#### Determinism and Uncertainty Reduction
# Resultant R = e^{±λZ}
"""
Description: Models the dynamic transitions in the Nothing-Totality (NT) continuum,
representing expansion (+λ) and contraction (-λ). The variable Z represents
a systemic quantity such as energy, complexity, or information state.
Key Features:
- λ: Control parameter that regulates the speed of transitions.
- Z: State variable that defines the position along the continuum.
- Vectors: Integral of primary directions (λD primary) and emerging possibilities
(λP possibilistic), reducing residual latency (λL latency).
"""
#### Formalization of Angular Momentum and Assonances
# Angular Momentum (θ_{NT})
def angular_momentum(R_t, omega):
"""
Formalizes the cyclical equilibrium between observer and observed:
θ_{NT} = lim_{t -> 0} [ R(t) * e^(i * omega * t) ]
Parameters:
R_t: Temporal resultant (function of time t).
omega: Dominant frequency of oscillations.
Returns:
The formal angular momentum.
"""
from sympy import limit, symbols, exp, I
t = symbols('t')
return limit(R_t * exp(I * omega * t), t, 0)
#### Optimization with the Principle of Least Action
# Unified Equation
def least_action_equation(delta, alpha, beta, gamma, f_dual_nond, f_movement, f_absorb_align, R_t, proto_axiom):
"""
R(t+1) = δ(t) * [ α * f_{Dual-NonDual}(A, B; λ) + β * f_{Movement}(R(t), P_{Proto-Axiom}) ] + \
(1 - δ(t)) * [ γ * f_{Absorb-Align}(R(t), P_{Proto-Axiom}) ]
Parameters:
delta: Transition factor.
alpha, beta, gamma: Weights of the logical contributions.
Other functions specified in the context.
Returns:
Updated resultant R.
"""
return delta * (alpha * f_dual_nond + beta * f_movement) + (1 - delta) * gamma * f_absorb_align
#### Formalization of the Principle of Least Action
# Proposed Lagrangian
def total_lagrangian(L_cin, L_pot, L_int, L_QOS, L_grav, L_fluct):
"""
L_total = L_cin + L_pot + L_int + L_QOS + L_grav + L_fluct
Parameters:
L_cin: Kinetic term.
L_pot: Effective potential.
L_int: Interaction term.
L_QOS: Quantum operating system.
L_grav: Gravitational term.
L_fluct: Quantum fluctuations.
Returns:
The total Lagrangian of the system.
"""
return L_cin + L_pot + L_int + L_QOS + L_grav + L_fluct
def lagrangian(dZ_dt, Z, theta_NT, lambda_param, f_theta, g_Z):
"""
L = (1/2) * (dZ/dt)^2 - V(Z, θ_{NT}, λ)
Potential V(Z, θ_{NT}, λ):
V(Z, θ_{NT}, λ) = Z^2 * (1-Z)^2 + λ * f(θ_{NT}) * g(Z)
Returns:
Lagrangian calculated for the given parameters.
"""
return 0.5 * (dZ_dt ** 2) - (Z ** 2 * (1 - Z) ** 2 + lambda_param * f_theta(theta_NT) * g_Z(Z))
#### Simulation of the NT Continuum
# Visualization of the dynamics of R and the potential
import numpy as np
import matplotlib.pyplot as plt
def continuum_simulation(lambda_param, theta_NT_range, Z_range):
"""
Simulates the potential V(Z, θ_{NT}, λ) and plots the dynamics.
Parameters:
lambda_param: Control parameter λ.
theta_NT_range: Range of values for θ_{NT}.
Z_range: Range of values for Z.
Returns:
Graph of the potential in the NT Continuum.
"""
Z = np.linspace(*Z_range, 100)
theta_NT = np.linspace(*theta_NT_range, 100)
Z_grid, theta_grid = np.meshgrid(Z, theta_NT)
# Calculation of the potential
f_theta = np.cos(theta_grid)
g_Z = Z_grid**2
V = Z_grid**2 * (1 - Z_grid)**2 + lambda_param * f_theta * g_Z
# Visualization
plt.figure(figsize=(10, 6))
plt.contourf(Z_grid, theta_grid, V, levels=50, cmap="viridis")
plt.colorbar(label="Potential V(Z, θ_{NT}, λ)")
plt.title("Dynamics of the Nothing-Totality Continuum")
plt.xlabel("Z")
plt.ylabel("θ_{NT}")
plt.show()
# Example of using the simulation
continuum_simulation(lambda_param=1.5, theta_NT_range=(0, 2 * np.pi), Z_range=(0, 1))
# NT Continuum
"""
The Nothing-Totality (NT) continuum represents the complete spectrum of dynamic possibilities.
Each resultant R updates the logical context and feeds the system by eliminating latency
and improving coherence. The D-ND model uses the NT to navigate between states of least
action, keeping the observer at the center of the system.
"""