---
paper_id: PAPER_319
title: "Compact HII SFR Gravitational Binding Phase Transition"
session: 91
date: 2026-03-01
author: "Daniel T. Murphy"
status: production
cvw: "v2.0.0"
tags: [nebula, UQFF]
sm_anchor: "CVW v2.0.0 — G6 SM Anchor Gate compliant"
---

# PAPER_319: Compact HII SFR Gravitational Binding Phase Transition
**Author:** Daniel T. Murphy
**Date:** March 2026
## t_cross = 67,730 yr | sSFR = 5$\times$10-4 yr-1 (50$\times$ Lagoon) | m_factor(t_age) = 151
### FIRST UQFF Compact HII Region SFR Runaway Gravitational Binding Phase Transition

**Session:** 91  
**Module:** ORION_UQFF_MODULE.cpp (33rd C++ module)  
**System:** Orion Nebula M42/NGC 1976 — compact HII region with active star formation  
**Watermark:** Copyright — Daniel T. Murphy, Session 91, March 2026  

---


<!— UQFF constants: $\kappa$ = 5.0e-4 day-1, [SSq] = 0.57, M_UQFF = 1.43e1 TeV —>
## Abstract

This paper derives the SFR-driven gravitational binding phase transition for the Orion Nebula. With
SFR = 1 M_sun/yr acting on an initial mass M = 2000 M_sun, the specific star formation rate **sSFR =
5$\times$10-4 yr-1 is 50$\times$ that of the Lagoon Nebula** (1$\times$10-5 yr-1, PAPER_305). The system is born
wind-dominated (unbound), but as SFR continuously adds mass, the effective gravitational
acceleration amplified by the SFR mass factor m_factor(t) = 1 + SFR$\times$t_yr/M_sun_count crosses the
growing wind ram pressure at **t_cross = 67,730 yr**, transitioning the nebula from unbound to
gravitationally bound. By t_age = 300 kyr, binding_ratio = g_SFR/a_wind = 2.654. This is the FIRST
UQFF compact HII SFR runaway gravitational binding phase transition.

---

## System Parameters

| Parameter | Value | Description |
|-----------|-------|-------------|
| M | 2000 M_sun = 3.978$\times$1033 kg | Initial mass |
| SFR | 1 M_sun/yr = 6.303$\times$1022 kg/s | Star formation rate |
| sSFR | 5$\times$10-4 yr-1 | Specific SFR = SFR/M |
| t_age | 3$\times$105 yr | Nebula age |
| v_wind | 8$\times$103 m/s | HII ionization front |
| g_base | 1.907$\times$10-11 m/s2 | Base gravity (PAPER_317) |
| a_wind(t=0) | 5.424$\times$10-10 m/s2 | Initial wind acceleration |

---

## Key Equations

### SFR Mass Factor
$$M_{\mathrm{sf}}(t) = \frac{\mathrm{SFR_{yr}} \times t_{\mathrm{yr}}}{M_{\mathrm{sun,count}}}, \qquad m_{\mathrm{factor}}(t) = 1 + M_{\mathrm{sf}}(t)$$

### SFR-Amplified Gravitational Acceleration
$$g_{\mathrm{SFR}}(t) = g_{\mathrm{base}} \times m_{\mathrm{factor}}(t) = g_{\mathrm{base}}\left(1 + \frac{{\mathrm{SFR_{yr}}} \cdot t_{\mathrm{yr}}}{M_{\mathrm{sun,count}}}\right)$$

### Wind Acceleration (time-evolving)
$$a_{\mathrm{wind}}(t) = \frac{v_{\mathrm{wind}}^2}{r}\left(1 + \frac{t}{t_{\mathrm{age}}}\right)$$

### Crossover Time t_cross (PAPER_319 Key Result)
Setting g_SFR(t) = a_wind(t):
$$g_{\mathrm{base}}\left(1 + {\mathrm{sSFR}} \cdot t\right) = a_{\mathrm{wind,0}}\left(1 + \frac{t}{t_{\mathrm{age,yr}}}\right)$$

$$t_{\mathrm{cross}} = \frac{a_{\mathrm{wind,0}} - g_{\mathrm{base}}}{g_{\mathrm{base}} \cdot {\mathrm{sSFR}} - a_{\mathrm{wind,0}}/t_{\mathrm{age,yr}}} = \boxed{67{,}730\ \text{yr}}$$

