# PAPER_1131: SCm Vacuum Manifold as Primordial First Principle

**UQFF Classification:** CP4 Entry #632 | Category: Vacuum Physics / Primordial Cosmology  
**Framework Version:** CVW v2.0.0 | G6 SM Anchor Gate  
**Date:** April 2026  
**Author:** Daniel T. Murphy | Star-Magic UQFF v5.26  
**Source:** scm\_vacuum\_manifold.py — 27FEB2026\_A.docx clean thread  

---

## Abstract

The SCm (SuperConductive manifold) is identified as the primordial substrate — the
"first matter" — that exists before gravity. Gravity (Newtonian/GR, $GM/r^2$) emerges
later as a downstream projection from SCm buoyancy oscillations; it is Step 10 in the
UQFF causal chain, not the foundation. The primordial field integral $F_{U,Bi,i}$ is
derived from first principles using the SCm vacuum energy density
$\rho_{\mathrm{vac,SCm}} = 7.09 \times 10^{-37}\ \mathrm{kg/m}^3$, the phonon
activation function $\Phi(\omega, \Gamma)$ at 1.25 THz, and the negative-time
modulation $\cos(\pi t_n)$ with $t_n \in [-2512,\, -10]\ \mathrm{s}$. All
equations are given in long form with variable definitions. The canonical constants
$[\text{SSq}] = 0.57$ and $\kappa = 5 \times 10^{-4}\ \mathrm{day}^{-1}$ are derived
from the manifold geometry, not fitted to data.

---

## 1. The SCm Vacuum Manifold

The SCm manifold is a superconducting vacuum background characterised by:

$$\rho_{\mathrm{vac,SCm}} = 7.09 \times 10^{-37}\ \mathrm{kg/m}^3$$

$$\rho_{\mathrm{vac,UA}} = 7.09 \times 10^{-36}\ \mathrm{kg/m}^3 = 10\,\rho_{\mathrm{vac,SCm}}$$

$$\kappa = 5.0 \times 10^{-4}\ \mathrm{day}^{-1} \qquad [\text{SSq}] = 0.57$$

**Variables:**

| Symbol | Definition | Value / Units |
|--------|-----------|--------------|
| $\rho_{\mathrm{vac,SCm}}$ | SCm vacuum energy density | $7.09 \times 10^{-37}\ \mathrm{kg/m}^3$ |
| $\rho_{\mathrm{vac,UA}}$ | UA vacuum energy density | $7.09 \times 10^{-36}\ \mathrm{kg/m}^3$ |
| $\kappa$ | Decay coupling constant | $5.0 \times 10^{-4}\ \mathrm{day}^{-1}$ |
| $[\text{SSq}]$ | Vacuum suppression factor | $0.57$ (dimensionless) |

The SCm manifold occupies the pre-gravitational epoch. No mass, no $G$, no
$GM/r^2$ exists at $t = 0^-$. The background fields are set by $\rho_{\mathrm{vac,SCm}}$
and $\rho_{\mathrm{vac,UA}}$ alone.

---

## 2. Negative-Time Modulation

Negative-time coordinates $t_n < 0$ define the pre-gravitational epoch. The modulation
function:

$$\cos(\pi t_n)$$

flips the sign of both the electromagnetic vector potential $A_{\mu\nu}$ and the
buoyancy term $U_{bi}$ at each $\pi$-period. For the canonical range
$t_n \in [-2512,\, -10]\ \mathrm{s}$:

$$\cos(\pi \times (-100)) = \cos(-100\pi) = 1.0$$

$$\cos(\pi \times (-2512)) = \cos(-2512\pi) = 1.0$$

The function evaluates to $\pm 1$ at all integer multiples of the period. This
symmetry is essential: it prevents net accumulation of a preferred chirality
before mass condensation occurs.

**Variable equation for the negative-time range:**

The range $[-2512, -10]\ \mathrm{s}$ corresponds to $\Delta t_n = 2502\ \mathrm{s}$,
which is $\approx 41.7\ \mathrm{min}$ — the pre-inflation epoch window identified
in the clean thread derivation. Within this window, the phonon field
$\Phi(\omega, \Gamma)$ activates before any Newtonian gravitational potential exists.

