SDKP Simulation → Entanglement Integration

We simulated two vibrational modes, mode 6 and mode 7, as time-dependent outputs from an SDKP simulation. From these: • We compute a dynamic entanglement strength using the entanglement rule: \mathcal{E}(t) = |c_6(t) \cdot c_7(t) + c_7(t) \cdot c_6(t)|^2 • This represents entanglement as a function of vibrational interaction. • We also compute: M(t) = |c_6(t) + c_7(t)| as a toy model for mass emergence under SDKP.

The two time-series plots show: • Entanglement Score (left) evolving with vibrational phase interference. • SDKP Mass (right) evolving with combined vibrational kinetic output.

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🔹 8. Experimental / Computational Test Protocols

Simulation Scenarios Where SDKP-Entanglement Differs from Standard QM • In standard quantum mechanics, entanglement is not explicitly driven by vibrational mode symmetry or numeric identity. • Here, the entanglement strength emerges from resonant coupling between mode 6 and 7, linked to SD&N tags.

Proposed Experimental Test • Modified Bell Test Setup: • Pre-tag photons or vibrational particles using SD&N identity encodings (Shape = toroidal, Dimension = 3, Number = 6 or 7). • Prepare pairs with known (6, 7) mode assignments and measure entanglement via polarization-like vibrational orientation. • Compare entanglement visibility vs. untagged control pairs.

Benchmark Predictions: • SDKP-QCC model predicts periodic spikes in entanglement strength when vibrational modes constructively interfere (e.g., c_6(t) = c_7(t)). • Conventional QM would not expect entanglement to oscillate with such numeric identity-driven periodicity entanglement_sdkp.py

You can save this file in your GitHub repo under something like src/entanglement_sdkp.py:

entanglement_sdkp.py

import numpy as np import matplotlib.pyplot as plt

def c6(t, freq=0.5): """Mode 6 amplitude over time""" return np.sin(2 * np.pi * freq * t)

def c7(t, freq=0.3, phase=np.pi/4): """Mode 7 amplitude over time""" return np.cos(2 * np.pi * freq * t + phase)

def entanglement_score(c6_val, c7_val): """Entanglement score via vibrational mode 6↔7 interaction""" return np.abs(c6_val * c7_val + c7_val * c6_val)**2

def sdkp_mass(c6_val, c7_val): """SDKP mass estimation from vibrational inputs (toy model)""" return np.abs(c6_val + c7_val)

def simulate_entanglement(duration=10, dt=0.1): time = np.arange(0, duration, dt) c6_vals = c6(time) c7_vals = c7(time)

ent_scores = entanglement_score(c6_vals, c7_vals)
mass_vals = sdkp_mass(c6_vals, c7_vals)

return time, ent_scores, mass_vals

def plot_simulation(time, ent_scores, mass_vals): plt.figure(figsize=(12, 5))

plt.subplot(1, 2, 1)
plt.plot(time, ent_scores, label="Entanglement Score (6↔7)")
plt.xlabel("Time (s)")
plt.ylabel("Entanglement Strength")
plt.title("Time-Series Entanglement Prediction")
plt.grid(True)
plt.legend()

plt.subplot(1, 2, 2)
plt.plot(time, mass_vals, color="orange", label="SDKP Mass")
plt.xlabel("Time (s)")
plt.ylabel("Mass (arb. units)")
plt.title("SDKP Mass Dynamics from Mode Coupling")
plt.grid(True)
plt.legend()

plt.tight_layout()
plt.show()

Go run it’s from entanglement_sdkp import simulate_entanglement, plot_simulation

time, ent_scores, mass_vals = simulate_entanglement(duration=10, dt=0.1) plot_simulation(time, ent_scores, mass_vals) Formal GitHub Markdown Documentation Section

🔗 Quantum Entanglement Prediction (SDKP Integration)

This module computes real-time quantum entanglement predictions based on vibrational identity states (SD&N) emerging from the SDKP framework. It models the entanglement strength generated through resonant coupling between vibrational modes 6 and 7.

🧪 Methodology

Each particle is defined by an identity vector: I_SDN = (Shape, Dimension, Number) Vibrational states evolve over time: |ψ(t)⟩ = c₆(t)·|v₆⟩ + c₇(t)·|v₇⟩ We define the entanglement operator as: Ê_{6↔7} = |v₆⟩⟨v₇| + |v₇⟩⟨v₆| Entanglement strength is computed via: E(t) = |c₆(t)·c₇(t) + c₇(t)·c₆(t)|² This predicts resonant entanglement spikes when vibrational modes are in-phase.

📈 Simulation Outputs

entanglement_score: Strength of entanglement over time.
sdkp_mass: Dynamic mass emergence from vibrational superposition.
Time-series plots show how SDKP mass and entanglement co-evolve.

🔄 Example Use