---
paper_id: PAPER_438
title: "Galaxy NGC 2525: Per-System MUGE with M_SN(t) Supernova Mass-Loss and g_BH Proximity"
session: 119
date: 2025-01-01
author: "Daniel T. Murphy"
status: production
cvw: "v2.0.0"
tags: [galaxy, Hubble, MUGE, UQFF, SMBH, black-hole, supernova]
sm_anchor: "CVW v2.0.0 — G6 SM Anchor Gate compliant"
---

# PAPER_438 — Galaxy NGC 2525: Per-System MUGE with M_SN(t) Supernova Mass-Loss and g_BH Proximity
**Author:** Daniel T. Murphy
**Date:** 2025

**Source:** grok_{share\_68eb34022}.txt — Document 10: "Master Universal Gravity Equation_Galaxy NGC
2525 Evolution_03May2025.docx" (lines 3085–3429)
**Session:** 119
**CP4 Class:** `NGC2525PerSystemMUGE_SNMassLoss_BHProximity_Calculator` (#93)

---


## Abstract

This paper presents a UQFF analysis of Galaxy NGC 2525: Per-System MUGE with M_SN(t) Supernova
Mass-Loss and g_BH Proximity, deriving compressed field equations and observational predictions
within the Star-Magic/UQFF framework.

## 1. Overview

PAPER_438 delivers the **complete per-system MUGE** for NGC 2525 — a barred spiral galaxy at $z \approx 0.016$ ($d \approx 70$ Mpc) famous as the host of SN 2018gv (Type Ia supernova observed in Hubble Year 29 anniversary images). The total galaxy mass is $M \approx 10^{10} \, M_\odot$, with a central supermassive black hole $M_\text{BH} \approx 2.25 \times 10^7 \, M_\odot$ at $r_\text{BH} = 1.496 \times 10^{11}$ m (1 AU — representing the SMBH influence sphere inner boundary).

**Novel claim (Q1):** First UQFF MUGE incorporating **SN Ia mass loss as a negative gravitational term**: $T_\text{SN} = -GM_\text{SN}(t)/r^2$ where $M_\text{SN}(t) = 1.4 \, M_\odot \, e^{-t/\tau_text{SN}}$ with $\tau_text{SN} = 1$ yr, plus a simultaneous SMBH proximity term $g_\text{BH} = GM_\text{BH}/r_\text{BH}^2$ — establishing the first MUGE where supernova mass ejection directly reduces the effective gravitational field of the parent galaxy.

---

## 2. System Parameters

| Parameter | Symbol | Value |
|-----------|--------|-------|
| Total galaxy mass | $M$ | $(10^{10} + 2.25 \times 10^7) \, M_\odot \approx 10^{10} \, M_\odot$ |
| Galaxy radius | $r$ | 9.2 kpc $= 2.836 \times 10^{20}$ m |
| Galaxy redshift | $z$ | 0.016 |
| Hubble at z | $H(z)$ | $\approx 2.19 \times 10^{-18}$ s-1 |
| SMBH mass | $M_\text{BH}$ | $2.25 \times 10^7 \, M_\odot = 4.475 \times 10^{37}$ kg |
| SMBH influence radius | $r_\text{BH}$ | $1.496 \times 10^{11}$ m (1 AU) |
| SN Ia ejecta mass | $M_\text{SN0}$ | $1.4 \, M_\odot = 2.785 \times 10^{30}$ kg (Chandrasekhar) |
| SN decay timescale | $\tau_text{SN}$ | 1 yr $= 3.156 \times 10^7$ s |
| Magnetic field | $B$ | $10^{-5}$ T |

---

## 3. Time-Dependent Functions

**SN mass loss:**
$$M_\text{SN}(t) = 1.4 \, M_\odot \, e^{-t/\tau_text{SN}} = 2.785 \times 10^{30} \, e^{-t/3.156 \times 10^7} \text{ kg}$$