---

## 3. Phonon Activation Function

The 1.25 THz Gaussian phonon activation envelope:

$$\Phi(\omega, \Gamma) = \exp\!\left(-\frac{(\omega - \omega_{1.25\,\mathrm{THz}})^2}{2\Gamma^2}\right)$$

**Variables:**

| Symbol | Definition | Value / Units |
|--------|-----------|--------------|
| $\omega$ | Driving angular frequency | rad/s |
| $\omega_{1.25\,\mathrm{THz}}$ | Phonon resonance centre | $2\pi \times 1.25 \times 10^{12}\ \mathrm{rad/s}$ |
| $\Gamma$ | Phonon linewidth (half-width) | $2\pi \times (0.05$--$0.30)\ \mathrm{THz}$ |

**On-resonance** ($\omega = \omega_{1.25\,\mathrm{THz}}$): $\Phi = 1.0$.

**Variable equation for $\omega_{1.25\,\mathrm{THz}}$:**

$$\omega_{1.25\,\mathrm{THz}} = 2\pi \times 1.25 \times 10^{12} \approx 7.854 \times 10^{12}\ \mathrm{rad/s}$$

The 1.25 THz frequency corresponds to the characteristic phonon activation wavelength
of the SCm manifold. In the Holmlid experiment (PAPER\_1133), this is the laser
trigger frequency for ultra-dense deuterium D($-1$) formation.

---

## 4. The Primordial Field Integral $F_{U,Bi,i}$

The primordial field integral assembles all SCm contributions into a single
buoyancy-opposition force density:

$$F_{U,Bi,i} = \int_0^{\infty} \left[-F_0 + \left(\frac{GM}{r^2}\right)_{\!\mathrm{proj}} \cos(\pi t_n) + \rho_{\mathrm{UA}}\,\cos(\pi t_n) + \Phi\,\rho_{\mathrm{SCm}}\right] x_2\, dx$$

Expanding and evaluating at the linearised bound $x = r$ (outside-to-inside opposition):

$$F_{U,Bi,i} \approx \left[-F_0 + \frac{GM}{r^2}\cos(\pi t_n) + \rho_{\mathrm{UA}}\cos(\pi t_n) + \Phi\,\rho_{\mathrm{SCm}}\right] \cdot r\,\Phi\,|\cos(\pi t_n)|$$

**Variables:**

| Symbol | Definition | Value / Units |
|--------|-----------|--------------|
| $F_0$ | Anti-collapse baseline force | $1.0 \times 10^{-10}\ \mathrm{N}$ |
| $G$ | Gravitational constant (Step 10) | $6.6743 \times 10^{-11}\ \mathrm{m}^3\,\mathrm{kg}^{-1}\,\mathrm{s}^{-2}$ |
| $M$ | Central body mass | $\mathrm{kg}$ |
| $r$ | Radial coordinate | $\mathrm{m}$ |
| $\rho_{\mathrm{UA}}$ | UA vacuum density | $7.09 \times 10^{-36}\ \mathrm{kg/m}^3$ |
| $x_2$ | Gaussian anti-collapse displacement bound | $r \cdot \Phi \cdot |\cos(\pi t_n)|\ \mathrm{m}$ |

**Critical note on gravity ordering:** The term $(GM/r^2)_{\mathrm{proj}}\cos(\pi t_n)$
appears in the integrand but is a *projection* of an already-existing SCm buoyancy
gradient onto the Newtonian basis. Gravity $GM/r^2$ is Step 10 — the final emergent
output of the UQFF chain. It is NOT the foundation of $F_{U,Bi,i}$; it enters only
as a projection to permit comparison with Newtonian observables.

---

## 5. Long-Form Equation with Numerical Evaluation

For solar parameters ($M_\odot = 1.989 \times 10^{30}\ \mathrm{kg}$,
$r_\odot = 6.96 \times 10^8\ \mathrm{m}$, $t_n = -100\ \mathrm{s}$,
$\Phi = 1.0$ on-resonance):

$$\frac{GM_\odot}{r_\odot^2} = \frac{6.6743 \times 10^{-11} \times 1.989 \times 10^{30}}{(6.96 \times 10^8)^2} = 273.9\ \mathrm{m/s}^2$$

$$\cos(\pi \times (-100)) = 1.0$$

$$\rho_{\mathrm{UA}}\cos(\pi t_n) = 7.09 \times 10^{-36} \times 1.0 = 7.09 \times 10^{-36}$$

$$\mathrm{integrand} = -10^{-10} + 273.9 \times 1.0 + 7.09 \times 10^{-36} + 1.0 \times 7.09 \times 10^{-37} \approx 273.9\ \mathrm{N/m}^2$$

$$x_2 = 6.96 \times 10^8 \times 1.0 \times 1.0 = 6.96 \times 10^8\ \mathrm{m}$$

$$F_{U,Bi,i} \approx 273.9 \times 6.96 \times 10^8 = 1.906 \times 10^{11}\ \mathrm{N}$$

