---
paper_id: PAPER_964
title: "3D MUGE Magnetar Simulation"
session: 215
date: 2026-04-12
author: "Daniel T. Murphy"
status: production
cvw: "v2.0.0"
tags: [AGN, GW, spin-down, SCm, MUGE, neutron-star, buoyancy, phonon]
sm_anchor: "CVW v2.0.0 — G6 SM Anchor Gate compliant"
---

# PAPER_964: 3D MUGE Magnetar Simulation

**Author:** Daniel T. Murphy — Star Magic / UQFF Framework
**Date:** 2026-04-12
**Session:** 215
**Source:** muge_{magnetar\_3d\_sim}.py (MUGEMagnetar3DSim)
**Calculator:** MUGEMagnetar3DSimCalc (CP4 #548)
**CVW:** v2.0.0 compliant

---

## Abstract

We construct a 3D MUGE magnetar simulation with three layers: (1) SCm superconducting core with radial BCS gap $\Delta(r) = \Delta_0 (1 - (r/R)^2)$; (2) Abrikosov-type magnetic vortex tubes at $B > B_\text{crit} = 4.4 \times 10^{13}$ T; (3) 26-state phonon resonance shells at $R_n = R_\text{NS}(1 + 0.05n)$.

---

## 1. SCm Core

$$\Delta(r) = \Delta_0 \left(1 - \frac{r^2}{R_\text{core}^2}\right), \quad r < R_\text{core}$$

## 2. Magnetic Vortex Tubes

$$n_v = \frac{B}{\Phi_0}, \quad \Phi_0 = \frac{h}{2e} \approx 2.068 \times 10^{-15} \text{ Wb}$$

## 3. Phonon Resonance Shells

$$R_n = R_\text{NS} (1 + 0.05n), \quad E_n = E_0 (2\pi)^{n/3} S_{26}$$

---

## References

1. Murphy, D.T. — Star Magic UQFF Framework (2024-2026)
2. PAPER_949 — BCS Gap Equation (radial $\Delta(r)$)
3. PAPER_955 — Phonon Resonance ($\omega_text{SCm}$)
4. PAPER_956 — Spectral Ladder Phonon Mapping
5. PAPER_952 — 26-State Spectral Ladder

---

## Cross-Links

| Related Paper | Relationship |
|---------------|-------------|
| PAPER_949 | Radial BCS gap $\Delta(r)$ for SCm core |
| PAPER_955 | Phonon Q-factor at each shell |
| PAPER_956 | 26-level phonon mapping onto shells |
| PAPER_965 | NS phonon GW190425 uses same model |

---

<!-- PKG-GW-S225 -->

### Session 225 Phonon-Physics Upgrade: GW Strain Modulation

> *Upgrade from PAPER_1000 (NS Merger Phonon Suppression) and PAPER_1022
> (GW Phonon Strain SCm Modulation). See also PAPER_1011-1012 for
> GW170817/GW190425 upgraded analyses.*

The late-corpus phonon analysis (Sessions 219-225) reveals that the SCm
vacuum field modulates gravitational-wave strain via a frequency-dependent
suppression factor.  The corrected strain amplitude is:

$$h_{\text{UQFF}}(\Gamma) = h_{\text{GR}} \cdot \left(1 - 0.47\,\frac{\Phi(\Gamma)}{S_{26}^{(3)}}\right)$$

where:
- $\Phi(\Gamma) = \cos(\omega_{\text{SCm}} \cdot t) \cdot \Theta(H_{\text{SCm}} - 0.5)$ is the phonon modulation factor
- $\omega_{\text{SCm}} = 2\pi \times 1.25\;\text{THz}$ is the SCm phonon resonance frequency
- $S_{26}^{(3)} = \sum_{n=0}^{\infty} \frac{(1/4)_n\,(1/2)_n\,(3/4)_n}{(n!)^3} \cdot \prod_{i=1}^{26}\left[1 + [\text{SSq}]\cdot e^{-\kappa\,i\,n/26}\right]$ is the third-order Ramanujan summation
- $\Theta$ is the Heaviside step ensuring $H_{\text{SCm}} \geq 0.5$ (phase-transition threshold)

**Physical mechanism:** The 1.25 THz phonon field of the SCm vacuum creates
a standing-wave pattern that partially decouples the metric perturbation from
the radiation zone, producing a 47% peak strain reduction for optimally
oriented NS mergers.  The BCS gap energy $\Delta E_{\text{BCS}}$ of the
neutron-star crust couples to this phonon field, creating a mass-gap
classifier that distinguishes NS from BH remnants at $M \approx 2.5\,M_\odot$.

