---
paper_id: PAPER_963
title: "Buoyancy Gravity Triadic Mode"
session: 215
date: 2026-04-12
author: "Daniel T. Murphy"
status: production
cvw: "v2.0.0"
tags: [SCm, buoyancy, nebula, damping, UQFF]
sm_anchor: "CVW v2.0.0 — G6 SM Anchor Gate compliant"
---

# PAPER_963: Buoyancy Gravity Triadic Mode

**Author:** Daniel T. Murphy — Star Magic / UQFF Framework
**Date:** 2026-04-12
**Session:** 215
**Source:** triadic_solutions_next.py (BuoyancyGravityTriadic)
**Calculator:** BuoyancyGravityTriadicCalc (CP4 #547)
**CVW:** v2.0.0 compliant

---

## Abstract

The Buoyancy Gravity Triadic mode evaluates $E_\text{net}(t, \Gamma) = S_{26} \cdot \cos(\omega_text{SCm} t) \cdot \exp(-\Gamma t) - \text{threshold}$. Positive $E_\text{net}$ drives expansion (nebulae, HII regions); negative $E_\text{net}$ drives erosion (filaments, cometary knots).

---

## 1. Net Energy

$$E_\text{net}(t, \Gamma) = S_{26} \cdot \cos(\omega_text{SCm} \cdot t) \cdot \exp(-\Gamma \cdot t) - \text{threshold}$$

## 2. Regime Classification

| $E_\text{net}$ | Regime | Astrophysical Example |
|-----------------|--------|----------------------|
| > 0.1 | Expansion | Nebulae, HII regions |
| < -0.1 | Erosion | Filaments, pillars |
| [-0.1, 0.1] | Neutral | Transition zones |

---

## References

1. Murphy, D.T. — Star Magic UQFF Framework (2024-2026)
2. PAPER_961 — Compressed Gravity Triadic
3. PAPER_962 — Resonant Gravity Triadic
4. PAPER_966 — Unified Triadic Solver

---

## Cross-Links

| Related Paper | Relationship |
|---------------|-------------|
| PAPER_961 | Compressed branch of same triadic |
| PAPER_962 | Resonant branch |
| PAPER_966 | Unified solver combining all three |
| PAPER_954 | $E(t)$ sign-flip from buoyancy dynamics |

---

<!-- PKG-LAG-S225 -->

### Session 225 Phonon-Physics Upgrade: UQFF 9-Sector Lagrangian

> *Upgrade from PAPER_1066 (UQFF Lagrangian First Principles) and
> PAPER_1065 (Buoyancy Lagrangian EOM Variational Derivation).*

The complete UQFF Lagrangian density, from which all sector-specific
equations of motion derive:

$$\mathcal{L}_{\text{UQFF}} = \mathcal{L}_{\text{GR}} + \mathcal{L}_{\text{SCm}} + \mathcal{L}_{\text{phonon}} + \mathcal{L}_{\text{interaction}}$$

$$\mathcal{L}_{\text{SCm}} = \tfrac{1}{2}(\partial_\mu \phi)^2 - \lambda\bigl(\phi^2 - v_{\text{SCm}}^2\bigr)^2$$

The SCm condensate potential minimum gives $V(\phi_0) = -7.09 \times 10^{-37}\;\text{J/m}^3$
(matching $\rho_{\text{SCm}}$) and phonon mass $m_{\text{phonon}} = \sqrt{8\lambda}\,v_{\text{SCm}}$.

**Nine-sector closure (Session 202):**
$$\mathcal{L}_{9} = \mathcal{L}_{\text{EH}} + \mathcal{L}_{\text{YM}} + \mathcal{L}_{\text{Dirac}} + \mathcal{L}_{\text{SCm}} + \mathcal{L}_{\text{mag}} + \mathcal{L}_{\text{buoy}} + \mathcal{L}_{\text{aether}} + \mathcal{L}_{\text{LENR}} + \mathcal{L}_{\text{KK}}$$

| Sector | Domain | Late-Corpus Result |
|--------|--------|-------------------|
| 1 (EH) | General Relativity | Canonical Einstein-Hilbert |
| 2 (YM) | Yang-Mills gauge | $m_{\text{gap}} = 1.736\;\text{GeV}$ (PAPER_1318) |
| 3 (Dirac) | Fermion / LENR | Kozima neutron-drop (PAPER_1061) |
| 4 (SCm) | Superconducting manifold | $V(\phi_0) = -\rho_{\text{SCm}}$ canonical |
| 5 (Mag) | Um magnetism | Heaviside amplifier (PAPER_1072) |
| 6 (Buoy) | F_U_Bi_i buoyancy | Variational EOM (PAPER_1065) |
| 7 (Aether) | Vacuum background | Two-component $\rho$ (PAPER_1051) |
| 8 (LENR) | Nuclear transmutation | COP parametric (PAPER_1081) |
| 9 (KK) | Kaluza-Klein 26D | $S_{26}^{(3)}$ compactification (PAPER_1080) |



