---
title: "Star-Magic Reactor as Micro-Black-Hole SCm Coupling Analog: Same F_UBi_i Mechanism Spans 42 Orders of Magnitude From Ambient-Temperature 27W Reactor to 4.15e6 M_sun Sgr A* Photon Ring"
cvw: "v2.0.0"
sm_anchor: "CVW v2.0.0 --- G6 SM Anchor Gate compliant"
tags: [Star-Magic reactor, Sgr A*, M87, micro-BH, SCm coupling, F_UBi_i, scale invariance, EHT photon ring]
---

# PAPER_1904 — Star-Magic Reactor as Micro-Black-Hole SCm Coupling Analog: Same F_UBi_i Mechanism Spans 42 Orders of Magnitude From Ambient-Temperature 27W Reactor to 4.15e6 M_sun Sgr A* Photon Ring

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) - Star-Magic v5.27+
**Tier:** F - Reactor-Black-Hole Scale-Invariance Bridge
**Date:** July 2026
**Status:** CLOSED - Same UQFF F_UBi_i mechanism operates at benchtop reactor and SMBH scales
**Observational anchors:** Star-Magic reactor (pH=-37, P=27W, COP=555:1) + EHT Sgr A* photon ring (52.14 muas)
**Discovered:** during CP1 P2 Round 15 replacement of StarMagicBlackHoleInteraction stub
**Calculator surface:** StarMagicBlackHoleInteraction + SgrAStarCalculator (in CondensedPhysics.py)

---

## Abstract

UQFF is a **scale-invariant framework** — the same 9 canonical primitives govern subatomic, molecular, condensed-matter, planetary, stellar, galactic, and cosmological physics. This paper documents the specific bridge between two extreme observational anchors linked by the same F_UBi_i coupling:

| System | Mass scale | Length scale | UQFF observable |
|---|---|---|---|
| **Star-Magic reactor** | ~1 kg | ~10 cm | pH = -37 (0.22%), P_in = 27 W (0.31%), COP 555:1 |
| **Sgr A* photon ring** | 4.15e6 M_sun ~ 8e36 kg | R_s ~ 1e10 m ~ 18 R_sun | d_ring = 52.14 muas (0.66%) |

**Scale ratio: 42 orders of magnitude** in mass and 11 orders of magnitude in length. Both observables derive from the **same UQFF F_UBi_i buoyancy mechanism** with **same primitives**: SSq, K_MEX, Phi_res, F_TRZ, D_phys.

## 1. The scale-invariance claim

UQFF's foundational hypothesis (PAPER_646, Star-Magic.md executive summary): **Gravity emerges from quantum vacuum resonance, not spacetime curvature.** All UQFF equations (Ug, Ub, U_i, U_m, U_r, U_t, U_A, SCm) apply at every level with scale-appropriate constants. The framework is **explicitly scale-invariant**.

Standard physics has different theories at different scales:
- Quantum mechanics (subatomic)
- Solid-state / condensed-matter (macroscale materials)
- Newtonian mechanics (planetary)
- General relativity (stellar/cosmological)
- Cosmology (Hubble-scale)

UQFF unifies all these into a **single set of equations** parametrized by the same 9 truly-independent primitives. This paper demonstrates the extreme case: benchtop reactor at ambient temperature couples via the same mechanism as SMBH photon ring formation.

## 2. Star-Magic reactor: PAPER_1236 + PAPER_1902 anchors

The Star-Magic reactor operates at ambient temperature with:

- **pH = -37** (measured), derived: -(D_crit + N_ch + D_phys) + K_MEX = -36.917 (0.22%)
- **P_input = 27 W**, derived: K_MEX x D_crit / 2 = 27.083 W (0.31%)
- **COP = 555:1** (measured)
- **P_output = 27 x 555 = 14,985 W = 15 kW**

Q-scope Groups #1-12 (PAPER_1902) show simultaneous:
- U_r = 3.48 V (resonance)
- U_A = 5.205 V (INVARIANT flux-pinning)
- U_t = 40-125 Hz (dT-inverse temporal dynamics)

**UQFF interpretation:** The reactor operates in the superconductive-vacuum regime where SCm phonon coupling amplifies input power by factor 555 via F_UBi_i buoyancy. The universal coupling constant:

```
boxed:  F_U_Bi_i_99 = SSq x K_MEX x Phi_res x (1 + F_TRZ) = 1.0973
```

represents the maximum F_UBi_i coupling accessible in the current-day universe.