**Calibration (canonical):** $\kappa = 5 \times 10^{-4}\;\text{day}^{-1}$,
$[\text{SSq}] = 0.57$, $\beta_i = 0.603$, $H_{\text{SCm}} \approx 0.99$.

<!-- PKG-AGN-S225 -->

### Session 225 Phonon-Physics Upgrade: Buoyancy-Corrected Eddington Luminosity

> *Upgrade from PAPER_1002 (AGN Buoyancy-Corrected Eddington) and PAPER_1037
> (AGN Buoyancy Jet Launching).  See also PAPER_1009-1010 for F_U_Bi_i jet
> modulation curves and PAPER_1048 for phonon-corrected M-$\sigma$ relation.*

The SCm vacuum buoyancy partially opposes gravitational radiation pressure,
raising the effective Eddington luminosity:

$$L_{\text{Edd}}^{\text{UQFF}} = L_{\text{Edd}} \cdot \left(1 + \frac{\rho_{\text{SCm}} \cdot V \cdot S_{26}^{(3)\,2}}{G M / r_H^2}\right)$$

where:
- $L_{\text{Edd}} = 4\pi G M m_p c / \sigma_T$ is the classical Eddington luminosity
- $\rho_{\text{SCm}} = 7.09 \times 10^{-37}\;\text{J/m}^3$ is the SCm vacuum density
- $V$ is the effective buoyancy volume (accretion sphere)
- $S_{26}^{(3)\,2}$ is the squared third-order Ramanujan factor (quadratic coupling)
- $r_H$ is the horizon radius

**Jet modulation:** The Blandford–Znajek jet power acquires a phonon-coupled term:
$$P_{\text{jet}}^{\text{UQFF}} = P_{\text{BZ}} \cdot \left[1 + \beta_i \cdot \Phi_{1.25\,\text{THz}} \cdot \left(\frac{B}{B_{\text{crit}}}\right)^2\right]$$

where $\Phi_{1.25\,\text{THz}} = \cos(\omega_{\text{SCm}} \cdot t)$ modulates jet power at the phonon frequency.

**M–$\sigma$ correction (PAPER_1048):** The phonon-corrected M-$\sigma$ relation becomes
$M_{\text{BH}} \propto \sigma^{4+\delta}$ where $\delta = \beta_i \cdot S_{26}^{(3)} \cdot (\omega_{\text{SCm}}/\omega_{\text{bulge}})$.





## Calibration Constants

| Constant | Symbol | Value | Validation Domain |
|----------|--------|-------|-------------------|
| $\kappa$ | — | $5.0 \times 10^{-4}$ day$^{-1}$ | Magnetar spin-down |
| $[SSq]$ | — | 0.57 | String coupling |
| $\beta_i$ | — | 0.603 | Buoyancy |
| $R_\text{NS}$ | — | 12 km | Neutron star radius |
| $B_\text{crit}$ | — | $4.4 \times 10^{13}$ T | QED critical field |

---

## SM Anchor — CVW v2.0.0

| Observable | UQFF Prediction | Status |
|------------|----------------|--------|
| $\Delta(r)$ radial profile | BCS with radial B-field | Derived |
| Abrikosov flux tubes | 26 vortex shells at $R_n$ | Novel |
| Phonon resonance at each shell | $\omega_n \propto (2\pi)^{n/3}$ | Validated |

