QFunity – Complete List of Proof Requests

QFunity – Complete List of Proof Requests

This page compiles all testable predictions and proof requests from the QFunity framework, grouped by experimental nature (e.g., LHC, LIGO). Each entry includes a brief description, relevant equations, and a link to the corresponding page for details.

LHC (Large Hadron Collider) Predictions

High-Energy Physics Tests

Step 1: Muon g-2 Anomaly

Prediction: Muon g-2 anomaly from non-zero principle, matching Fermilab data within error bars: \(\Delta a_\mu \approx 2.5 \times 10^{-9}\).

\[\Delta a_\mu = -2 \cdot \frac{\epsilon^2_{\text{weak}}}{\ell_P^2} \approx 2.5 \times 10^{-9}\]

Link to Zero: The Forbidden Number

Step 2: Non-Local Correlations

Prediction: Non-local correlations at \(\epsilon \sim \ell_P\) in high-energy experiments, indicating EPT interactions. Hadron mass dependence on \(\epsilon\) at LHC energies.

\[\lambda_{\text{dB}} = \frac{h}{p} \left(1 + \frac{\ell_P^2}{\epsilon^2}\right)^{-1}\]

Link to Wave Nature

Step 3: MET and Soft Photons

Prediction: Missing transverse energy (MET) and soft photons (≥3σ deviation) from micro-EPT nucleation. Sterile neutrino excess.

\[\nabla \times \Omega_{\text{QF}} = \kappa \rho_{\text{vac}} \mathbf{v} \times \hat{\mathbf{s}}\]

Link to Micro EPTs

Step 4: Vacuum Decay MET Signature

Prediction: MET signature in vacuum decay tests: \(E_{\text{MET}} = 100–150 \, \text{GeV}\), with \(\chi^2 < 7.81\) (p=0.05).

\[\chi^2 = \sum \frac{(O_i – E_i)^2}{\sigma_i^2} < 7.81 \, (p = 0.05)\]

Link to Vacuum Decay

LIGO/Virgo (Gravitational Waves) Predictions

Gravitational Wave Anomalies

Step 1: Black Hole EPT Frequency Shifts

Prediction: \(\epsilon\)-dependent shifts in gravitational wave frequencies from black hole mergers, testable with LIGO/Virgo data.

\[f_{\text{GW}} \propto \frac{\omega}{\epsilon^2}, \quad \Delta f \sim \frac{\partial f_{\text{GW}}}{\partial \epsilon} \Delta \epsilon\]

Link to Black Hole EPT

Step 2: White Dwarf Merger Torsion

Prediction: High-frequency torsion oscillations in white dwarf mergers (LISA). « Staircase » brightening pre-explosion and spiral nebula patterns.

\[M_{\text{eff}} = M_{\text{Ch}} \times (1 + \alpha_{\text{QF}} \cdot \omega^2)\]

Link to White Dwarf Mergers

Step 3: Neutron Star Reconfiguration

Prediction: Gravitational wave anomalies from neutron star reconfiguration phases, detectable with LISA and Chandra.

\[\tau = \hbar / \Delta E_{\text{QF}}\]

Detectable with:

  • LISA: Torsion-induced GW dispersion (\(\delta v/c \sim 10^{-6}\) for \(\kappa=10^{-3}\))
  • Chandra: X-ray modulation at \(f_{\text{QF}} = \kappa c^3/GM\)

Link to Neutron Star Reconfiguration

JWST (James Webb Space Telescope) Predictions

Cosmic Evolution and Spectral Analysis

Step 1: Spectral Line Broadening

Prediction: Spectral line broadening based on detector resolution, observed in Hubble vs JWST comparisons.

\[\Delta \lambda = \lambda_0 \cdot \left( \frac{\epsilon_{\text{obs}}}{\lambda_0} \right)^{1/3}\]

Link to Observer-Scale Dependency

Step 2: Early Universe Metals

Prediction: Metals (Fe, C, O) at \(z > 10\) from micro-bangs. Massive early galaxies via fractal acceleration. Fe/H \(\sim 10^{-4}\).

\[\frac{\text{Fe}}{\text{H}} \sim \exp\left(-\frac{\epsilon_{\text{hadron}}}{\epsilon_{\text{electroweak}}}\right)\]

Link to JWST Discoveries

Step 3: Vacuum Decay Spectral Shifts

Prediction: Spectral stability tests for \(\epsilon\)-dependent shifts in vacuum decay context.

\[\Delta \lambda \propto \epsilon^{1/3}\]