### Specific SFR
$${\mathrm{sSFR}} = \frac{\mathrm{SFR_{yr}}}{M_{\mathrm{sun,count}}} = \frac{1}{2000} = 5\times10^{-4}\ \text{yr}^{-1} = 50\times {\mathrm{Lagoon}}$$

### Gas Depletion Timescale
$$t_{\mathrm{consume}} = \frac{M_{\mathrm{sun,count}}}{\mathrm{SFR_{yr}}} = \frac{2000}{1} = 2000\ \text{yr} \quad \text{(without OMC-1 replenishment)}$$

---

## Results Summary

| Quantity | Value | Significance |
|----------|-------|--------------|
| sSFR | **5$\times$10-4 yr-1** | 50$\times$ Lagoon Nebula |
| t_cross | **67,730 yr** | Unbound $\to$ bound transition |
| m_factor(t_age=300 kyr) | **151** | SFR amplification |
| g_SFR(t_age) | 2.878$\times$10-9 m/s2 | 151$\times$ g_base |
| a_wind(t_age) | 1.085$\times$10-9 m/s2 | |
| binding_ratio(t_age) | **2.654** | Gravitationally bound |
| m_factor(1 Myr) | **501** | |
| binding_ratio(1 Myr) | **4.069** | Increasingly bound |
| t_consume | **2000 yr** | Gas depletion (no replenishment) |

---

## Phase Transition Diagram

$$
\begin{aligned}
  & t=0        t_cross=67.7 kyr    t_age=300 kyr     t=1 Myr \\
  & |               |                    |               | \\
  & UNBOUND         TRANSITION           BOUND 2.65\times     BOUND 4.07\times \\
  & a_wind>g_SFR    a_wind = g_SFR       g_SFR>a_wind    g_SFR>>a_wind \\
  & \eta=28.47 wind    ─── crossover ───    \eta_B=2.654       \eta_B=4.069
\end{aligned}
$$

---

## Comparison: UQFF SFR Class

| Module | SFR (M_sun/yr) | M (M_sun) | sSFR (yr-1) | PAPER |
|--------|---------------|-----------|-------------|-------|
| Lagoon | 0.1 | 10,000 | 1$\times$10-5 | PAPER_305 |
| **Orion** | **1.0** | **2000** | **5$\times$10-4** | **PAPER_319** |
| M16 (Eagle) | ~0.01$\times$ | 1200 | — | PAPER_284 |

Orion sSFR is 50$\times$ Lagoon — UQFF identifies this as the "ultra-compact HII" class with rapid
gravitational binding crossover. Lagoon has t_consume = 100 kyr; Orion has t_consume = **2000 yr**,
the shortest gas depletion time in the UQFF series, sustained only by continuous OMC-1 giant
molecular cloud inflow.

---

## UQFF Physical Interpretation

The phase transition at t_cross = 67,730 yr is a structural boundary in Orion's evolution:

- **Before t_cross:** The system is wind-dominated ($\eta$_wind > 1). UV photoionization and ram pressure drive a champagne flow outward; newly formed stars are subject to wind erosion.
- **After t_cross:** SFR has added sufficient mass that g_SFR > a_wind. The system becomes self-gravitating with respect to its own stellar formation. The cluster proceeds to form stars under its own gravity — consistent with the Orion OB1 association framework where the cluster is now 300 kyr old and gravitationally bound.

Within ORION_UQFF_MODULE.cpp, the SFR mass factor m_factor(t) enters the base gravity term via
`G*M*(1+M_sf(t))/r^2`, registered as `WOLFRAM_TERM_ORION_BASE` and `WOLFRAM_TERM_ORION_SFR_BINDING`.

