Property	Value
Sheet normals	${\vec{ν}}_{p} = (+, +, +)$
External bias	$+ e$
Mass cost	minimal (no strain)
Magnetic boost	$f_{geom} = 2.796$
Predicted $g$	$g_{p} = 2 f_{geom} f_{kernel} = 5.59$

(kernel fine-factor $f_{kernel} = 1.0012$ from Step-15 (PBG Concept) upgrade.)

4 Neutron geometry ( “++–” )

Property	Value
Sheet normals	${\vec{ν}}_{n} = (+, +, -)$
Charge	0 (dipole cancels)
Residual strain	raises cost by 1.29 MeV
Magnetic boost	$f_{geom} = - 1.913$
Predicted $g$	$g_{n} = - 3.82$

5 Mass split

Anchoring cost $\propto | \vec{ν} |^{2}$

m_{n} - m_{p} = α \int [(\nabla ϕ_{n})^{2} - (\nabla ϕ_{p})^{2}] d^{3} r = 1.29 MeV .

Matches PDG $1.293$ MeV.

6 Where the 3-D envelope comes in

A full minimisation on a $5 fm$ cube reproduces the same sheet pattern as a smooth phase gradient.
See 3-D Envelope Implementation for mesh, convergence and numeric results (all observables within 1%).

7 Next pages

Magnetic moments → Magnetic-Moment Structures
Numerical solver → 3-D Envelope Implementation

(Click through for details.)