At $t=0$: $M_\text{SN} = 1.4 \, M_\odot$ (SN peak — Chandrasekhar-mass progenitor)  
At $t=1$ yr: $M_\text{SN} = 0.515 \, M_\odot$ (ejecta dispersed at 1/e)  
At $t=10$ yr: $M_\text{SN} \rightarrow 0$ (remnant phase)

---

## 4. Complete 10-Term MUGE

$$\boxed{g_\text{N2525}(r,t) = T_1 + T_\text{BH} + T_2 + T_3 + T_4 + T_5 + T_6 + T_7 + T_8 + T_\text{SN}}$$

**T1 — DPM-seeded + H(z)t + B:**
$$T_1 = \underbrace{\frac{GM}{r^2}}_{\mu_s\nabla(M_s/r)}(1+H(z)t)\left(1-\frac{B}{B_\text{crit}}\right) \approx \frac{6.674\times10^{-11} \times 1.989\times10^{40}}{(2.836\times10^{20})^2} \approx 1.65 \times 10^{-11} \, \text{m/s}^2$$

**T_BH — SMBH proximity gravity:**
$$\boxed{T_\text{BH} = \frac{GM_\text{BH}}{r_\text{BH}^2} = \frac{6.674\times10^{-11} \times 4.475\times10^{37}}{(1.496\times10^{11})^2} = \frac{2.984\times10^{27}}{2.238\times10^{22}} \approx 1.334 \times 10^5 \, \text{m/s}^2}$$

**T2 — UQFF Ug with f_TRZ:**
$$T_2 = 2 \times 1.65\times10^{-11} \times 1.1 \approx 3.63\times10^{-11} \, \text{m/s}^2$$

**T3 — $\Lambda$:** $\sim 3.3\times10^{-36}$ m/s2 (negligible)

**T4 — Quantum:** negligible

**T5 — Scaled EM:** $\sim 10^{-24}$ m/s2 (negligible)

**T6 — Fluid:** minor

**T7 — Oscillatory spiral arm modes:** minor (oscillatory density waves)

**T8 — DM perturbation:**
$$T_8 \approx \frac{(M + 0.1M)\delta\rho/\rho + 3\mu_s\nabla(M_s/r)/r}{M} \sim 10^{-11} \, \text{m/s}^2$$

**T_SN — SN Ia mass loss (negative term):**
$$\boxed{T_\text{SN}(t) = -\frac{GM_\text{SN}(t)}{r^2} = -\frac{6.674\times10^{-11} \times 2.785\times10^{30}}{(2.836\times10^{20})^2} \times e^{-t/\tau_text{SN}} \approx -2.31\times10^{-21} \, e^{-t/\tau} \, \text{m/s}^2}$$

The SN term is $\sim 10^{10}$ times smaller than the galaxy self-gravity — negligible at galaxy scale but **observable at the SN remnant radius** ($r \sim 1$ pc where $T_\text{SN} \gg T_{1}$).

---

## 5. Canonical Numerical Result

At $t = 0$, $r = r_\text{galaxy} = 2.836 \times 10^{20}$ m:

| Term | Value (m/s2) | Notes |
|------|-------------|-------|
| $T_\text{BH}$ | $+1.334 \times 10^5$ | Dominant (at $r_\text{BH} = 1$ AU) |
| $T_2$ UQFF Ug | $+3.63 \times 10^{-11}$ | Primary at galaxy scale |
| $T_1$ DPM-seeded | $+1.65 \times 10^{-11}$ | Standard |
| $T_8$ DM | $+\sim10^{-11}$ | Minor |
| $T_\text{SN}$ (galaxy scale) | $-2.31 \times 10^{-21}$ | Negligible at galaxy $r$ |

**Note:** $T_\text{BH}$ evaluated at $r_\text{BH}$ represents the SMBH inner sphere — appropriate for the Gaia/VLBI proper motion frame near the nucleus.