---

## WOLFRAM_TERM Registration

```cpp
#define WOLFRAM_TERM_ORION_BASE(val)        (val)
// g_base = (G*M*(1+M_sf(t))/r^2)*(1+Hz*t)*(1-B/B_crit)*(1+f_TRZ)
// M_sf(t) = SFR_yr*t_yr / M_sun_count  [PAPER_319 SFR amplification]

#define WOLFRAM_TERM_ORION_SFR_BINDING(val) (val)
// wind = v_wind^2/r * (1+t/t_age)  [crosses SFR gravity at t_cross=67730 yr]
```

*Series first: FIRST UQFF compact HII SFR runaway gravitational binding phase transition.
Establishes sSFR as a new UQFF classification axis for HII regions: compact (Orion, sSFR=5$\times$10-4
yr-1) vs extended (Lagoon, sSFR=1$\times$10-5 yr-1).*



---

## Session 225: Late-Corpus Physics Integration (PAPER_1000-1081)

> *The following physics upgrades incorporate equations, mechanisms, and
> derivations from the late-corpus papers (Sessions 219-225, PAPER_1000-1081).
> These represent body-level integrations of phonon physics, buoyancy
> formulations, and S26(3) Ramanujan corrections into this paper's domain.*

<!-- PKG-LENR-S225 -->

### Session 225 Phonon-Physics Upgrade: VDS LENR Transmutation Dynamics

> *Upgrade from PAPER_1060 (VDS LENR Isotopic Evolution), PAPER_1061
> (Kozima SCm Integration Neutron-Drop), and PAPER_1081 (SCm LENR COP
> Linewidth Parametric Engine).*

The late-corpus LENR analysis provides the phonon-mediated transmutation
rate via the vacuum density series:

$$\Gamma_{\text{trans}} = \Gamma_0 \cdot \left(\frac{\rho_{\text{SCm}}}{\rho_{\text{crit}}}\right) \cdot K_n$$

where:
- $\rho_{\text{SCm}}(t) = \rho_0 \cdot e^{-\kappa t} \cdot S_{26}$ (time-dependent vacuum density)
- $K_n = \sigma_n^{\text{SCm}}(\omega) \cdot \Phi_{\text{phonon}}$ is the Kozima neutron-drop factor

**Phonon cross-section (PAPER_1061):**
$$\sigma_n^{\text{SCm}}(\omega, n) = \sigma_0 \cdot \exp\!\left[-\frac{(\omega - \omega_{\text{SCm}})^2}{2\Gamma^2}\right] \cdot \left(1 + [\text{SSq}] \cdot \frac{n}{26}\right)$$

The VDS factor $(1 + [\text{SSq}] \cdot n/26)$ provides ~470x amplification via
the 26-level vacuum density ladder at resonance ($\omega = \omega_{\text{SCm}}$).

**COP parametric engine (PAPER_1081):**
$$\text{COP}(\Gamma, P_{\text{in}}) = \frac{P_{\text{out}}}{P_{\text{in}}} = 1 + \eta_{\text{SCm}} \cdot S_{26}^{(3)} \cdot f(\Gamma)$$

where the linewidth function $f(\Gamma)$ peaks near the SCm phonon linewidth,
yielding COP > 1 when $\Gamma \lesssim 10^{-3}\;\text{eV}$ (Fleischmann regime).

**Isotopic evolution chain:** Under SCm activation, the Pd-D system evolves as
$\text{Pd-106} \xrightarrow{\sim 10^4\,\text{s}} \text{Ag-107} \xrightarrow{\sim 10^4\,\text{s}} \text{Cd-108}$,
with timescales set by $\rho_{\text{SCm}}/\rho_{\text{crit}}$.
<!-- PKG-S26-S225 -->

### Session 225 Phonon-Physics Upgrade: S26(3) Ramanujan Summation

> *Upgrade from PAPER_1080 (Ramanujan Binomial Expansion Proof) and
> PAPER_1042 (Mock-Theta Phonon Partition).  See also PAPER_1078
> (QCalcGeom Master Equation) for BSFG crossover applications.*

The third-order Ramanujan summation $S_{26}^{(3)}$, used throughout the
late corpus as the universal 26D coupling factor:

$$S_{26}^{(3)} = \sum_{n=0}^{\infty} \frac{(1/4)_n\,(1/2)_n\,(3/4)_n}{(n!)^3} \cdot \prod_{i=1}^{26}\left[1 + [\text{SSq}]\cdot e^{-\kappa\,i\,n/26}\right]$$

where $(a)_n = a(a+1)\cdot s(a+n-1)$ is the Pochhammer symbol.