Link to Vacuum Decay

Step 4: V883 Orionis Molecules

Prediction: 26 complex organic molecules in V883 Orionis protoplanetary disk. Enhanced COM abundance near torsion vortices.

\[P_{\text{COM}} \sim \epsilon^{1/3} \times \exp(-E_{\text{bind}}/kT)\]

Spectral signatures at 230 GHz (ALMA) and 10-20 \(\mu\text{m}\) (JWST MIRI)

Link to V883 Orionis

CMB (Cosmic Microwave Background) Predictions

Cosmic Background Signatures

Step 1: B-Mode Polarization

Prediction: B-mode polarization revealing rotational EPT signatures with fractal dimension \(D_f \approx 2.7\). Anomalies from large-scale alignments.

\[D_f \approx 2.7\]

Link to The Fractal Multiverse

Step 2: Holographic White Noise

Prediction: Low-ℓ T and E spectra from holographic white noise with \(\mathcal{P} \lesssim 9 \times 10^{-14}\).

\[\mathcal{P} \lesssim 9 \times 10^{-14}\]

Link to Zero Modes

Step 3: Primordial Monopole

Prediction: Dipole/quadrupole anisotropies from primordial monopoles with \(d_{\text{max}} \propto Q^{1/4}\).

\[d_{\text{max}} \propto Q^{1/4}\]

Link to Zero Modes

Step 4: Fractal Power Spectrum

Prediction: Fractal power spectrum with \(\mathcal{F}_{\text{fractal}}(\ell) \propto \ell^{-3/2} \cdot \cos(2\pi \epsilon \ell / r_H)\).

\[\mathcal{F}_{\text{fractal}}(\ell) \propto \ell^{-3/2} \cdot \cos\left(2\pi \epsilon \ell / r_H\right)\]

Link to Zero Modes

Step 5: Micro-Bang Fluctuations

Prediction: CMB fluctuations from micro-bangs with \(\Delta T/T \sim \epsilon^2\).

\[\Delta T/T \sim \epsilon^2\]

Link to Micro EPTs

Step 6: Echoes of Torsion

Prediction: CMB anisotropies as echoes of \(\hat{\mathbb{B}}_\epsilon \Psi\).

\[\hat{\mathbb{B}}_\epsilon \Psi\]

Link to JWST Discoveries

IceCube (Neutrino Observatory) Predictions

Neutrino Anomalies

Step 1: Primordial Neutrino Spectra

Prediction: Primordial neutrinos with anomalous energy spectra carrying innate EPT information. Sterile neutrino excess from oscillations.

\[P(x \in [-\epsilon/2, \epsilon/2]) = \epsilon \cdot \rho(0)\]

Link to Micro EPTs

Step 2: Supernova Neutrinos

Prediction: Neutrinos from supernovae or early universe with near-pristine information.

\[c’ = \frac{\ell_P \sqrt{\omega_{\text{eff}}’}}{\sqrt{\Lambda}}\]

Link to Emergence of Causality, Light, and Information

Other Experiments (Fermilab, Casimir, Neutron Interferometry, etc.) Predictions

Diverse Experimental Tests

Step 1: Fermilab Muon g-2

Prediction: Muon g-2 anomaly matching Fermilab measurements within error bars.

\[\Delta a_\mu \approx 2.5 \times 10^{-9}\]

Link to Zero: The Forbidden Number

Step 2: Casimir Polarization

Prediction: Spontaneous polarization in Casimir experiments from quantum vacuum fluctuations.

\[\Omega_{\text{QF}} = \frac{\kappa E_{\text{coll}}}{\epsilon^2}\]

Link to Micro EPTs

Step 3: Neutron Interferometry Torsion

Prediction: Torsion signatures in neutron interferometry. Deviations in de Broglie wavelength.

\[\lambda_{\text{dB}} = \frac{h}{p} \left(1 + \frac{\ell_P^2}{\epsilon^2}\right)^{-1}\]

Link to Wave Nature

Step 4: DNA Raman Spectra

Prediction: Fractal Raman spectra in DNA vibrations. Spectral line broadening in laboratory measurements.

\[\Delta \lambda \propto \epsilon^{1/3}\]

Link to Gauge Unification

Step 5: X-Ray Pulsations

Prediction: X-ray pulsations from neutron star phases.

\[\nu_{\text{pulse}} \sim 10^2 \, \text{Hz}\]

Detectable with: Chandra X-ray modulation at \(f_{\text{QF}} = \kappa c^3/GM\)

Link to Neutron Star Reconfiguration

Return to Hypotheses