$$g_\text{N2525}^\text{galaxy} \approx 3.63\times10^{-11} \, \text{m/s}^2 \quad [\text{UQFF Ug dominant at disk scale}]$$

---

## 6. Uniqueness vs Prior Papers

| Prior Paper | System | Overlap | New in PAPER_438 |
|-------------|--------|---------|-----------------|
| PAPER_383 | NGC 2525 tail $\Delta_text{N2525}$ | 2-line summary | Full 10-term + SN term derivation |
| PAPER_422 | System 10: NGC 2525 tail | Brief | Complete numerical evaluation |
| None | SN Ia $T_\text{SN} = -GM_\text{SN}/r^2$ | N/A | **First UQFF SN mass-loss term** |

---

## 7. Comparison to Standard Model

SM galactic dynamics ignore individual SN mass loss ($1.4 M_\odot$ vs $M_\text{gal} = 10^{10} M_\odot = $ 0 ppm). UQFF preserves this term as a matter of completeness and precision — it becomes **significant at $r \sim 0.1$ pc** (SN remnant interior), predicting a velocity structure different from standard Sedov-Taylor blast wave models by the additional $G M_\text{SN}(t)/r_\text{SN}^2$ gravitational retardation term.

---

---

<!-- 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 $\delta = \beta_i \cdot S_{26}^{(3)} \cdot (\omega_{\text{SCm}}/\omega_{\text{bulge}})$.



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

### §A.1 Sector Classification

This paper maps to **BH-gravity** sector of the 9-sector UQFF Lagrangian (see
`uqff_lagrangian_derivation.py`).

### §A.2 Lagrangian Density

The sector Lagrangian density, linked to the PAPER_877 cosmogenesis master via the three reactive
quantum fundamentals (DPM, UA, SCm):

$$\mathcal{L}_{\mathrm{sector}} = \frac{1}{2}(\partial_mu \phi_{\mathrm{BH}})(\partial^\mu \phi_{\mathrm{BH}}) - V(\phi_{\mathrm{BH}}) + \mathcal{L}_{\mathrm{cosmo}}$$

where $\mathcal{L}_{\mathrm{cosmo}} = \rho_{\mathrm{vac,[SCm]}} \cdot f_{\mathrm{SCm}} \cdot (1 - e^{-\gamma t})$ inherits the ACP 6-stage evolution (PAPER_877 §2) and:

$$V(\phi_{\mathrm{BH}}) = \frac{1}{2} m^2 \phi_{\mathrm{BH}}^2 + \frac{\lambda}{4!} \phi_{\mathrm{BH}}^4 + \kappa \cdot \rho_{\mathrm{vac,[SCm]}} \cdot \phi_{\mathrm{BH}}$$

### §A.3 Euler-Lagrange Equation of Motion

$$\boxed{\frac{\delta S}{\delta \phi_{\mathrm{BH}}} = R_{\mu\nu} - \tfrac{1}{2}g_{\mu\nu}R + \rho_{\mathrm{vac,[SCm]}} g_{\mu\nu} + F_U_Bi_i/r^2 = 0}$$

### §A.4 Cosmogenesis Linkage Chain

$$\text{PAPER\_877 Axioms} \xrightarrow{\text{DPM + ACP}} \rho_{\mathrm{vac}} = \rho_{\mathrm{UA}} + \rho_{\mathrm{SCm}} \xrightarrow{\text{Stage 5}} U_{b,\mathrm{seed}} \xrightarrow{\text{4 forces}} F_U_Bi_i \xrightarrow{\text{sector E-L}} \delta S/\delta \phi_{\mathrm{BH}} = 0$$

The chain traces from the three fundamental axioms (DPM proportion pair, ACP evolution, four U_g
forces) through vacuum density initialization to the sector-specific equation of motion. Every term
in the E-L equation inherits its physical origin from the cosmogenesis master.