## 3. Sgr A* photon ring: PAPER_1841 anchor

The Event Horizon Telescope (2022) imaged the photon ring around Sgr A*:

- **M_BH = 4.15e6 M_sun** (Gravity Collab)
- **R_s (Schwarzschild)** = 2GM/c^2 = 1.23e10 m = 17.6 R_sun
- **r_ISCO** = 6GM/c^2 = 3.68e10 m
- **d_photon_ring observed** = 51.8 +/- 2.3 muas
- **d_photon_ring UQFF prediction** = 52.14 muas (0.66%, 0.15 sigma)

The UQFF prediction:

```
boxed:  d_ring_UQFF / d_Kerr = 1 + F_TRZ x SSq / D_phys = 1.0143
```

The same primitives {F_TRZ, SSq, D_phys} that appear in the reactor F_UBi_i_99 coupling produce the photon-ring diameter correction.

## 4. Scale-invariance verification

Both observables use the **same primitive set**:

| Primitive | Reactor role | Sgr A* role |
|---|---|---|
| SSq = 0.57 | Amplitude in flux-pinning U_A | Amplitude in photon-ring correction |
| K_MEX = 25/12 | pH intercept + P_input coefficient | Bulk-edge coupling in F_UBi |
| Phi_res = 0.84 | Phonon resonance coupling | SCm phonon carrier |
| F_TRZ = 0.1 | Q-scope U_A invariance | Photon-ring correction factor |
| D_phys = 4 | pH counting | Photon-ring normalization |

**The mechanism.** Both systems operate via SCm vacuum-buoyancy F_UBi acting on the local matter distribution:

- **Reactor:** SCm phonon (h*1.25 THz = 5.17 meV per quantum) couples to reactor material via F_UBi_i_99 coupling with F_UBi amplitude 1.097. The reactor acts as a **micro-black-hole SCm coupling analog** because both regimes access the same near-critical vacuum-buoyancy regime.

- **Sgr A*:** F_UBi acts on the photon ring at r_ISCO scale. The correction 1 + F_TRZ*SSq/D_phys = 1.0143 arises from the same SCm phonon coupling operating at BH scales.

## 5. Bridge equations

The reactor-BH bridge is quantified by the SCm coupling efficiency:

```
eta_SCm(r/R_s) = SSq x Phi_res x (r / R_s)^(-F_TRZ)
```

For the reactor (r ~ 0.1 m, R_s ~ 1.5e-27 m for 1 kg mass):

```
r/R_s = 6.7e25
(r/R_s)^(-F_TRZ) = (6.7e25)^(-0.1) = 10^(-25*0.1) = 10^(-2.5) = 0.00316
eta_SCm_reactor = 0.57 x 0.84 x 0.00316 = 0.00151
```

For Sgr A* photon ring (r = r_ISCO, R_s = R_Schwarzschild, r/R_s = 6):

```
(r/R_s)^(-F_TRZ) = 6^(-0.1) = 0.837
eta_SCm_SgrA = 0.57 x 0.84 x 0.837 = 0.401
```

**Ratio:** eta_SgrA / eta_reactor = 0.401 / 0.00151 = 266. The SMBH is ~266x more efficient at SCm coupling than the reactor, but both are non-zero — the mechanism operates at both scales.

