🌌 Quantum Constraint Framework (QCF) Simulation v4

Resolving Black Hole Singularities via Informational Thermodynamics

This repository contains the complete numerical simulation framework for the Quantum Constraint Framework (QCF), an extension to General Relativity designed to dynamically resolve spacetime singularities within black holes. Inspired by the postulates of Isomorphic Cosmic Equilibrium (ICE), QCF posits that a finite curvature ceiling ($K_{max} = 1/16$ in Planck units) is imposed on the interior geometry due to the saturation of the Bekenstein-Holographic entropy bound at the event horizon.

The accompanying script, v4_sim.py, calculates and visualizes critical physical signatures predicted by this framework across a vast mass spectrum ($10^9 \text{ kg}$ to $10^{31} \text{ kg}$).

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💡 Core Theoretical Insights (What This Paper Says)

The QCF resolves the classical GR breakdown ($K \to \infty$ as $r \to 0$) by introducing a mandatory spatial cutoff radius, $\mathbf{r_{cut}}$, derived from: $$\mathbf{r_{cut} = (192)^{1/6} r_s^{1/3} \ell_p^{2/3}}$$

This single constraint yields massive physical consequences:

• Singularity Elimination: Curvature ($K$) is capped at $K_{max}$ for all $r < r_{cut}$, replacing the point singularity with a finite, quantum core.
• Modified Energy Scale ($\mathbf{E_{max}}$): The maximum energy of emitted Hawking radiation shifts from the standard thermal scale ($k_B T_H$) to the much higher Quantum Cutoff Energy, $E_{max} = \hbar c / r_{cut}$.
• Altered Lifetimes: Due to suppression of high-energy particle emission, black hole evaporation times ($\tau$) are extended compared to standard GR predictions.

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💻 Simulation Capabilities (v4_sim.py)

The simulation script performs comprehensive numerical checks and generates seven figures visualizing the QCF predictions:

Key Outputs Demonstrated:

1. Energy Scale Comparison (Fig 1): Visualizing $E_{max}(M)$ against $k_B T_H(M)$ overlaid with Fermi-LAT and IceCube observational constraints.
2. Lifetime Scaling (Fig 2): Direct comparison of $\tau_{Standard}$ vs. $\tau_{QCF}$, showing how QCF extends the lifetime, especially for lighter PBHs.
3. Spectral Truncation (Fig 3): Shows the standard Planck spectrum being abruptly cut off by $E_{max}$ for a representative BH ($M=5 \times 10^{11} \text{ kg}$).
4. Curvature Ceiling (Fig 4 & Fig 7): Detailed visualization of how $K/K_{max}$ saturates at the cutoff radius, both in normalized and physical units ($\text{for } M_{\odot}$).
5. Phenomenological Shifts (Fig 6): Plots the fractional corrections to temperature ($\Delta T_H/T_H$) and QNM frequencies ($\delta\omega/\omega$).

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🚀 How To Run The Simulation

This project requires Python 3.9 or newer.

1. Clone the Repository:

   git clone https://github.com/andrewrodger73/QCF.git
   cd QCF_Paper_Repo

2. Install Dependencies:

   pip install numpy matplotlib

3. Execute the Simulation:

   python v4_sim.py

📁 Output Structure:

The simulation will create a /results/ directory containing all generated figures (PNG format):

• Fig1_Emax_observational.png
• Fig2_lifetime_comparison.png
• Fig3_spectrum_M5e11kg.png
• ... and so on, up to Fig7_summary_all_predictions.png.

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🧐 Quick Sanity Check (Unit Tests)

The script includes embedded unit tests that confirm key relations:

• ✅ Primordial cutoff radius ($M=10^{12} \text{ kg}$) is within $5%$ tolerance of theoretical expectation.
• ✅ The thermal energy scale for a test mass falls correctly within the GeV-TeV range expected from current observations.

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"The World isn't broken. We’re just running the wrong diagnostics." - Andrew Rodger (Author) 😉