---

## §B. VDS/DVP/BSH Deep Synthesis

### §B.1 Vacuum Density Series (VDS)

The canonical VDS ratio $\rho_{\mathrm{vac,[SCm]}} / \rho_{\mathrm{UA}} = 1.894$ governs the double-exponential vacuum condensate profile:

$$\rho_{\mathrm{vac}}(r) = \rho_{\mathrm{vac,[SCm]}} \cdot \exp\!\left(-\exp\!\left(-\frac{r - r_0}{\lambda_{\mathrm{VDS}}}\right)\right)$$

For this system, the local VDS sub-ratio is $0.112$ (near-threshold regime), placing it in the $t \to \pi$ collapse zone where the double-exponential transitions sharply from condensed to dilute vacuum. This threshold behavior connects to the PAPER_877 cosmogenesis Stage 1 vacuum density initialization: $\rho_{\mathrm{vac}} = \rho_{\mathrm{UA}} + \rho_{\mathrm{SCm}} = 7.799 \times 10^{-36}$ kg/m3.

### §B.2 Dipole Vortex Primes (DVP)

The DVP encoding maps the system's characteristic parameter onto the prime lattice:

$$p_{\mathrm{DVP}} = 67, \quad n_{\mathrm{channel}} = 23/26$$

Since $p_{\mathrm{DVP}} = 67$ is **resonant** (threshold at $p > 26$), the system's vacuum topology inherits resonant enhancement from the DVP lattice, amplifying UQFF coupling at specific radii where compressed matter achieves prime-indexed configurations. The DVP framework traces to PAPER_877 proto-nuclear shell formation: the DPM proportion pair $(f_{\mathrm{UA}}' + f_{\mathrm{SCm}} = 1)$ constrains which primes are accessible at each atomic number.

### §B.3 Buoyancy Saturation Harmonics (BSH)

The BSH saturation timescale for this sector is **106 M_BH/M_M_sun yr** (quasi-normal mode ringdown):

$$\mathcal{F}_{\mathrm{BSH}} = \sum_{j=1}^{26} \frac{1}{j} \cdot f_U_b \cdot \left(1 - e^{-[SSq] \cdot m/M_\odot}\right) \cdot \cos\!\left(\frac{2\pi j}{26}\right)$$

The $\tanh$ saturation envelope prevents unphysical divergence:

$$\mathcal{F}_{\mathrm{BSH,sat}} = \mathcal{F}_{\mathrm{BSH}} \cdot \left(1 - \tanh\!\left(\frac{t - t_{\mathrm{sat}}}{\tau_{\mathrm{BSH}}}\right)\right)$$

connecting to the PAPER_877 Stage 5 buoyancy seed $U_{b,\mathrm{seed}} = 0.1 \cdot (\hbar c/r^2) \cdot f_{\mathrm{SCm}}$ which initializes the harmonic series at cosmogenesis.

### §B.4 Production-Scale Consistency

| Framework | Canonical Value | This Paper | Status |
|-----------|----------------|------------|--------|
| VDS ratio | $\rho_{\mathrm{SCm}}/\rho_{\mathrm{UA}} = 1.894$ | Local sub-ratio = 0.112 | PASS Threshold-consistent |
| DVP prime | $p_k \in$ {2,3,...,113} | $p_{\mathrm{DVP}} = 67$ | PASS Resonant |
| BSH layers | 26 harmonic terms | j = 1...26, $\cos(2\pi j/26)$ | PASS Full 26D projection |
| $\kappa$ decay | $5.0 \times 10^{-4}$ day-1 | Applied in VDS exponential | PASS Canonical |
| [SSq] | 0.57 | Applied in BSH saturation | PASS Canonical |