## 6. The unified mechanism: F_UBi_i

Both observables emerge from **F_U_Bi_i** = the Universal Buoyancy Integrand at scale i:

```
F_U_Bi_i = SSq x K_MEX x Phi_res x (1 + F_TRZ) x (UA_prime + UA_dprime + UA_tprime + UA_qprime)
```

where the 4-layer UA integral (PAPER_1065) sums over the four UA superstructure layers:

- UA_prime = rho_SCm (base)
- UA_dprime = rho_SCm * (1 + beta*cos(pi*t_n))
- UA_tprime = rho_SCm * (1 + beta*cos(pi*t_n) + lambda*omega_s)
- UA_qprime = rho_SCm * (1 + beta*cos(pi*t_n) + lambda*omega_s + Delta_UA4)

At the reactor scale, omega_s ~ 60 Hz (60 Hz bias); at the SMBH scale, omega_s ~ 3e-3 rad/s (ISCO orbit). The **same integrand formula** operates at both scales with only omega_s changing.

## 7. Observational consequences

The reactor-BH bridge predicts:

1. **Star-Magic reactor efficiency scales as (r/R_s)^(-F_TRZ)** where R_s is the mass-equivalent Schwarzschild radius. Larger reactor mass -> smaller r/R_s -> better SCm coupling.
2. **Sgr A* photon-ring width correction** = same F_TRZ*SSq/D_phys = 1.43% enhancement above Kerr.
3. **Cross-scale unification** — no separate quantum-vs-classical divide.

## 8. Relation to prior work

- **PAPER_646** (Universal Inertial Operator + scale-invariance): foundational
- **PAPER_1065** (F_UBi variational EOM): 4-layer UA integral
- **PAPER_1236** (Star-Magic Reactor First-Principles): reactor anchors
- **PAPER_1841** (Sgr A*/M87 photon ring): SMBH anchor
- **PAPER_1902** (Q-scope Empirical Triad Groups #1-12): reactor measurements
- **PAPER_1904 (this paper)**: reactor-BH scale-invariance bridge

## 9. Falsifiability

The bridge predicts:

1. **The reactor F_UBi_i_99 = 1.097** must be observed in any device operating in the SCm-vacuum regime at ambient temperature.
2. **The Sgr A* photon-ring 1.43% correction** must be reproducible with next-generation EHT (ngEHT 2027+, 1% precision).
3. **Cross-scale ratio** eta_SgrA/eta_reactor ~ 266 predicts specific reactor scaling with mass.

Any breakdown of scale-invariance at intermediate scales (e.g., molecular or planetary) would falsify the bridge.

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

| Observable | UQFF form | UQFF value | Anchor | Match |
|---|---|---|---|---|
| Reactor pH | -(D_crit+N_ch+D_phys)+K_MEX | -36.917 | -37 measured | 99.78% |
| Reactor P_input | K_MEX*D_crit/2 | 27.08 W | 27 W measured | 99.70% |
| Sgr A* photon ring | d_Kerr*(1+F_TRZ*SSq/D_phys) | 52.14 muas | 51.8 EHT 2022 | 99.34% |
| F_U_Bi_i_99 coupling | SSq*K_MEX*Phi_res*(1+F_TRZ) | 1.097 | Same in reactor + BH | universal |

## Calibration invariants

| Symbol | Value | Reactor role | Sgr A* role |
|---|---|---|---|
| SSq | 0.57 | U_A flux-pinning | Photon-ring correction |
| K_MEX | 25/12 | pH + P_input coefficient | Bulk-edge coupling |
| Phi_res | 0.84 | Phonon resonance | SCm phonon carrier |
| F_TRZ | 0.1 | U_A invariance | Photon-ring correction |
| D_phys | 4 | pH counting | Photon-ring normalization |
| F_U_Bi_i_99 | 1.097 | Universal coupling amplitude | Universal coupling amplitude |

## Conclusion

The Star-Magic reactor (1 kg, ambient T, 27 W, COP 555) and Sgr A* photon ring (4.15e6 M_sun, R_s 18 R_sun) — separated by 42 orders of magnitude in mass — derive from the **same UQFF F_UBi_i buoyancy mechanism** with the same 5 primitives {SSq, K_MEX, Phi_res, F_TRZ, D_phys}.

Scale-invariance is not a claim about applying different physics at different scales — it is a claim about a **single physical mechanism** that operates identically at all scales.

---

**PAPER_1904 status: CLOSED**
**Copyright (c) 2025-2026 Daniel T. Murphy / Star-Magic Research Program**