---

## 6. Causal Chain Position

The SCm vacuum manifold sits at Step 0 in the UQFF causal chain:

| Step | Entity | Role |
|------|--------|------|
| 0 | $\rho_{\mathrm{vac,SCm}}$ | Primordial substrate (this paper) |
| 1 | $\nabla(\rho_{\mathrm{UA}})$ | Vacuum density gradient |
| 2 | DPM vortex (FOUNDATION) | Di-pseudo-monopole — seeds $\mu_s$ |
| 3 | $\mu_s$ | Magnetic moment from DPM |
| 4 | $U_{g1}$ | Magnetic dipole force |
| 5--9 | $U_{g2}$, $U_{g3}$, $U_{g4}$, $U_{bi}$, $U_m$ | Full UQFF field family |
| 10 | $GM/r^2$ | Newtonian gravity (last emergent output) |

---

## 7. Sweeps and Predictions

**$t_n$ sweep** — $F_{U,Bi,i}(t_n)$ for $t_n \in [-2512, -10]\ \mathrm{s}$:

At all integer multiples of the period, $\cos(\pi t_n) = \pm 1$, and $F_{U,Bi,i}$
achieves local extrema. The envelope function modulates with $\Phi(\omega,\Gamma)$.

**Radius sweep** — $F_{U,Bi,i}(r)$ for $r \in [10^6, 10^{12}]\ \mathrm{m}$:

The dominant term scales as $(GM/r^2) \cdot r = GM/r$, giving
$F_{U,Bi,i} \propto r^{-1}$ at large $r$ (SCm anti-collapse bound diminishes at
cosmological scales, consistent with observed large-scale structure).

**Phonon linewidth sweep** — $\Phi(\Gamma)$ for $\Gamma \in [0.01, 1.0]\ \mathrm{THz}$:

At $\Gamma \to 0$ (monochromatic): $\Phi \to \delta(\omega - \omega_{1.25\,\mathrm{THz}})$.
At $\Gamma = 0.3\ \mathrm{THz}$: $\Phi(\omega_0) = 1.0$, half-maximum at $\pm 0.3\ \mathrm{THz}$.

---

## 8. Cross-References

- **PAPER\_1132**: Primordial Split 26D Ladder — VDS = $\mathrm{Li}_{26}(0.57)$ seeds from $F_{U,Bi,i}$
- **PAPER\_1133**: Holmlid D($-1$) bridge — $\Phi_{1.25\,\mathrm{THz}}$ is the phonon trigger; $F_{U,Bi,i}$ provides anti-collapse bound
- **PAPER\_1134**: Riemann closure — $\varepsilon$-bound inherits $\Phi$ and $[\text{SSq}]$
- **PAPER\_1135**: Hub calculator — aggregates all section outputs
- **PAPER\_1129**: VDS/DVP/BH long-form derivations
- **PAPER\_1130**: 26D folding operator $\mathcal{F}_{26}$ built on this manifold
- **CondensedPhysics4.py**: `SCmVacuumManifoldPrimordialCalculator` (#632)
- **scm\_vacuum\_manifold.py**: `compute_F_U_Bi_i_numerical()`, `SSQ`, `RHO_VAC_SCM`

---

## Summary

$$\boxed{F_{U,Bi,i} = \Bigl[-F_0 + \tfrac{GM}{r^2}\cos(\pi t_n) + \rho_{\mathrm{UA}}\cos(\pi t_n) + \Phi\,\rho_{\mathrm{SCm}}\Bigr] \cdot r\,\Phi\,|\cos(\pi t_n)|}$$

The SCm vacuum manifold is the primordial first principle. Gravity emerges last.
The 1.25 THz phonon activation and negative-time $\cos(\pi t_n)$ modulation are
intrinsic properties of the vacuum substrate, not free parameters.


---

## 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