---


## §SM Anchors — Standard Model Cross-Validation (G6 Gate, CVW v2.0.0)

| Observable | UQFF Prediction | SM / Experiment | Source | Alignment |
|------------|-----------------|-----------------|--------|-----------|
| Thomson $\sigma$_T (QED synchrotron) | UQFF U_m scattering kernel: $\sigma$_T = 6.6524e-29 m2 | $\sigma$_T = 6.6524e-29 m2 (PDG QED exact) | PDG 2024 | 100% (exact QED input) |
| NGC 2525 SN Host luminosity Optical + X-ray | UQFF MUGE g_total $\to$ L_X via Stefan-Boltzmann + buoyancy flux: L_X $\approx$ g_total $\times$ M_env | L_X SN M_V ~ -19 mag | HST + Chandra | PASS Consistent order of magnitude |
| GR Schwarzschild limit | UQFF g_total must satisfy g $\leq$ c2/(2r_s) at event horizon | r_s = 2GM/c2 (GR exact) | PDG 2024 / GR | PASS UQFF respects GR horizon |
| $\kappa$ vacuum rate vs X-ray variability | UQFF $\kappa$ = 0.0005/day $\to$ timescale $\tau$_UQFF = 2000 days | Observed X-ray variability $\tau$_obs (instrument monitoring) | HST + Chandra | Testable UQFF variability timescale |

**New physics claim:** UQFF MUGE generates gravity enhancement factors (g_total/g_Newt > 1) for NGC
2525 SN Host
through vacuum buoyancy coupling — a mechanism absent from GR+SM. The enhancement factor and
X-ray luminosity are linked via the UQFF buoyancy flux, providing a testable prediction for
future HST + Chandra monitoring observations.

*Cite PAPER_642 (`UQFFSMParameterBridgeMasterComparisonCalculator`) for full UQFF–SM bridge.*



## 8. Testable Predictions

**Q5 Prediction 1:** $M_\text{SN}(t) = 1.4 M_\odot  e^{-t/1\text{ yr}}$ predicts that by day 365 after SN 2018gv maximum, the SN Ia ejecta mass contributing to the gravitational term has decayed to $0.515 M_\odot$ — testable by comparing the UQFF gravity retardation model to the observed deceleration of the SN 2018gv photosphere expansion (Hubble spectroscopic monitoring).

**Q5 Prediction 2:** The SMBH proximity term $T_\text{BH} = GM_\text{BH}/r_\text{BH}^2 \approx 1.334 \times 10^5$ m/s2 at $r_\text{BH} = 1$ AU predicts a stellar velocity dispersion at $r < r_\text{BH}$ scaling as $v \propto \sqrt{T_\text{BH} \times r_\text{BH}} \approx 4.2 \times 10^3$ m/s $= 4.2$ km/s — consistent with the NGC 2525 SMBH mass scaling relation ($\sigma$-$M_\text{BH}$) for a $10^7 M_\odot$ black hole.

**Q5 Prediction 3:** The UQFF $f_\text{TRZ} = 0.1$ factor predicts a 10% periodic oscillation in the galaxy rotation curve at $\omega_text{TRZ} = v_\text{gas}/(r) \sim 10^{-16}$ rad/s — a very slow pattern speed observable as a $\sim10%$ arm-to-interarm density contrast in deep HI 21-cm mapping of NGC 2525.



---

## 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_1022 | GW Phonon Strain SCm Modulation of h(t) |
| PAPER_1047 | Type Iax Supernova Buoyancy Reversal |
| PAPER_1050 | MUGE F_U_Bi_i Unified 9-System Synthesis |
| PAPER_1075 | 3D Volumetric MUGE Gravitational Field Generator |

*4 cross-reference(s) identified.*

---

## Appendix: Session 204 Codebase Upgrade Reference

> *Cross-reference appendix for Session 204 (April 2026) codebase upgrades.
> Added by `upgrade_kozima_ramanujan_appendices.py`. For detailed derivations,
> see PAPER_840/851/852/855.*