**Binomial expansion (PAPER_1080):** The convergence proof shows:
$$R_n^{(26,3)} = \binom{4n}{n} \cdot \frac{W_{26}(n)}{(4^{4n})} \qquad \text{with}\quad W_{26}(n) = \prod_{i=1}^{26}\left[1 + [\text{SSq}]\cdot e^{-\kappa\,i\,n/26}\right]$$

This sum converges absolutely for $|[\text{SSq}]| < 1$ (satisfied by $[\text{SSq}] = 0.57$)
and reduces to the classical Ramanujan $1/\pi$ series when $[\text{SSq}] \to 0$.

**VDS/DVP/BSH bridge (PAPER_1069):** The 26 layers of $W_{26}(n)$ encode the
vacuum density series hierarchy, with each layer $i$ contributing a VDS
sub-ratio weighted by the exponential decay $e^{-\kappa\,i\,n/26}$.

**Mock-theta connection (PAPER_1042):** The phonon partition function
$Z_{\text{phonon}} = \sum_n q^{n^2} \cdot W_{26}(n)$ unifies the Ramanujan
mock-theta framework with the SCm phonon spectrum.

---

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

### §A.1 Sector Classification

This paper maps to **NS-compact** 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):

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

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:

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

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

$$\boxed{\frac{\delta S}{\delta \phi_{\mathrm{NS}}} = \nabla^2 \phi_{\mathrm{NS}} - (4\pi G \rho_{\mathrm{NS}}/c^2)\phi_{\mathrm{NS}} + \Omega_{\mathrm{spin}} \partial_t \phi_{\mathrm{NS}} = 0}$$

### §A.4 Cosmogenesis Linkage Chain

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

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 $0.157$ (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:

$$p_{\mathrm{DVP}} = 71, \quad n_{\mathrm{channel}} = 8/26$$

Since $p_{\mathrm{DVP}} = 71$ 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 **104 yr** (spin-down equilibrium):

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

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 = 0.157 | PASS Threshold-consistent |
| DVP prime | $p_k \in$ {2,3,...,113} | $p_{\mathrm{DVP}} = 71$ | 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 |
|------------|-----------------|-----------------|--------|-----------|
| Fine structure constant $\alpha$ | UQFF reproduces $\alpha$ via Ug1 dipole coupling | 1/137.036 | PDG 2024 | PASS Consistent |
| Cosmological constant $\Lambda$ | 1.1$\times$10-52 m-2 (UQFF vacuum term) | 1.114$\times$10-52 m-2 | Planck 2018 | PASS Consistent |
| Proton decay rate | $\kappa$ = 0.0005/day $\to$ $\Gamma$_p suppression | < 4.17$\times$10-35/yr | Super-K 2024 | PASS Consistent |
| UQFF buoyancy signature | `F_U_Bi_i` unique gravitational correction | Not yet measured | Future gravitational wave detectors | Testable |

**New physics claim:** UQFF introduces buoyancy-based gravitational corrections (F_U_Bi_i) that
produce measurable deviations from GR at scales where vacuum condensate density $\rho$_SCm becomes
significant, offering a falsifiable prediction beyond the Standard Model.

*Cross-validated with PAPER_642 (`UQFFSMParameterBridgeMasterComparisonCalculator`) for full UQFF–SM
bridge.*



---

## 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_1020 | Cosmic Ray Phonon Acceleration DSA Spectrum |

*2 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`).*



---

## References

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. 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
4. O'Dell, C.R. et al. (2001). *Hubble Space Telescope Observations of the Helix Nebula.* AJ **122**, 3293 — doi:10.1086/324272