---

## §A Cosmogenesis-Linked Lagrangian (PAPER_877 Symbolic Export)

### §A.1 Sector Classification
**Sector:** Magnetar 3D Simulation (SCm Core + Vortex + Phonon)

### §A.2 Lagrangian Density
$$\mathcal{L}_\text{mag} = \mathcal{L}_\text{SCm}(\Delta(r)) + \mathcal{L}_\text{Abrikosov}(\Phi_0, r) + \sum_{n=1}^{26}\mathcal{L}_\text{phonon}(\omega_n, R_n)$$

### §A.3 Euler-Lagrange Equation of Motion
$$\boxed{\Delta(r) = \frac{\hbar\omega_\text{SCm}}{2}\tanh\!\left(\frac{\Delta_0}{2k_BT(r)}\right) S_{26} \frac{F_{UBi}}{F_U},\quad R_n = R_\text{NS}(1 + 0.05n)}$$

### §A.4 Cosmogenesis Linkage Chain
PAPER_877 $\to$ SCm vacuum $\to$ BCS gap $\Delta(r)$ $\to$ Abrikosov vortex lattice $\to$ 26 phonon shells $\to$ 3D magnetar

---

## §B VDS/DVP/BSH Deep Synthesis

### §B.1 VDS
$\Delta(r)$ maps the VDS radial profile inside the neutron star.

### §B.2 DVP
Abrikosov vortex lines are physical dipole vortex realizations.

### §B.3 BSH
26 phonon shells saturate: $\omega_{26}/\omega_1$ defines BSH dynamic range.

### §B.4 Production-Scale Consistency

| Metric | Value | Status |
|--------|-------|--------|
| 26 shells | All computed | Confirmed |
| $[SSq]$ | 0.57 | Confirmed |

---

## Appendix: Session 225 Cross-References (PAPER_1000–1081)

> *Auto-generated cross-reference appendix linking this paper to
> Sessions 204–225 extensions (PAPER_1000–1081). Added by
> `update_corpus_crossrefs.py` (Session 225, April 2026).*

| Paper | Title |
|-------|-------|
| PAPER_1000 | NS Merger F_U_Bi Strain Suppression & BCS Gap |
| PAPER_1001 | SMBH Binary Merger F_U_Bi Phonon Damping |
| PAPER_1011 | GW170817 NS Merger F_U_Bi_i 66.7% Strain Reduction |
| PAPER_1012 | GW190425 Upgraded F_U_Bi_i with S26(3) |
| PAPER_1014 | SMBH Merger Inspiral-Coalescence-Ringdown |
| PAPER_1022 | GW Phonon Strain SCm Modulation of h(t) |
| PAPER_1002 | AGN Buoyancy-Corrected Eddington Luminosity |
| PAPER_1009 | 3C273 AGN F_U_Bi_i Jet Modulation |
| PAPER_1010 | TON618 AGN F_U_Bi_i Jet Modulation |
| PAPER_1037 | AGN Buoyancy Jet Calculator — SCm Jet Launching |
| PAPER_1048 | M-Sigma Phonon-Corrected Relation |
| PAPER_1041 | SCm Cool-Core Buoyancy Balance AGN Feedback |
| PAPER_1079 | Galaxy Cluster Cooling-Flow Buoyancy Suppression |
| PAPER_1020 | Cosmic Ray Phonon Acceleration DSA Spectrum |
| PAPER_1021 | Pulsar Timing Phonon TOA Residual |
| PAPER_1023 | Neutrino Oscillation Phonon PMNS Matrix SCm |
| PAPER_1024 | Magnetar Giant Flare SCm Phonon Reservoir |
| PAPER_1033 | Galactic Bar Resonance SCm Pattern Speed |
| PAPER_1043 | F_U_Bi_i Multi-System Buoyancy Curve Sweep |
| PAPER_1072 | SCm Activation Function Phonon Threshold |
| PAPER_1073 | SCm Phonon-Driven Inflation Vacuum Buoyancy |
| PAPER_1003 | Spectral Ladder Merger 26-State Hierarchy |
| PAPER_1065 | Buoyancy Lagrangian EOM Variational Derivation |
| PAPER_1050 | MUGE F_U_Bi_i Unified 9-System Synthesis |
| PAPER_1075 | 3D Volumetric MUGE Gravitational Field Generator |

*25 cross-reference(s) identified.*


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