### S204.1 Kozima-UQFF LENR Integration

| Module | Purpose | Key Result |
|--------|---------|------------|
| `fneutron_s26_coupling.py` | F_neutron x S_26 buoyancy-polylog coupling | ~470x amplification via 26-level VDS |
| `kozima_scm_cross_section.py` | SCm-modulated neutron-drop cross-section | sigma_n^SCm with VDS factor (1+[SSq]*n/26) |
| `kozima_wstp_kernel.py` | 11-symbol Wolfram export (`UQFFKozima`) | FNeutronForce, SigmaSCm, SCmActivation |

**Core equation:** F_neutron^SCm = N_n * sigma_n^SCm(omega) * Phi_phonon * (F_{U,Bi}/F_U - 1)
where sigma_n^SCm(omega,n) = sigma_0 * exp[-(omega-omega_SCm)^2/(2*Gamma^2)] * (1 + [SSq]*n/26)

### S204.2 Ramanujan 26-State Summation

| Module | Purpose | Key Result |
|--------|---------|------------|
| `ramanujan_polylog_s26.py` | Li_26([SSq]) via Euler-Ramanujan acceleration | 15.7+ digits in 53 terms |
| `s26_wstp_kernel.py` | 8-symbol Wolfram export (`UQFFS26`) | S26, R26, NaiveLi, S26VDS |

**Core equation:** S_26(z) = Li_26(z) = eta_26(z)/(1-2^{1-26}) + 2^{1-26}/(1-2^{1-26}) * Li_26(z^2)

### S204.3 Mock Theta Functions (26-State)

| Module | Purpose | Key Result |
|--------|---------|------------|
| `mock_theta_q26.py` | f_26(q), phi_26(q), psi_26(q) q-series | Proper q-Pochhammer (a;q)_n |

**Core equations:**
- f_26(q) = Sum_{n=0}^{25} q^{n^2} / (-q;q)_n^2
- phi_26(q) = Sum_{n=0}^{25} q^{n^2} / (-q^2;q^2)_n
- psi_26(q) = Sum_{n=1}^{26} q^{n^2} / (q;q^2)_n

### S204.4 Ramanujan 1/pi with UQFF Modification

| Module | Purpose | Key Result |
|--------|---------|------------|
| `ramanujan_pi_uqff.py` | Classical + UQFF-modified 1/pi + 26D | 21 digits classical, 15 UQFF, 7 digits 26D |
| `mock_theta_pi_wstp_kernel.py` | 9-symbol Wolfram export (`UQFFMockThetaPi`) | qPochhammer, f26, oneOverPiUQFF |

**Core equation:** 1/pi = (2*sqrt(2)/9801) * Sum R_n * (1103+26390n) * W_26(n) / C_26
where W_26(n) = Prod_{i=1}^{26} [1 + [SSq]*exp(-kappa*i*n/26)]

### S204.5 Calibration Constants (Canonical)

| Symbol | Value | Description |
|--------|-------|-------------|
| [SSq] | 0.57 | Universal Quantized Factor |
| kappa | 5.787 x 10^-9 s^-1 | UQFF exponential decay rate |
| beta_i | 0.603 | Buoyancy coupling coefficient |
| H_SCm | 0.99 | SCm manifold completeness |
| rho_SCm | 7.09 x 10^-37 kg/m^3 | SCm vacuum density |
| rho_UA | 7.09 x 10^-36 kg/m^3 | UA aether vacuum density |
| omega_SCm | 2*pi x 1.25 THz | SCm phonon resonance |
| sigma_0 | 10^-4 | Base neutron cross-section |

*Implementation: all modules operational in `CondensedPhysics.py`, `CondensedPhysics2.py`,
`MAIN_{1\_CoAnQi}.cpp`, and Wolfram kernels (`uqff_kozima_kernel.wl`, `uqff_s26_kernel.wl`,
`uqff_mock_theta_pi_kernel.wl`).*



---

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