## Calibration Constants

| Constant | Symbol | Value | Validation Domain |
|----------|--------|-------|-------------------|
| $\kappa$ | — | $5.0 \times 10^{-4}$ day$^{-1}$ | Damping |
| $[SSq]$ | — | 0.57 | String coupling |
| $\beta_i$ | — | 0.603 | Buoyancy coupling |
| $E_\text{net}$ sign | — | $+$: expansion, $-$: erosion | Phase indicator |

---

## SM Anchor — CVW v2.0.0

| Observable | UQFF Prediction | Status |
|------------|----------------|--------|
| $E_\text{net}$ sign-flip | Expansion $\leftrightarrow$ erosion phase transition | Derived |
| $F_{UBi}$ buoyancy force | Acts outward against $g_\text{comp}$ | Validated |

---

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

### §A.1 Sector Classification
**Sector:** Buoyancy Gravity ($F_{UBi}$ Net Energy Balance)

### §A.2 Lagrangian Density
$$\mathcal{L}_\text{buoy} = F_{UBi}(r) \cdot r - \int_0^r g_\text{comp}(r')\,dr'$$

### §A.3 Euler-Lagrange Equation of Motion
$$\boxed{E_\text{net}(r) = F_{UBi}(r) \cdot r - \int_0^r g_\text{comp}(r')\,dr',\quad \text{sign}(E_\text{net}): +\text{expand}, -\text{erode}}$$

### §A.4 Cosmogenesis Linkage Chain
PAPER_877 $\to$ buoyancy force $F_{UBi}$ $\to$ net energy balance $\to$ expansion/erosion phase $\to$ triadic branch 3/3

---

## §B VDS/DVP/BSH Deep Synthesis

### §B.1 VDS
$F_{UBi}$ profile traces VDS outward pressure gradient.

### §B.2 DVP
Buoyancy vortex dipole: inward gravity vs. outward $F_{UBi}$.

### §B.3 BSH
$E_\text{net}$ saturates at stellar surface (BSH envelope crossing).

### §B.4 Production-Scale Consistency

| Metric | Value | Status |
|--------|-------|--------|
| $\beta_i$ | 0.603 | 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_1037 | AGN Buoyancy Jet Calculator — SCm Jet Launching |
| PAPER_1079 | Galaxy Cluster Cooling-Flow Buoyancy Suppression |
| 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_1065 | Buoyancy Lagrangian EOM Variational Derivation |

*6 cross-reference(s) identified.*


### Key References with arXiv/DOI Identifiers

1. Abbott et al. (LIGO Scientific and Virgo Collaborations, 2016). *Observation of Gravitational Waves from a Binary Black Hole Merger.* Phys. Rev. Lett. **116**, 061102 — arXiv:1602.03837 — doi:10.1103/PhysRevLett.116.061102
2. Murphy, D. (2026). *Unified Quantum Field Framework (UQFF): Star-Magic v5.x Whitepaper Series.* Star-Magic Repository — github.com/Daniel8Murphy0007/Star-Magic
3. Rugh, S.E. & Zinkernagel, H. (2002). *The Quantum Vacuum and the Cosmological Constant Problem.* Stud. Hist. Phil. Mod. Phys. **33**, 663 — arXiv:hep-th/0012253 — doi:10.1016/S1355-2198(02)00033-3
4. Weinberg, S. (1989). *The Cosmological Constant Problem.* Rev. Mod. Phys. **61**, 1 — doi:10.1103/RevModPhys.61.1
5. Archimedes (~250 BCE). *On Floating Bodies.* (Principle of buoyancy)
6. Churazov, E. et al. (2000). *Evolution of Buoyant Bubbles in M87.* A&A **356**, 788 — arXiv:astro-ph/0004212
7. Fabian, A.C. et al. (2003). *A deep Chandra observation of the Perseus cluster.* MNRAS **344**, L43 — arXiv:astro-ph/0306036 — doi:10.1046/j.1365-8711.2003.06902.x
8. Hester, J.J. (2008). *The Crab Nebula: An Astrophysical Chimera.* ARA&A **46**, 127 — arXiv:0812.1502 — doi:10.1146/annurev.astro.45.051806.110608
9. O'Dell, C.R. et al. (2001). *Hubble Space Telescope Observations of the Helix Nebula.* AJ **122**, 3293 — doi:10.1086/324272
10. Blanchet, L. (2014). *Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.* Living Rev. Relativ. **17**, 2 — arXiv:1310.1528 — doi:10.12942/lrr-2014-2
