Hyperspace Nine

[Josef_Founder]

hyperspace6.py

The other day I was sort of feeling the embarassmental projections through the internet of the silent troll majority.

“This guy can’t do maths”.

Well foo, yes I can do math. I’m just not always so great at articulating, and am perceived to overshare. Could we please do something, you and I, here forward?

Think outside the box, and learn together what the truth is?. Sincerely, your friend, Josef VII.

God bless you.

https://zchg.org/hott/late%20episodes/514%20-%2028-Dec-94%20-%20Envoys%20of%20Mankind%20%231.mp3

.. and further, there’s a reason for the annoyingly enormous volume of my output. Kindly listen? Seeking partnerships. Seeking friendships. Seeking purpose, meaning, and art. Prefer rekindling of old friendships and if the striking of new, simply put I value genuine relationship and don’t have much utility any longer for the inverse. And I say again, God bless you.

The following is a flattened means to solve for the above. No differential equations, nor even factoring. And it plays nice with Trinary or analog logic. From this several compute-relevant techniques are borne. Costs less to compute, and even derives new forms of radio communication.

Caveat - We are working in **Hotswap** BINARY/TRINARY

y,x = 0, p = 1, m= -1; the below is not in order, per se.  In symbolics, we allow atypical presumptions to build out striking new ground..

Y^2 - 2pxy + p^2(x^2-1) = m^2
-x^2*y^2 +x^2 - 1 = (m^2 - y^2)/p^2
-x^3*y^2 + x^3 - X = (m^2 - y^2)/p^2
—X = ((m^2 - y^2)/p^2) + x^3*y^2 + x^3
X = -((m^2 - y^2)/p^2) - x^3*y^2 - x^3
X = -x((m^2 - y^2)/p^2) - x^4*y^2 - x^4
1 = -((m^2 - y^2)/p^2) - x^3*y^2 - x^3
Y - pxy + p(x-1) = m
my = y^2 -pxy^2 + py(x-1)
m = y - pxy + p(x-1)
Y = ((y^2 -pxy^2 + py(x-1))/((y - pxy + p(x-1))
1 = (y - pxy + p(x-1)) / (y - pxy + p(x-1))
1 = (1/1)
1 = 1
-((m^2 - y^2)/p^2) - x^3*y^2 - x^3 =  (y - pxy + p(x-1)) / (y - pxy + p(x-1))
Y - pxy + p(x-1) = m
Pm = y - p^2xy + p^2(x-1)
P = (y - p^2xy + p^2(x-1)) / m
P = (y - p^2xy + p^2(x-1))/ (y - pxy + p(x-1))
P^2 = ((py- p^3xy + p^3(x-1)) / (py - pxy + p^2(x-1))
P^2 = ((y - p^2xy + p^2(x-1)) / (y - xy + p(x-1))
P^2 = ((py - p^3xy + p^3(x-1)) / (py - pxy + p^2(x-1))
1 = ((yp) - pxy + p(x-1) / p^2y - p^2xy + p^3(x-1) 
1 = (( y ) - xy + (x-1) / py - pxy + p^2(x-1) 
P = y - xy + x-1 / y - xy + p(x-1)
P = (y - xy / y - xy) + (x-1)/p(x-1)
P =  (x-1)/p(x-1)
P^2 = x-1 / x-1
P^2 = 1
P = 1^(1/2)
P ‎ = 1
1 = ((y - xy + (x-1)) / (y - xy + (x-1))
 (y - xy + (x-1)) =  (y - xy + (x-1))
Y - xy = y - xy 
Y(1-x) = y(1-x)
1 - x = 1 - x
1 -x - 1 = 1 - x - 1
-x = -x
X = x 
1 = 1
P =  (x-1)/p(x-1)
1 = (x-1)/(x-1)
X - 1 = x - 1
Y^2 - xy + (x^2-1) = m^2
Y^2 - xy + x^2-1 = Y^2 - xy + x^2-1
((y^2 -xy^2 + y(x-1))/((1 - x + y(x-1)) = y^2
((y^2 -xy^2 + y(x-1))/((1 - x + y(x-1)) - xy + x^2-1 = ((y^2 -xy^2 + y(x-1))/((1 - x + y(x-1))  - xy + x^2-1
1/((1 - x + y(x-1)) - xy + x^2-1) = 1/((1 - x + y(x-1))  - xy + x^2-1)
Y = ((y^2 - xy^2 + y(x-1))/((y - xy + (x-1))
Y(((y - xy + (x-1))) = y^2 - xy^2 + y(x-1)
Y^2 - xy^2 + yx - y = y^2 - xy^2 + y(x-1)
-xy^2 + yx - y = - xy^2 + y(x-1)
y = xy^2 + -y(x-1) + xy^2 - yx 
Y = y(x^2 - x + 1 + xy - x)
1 = (x^2 - x + 1 + xy - x)
1 = 1 + xy
Xy = 0
Y = 0
X = 0 
m = y - pxy + p(x-1)
m = 0 + -1
m ‎ = -1 
Y^2 - 2pxy + p^2(x^2-1) = m^2
0 - 1(-1) ‎ = 1
1 = 1 
0 = 0

y,x = 0, p = 1, m= -1, 1, i, -i

hyperspace9.zip (15.1 KB)

Continues from:

Flattening Diff Eq with a Jr High Textbook

[image] [image] The following is a flattened means to solve for the above. No differential equations, nor even factoring. And it plays nice with Trinary or analog logic. From this several compute-relevant techniques are borne. Costs less to compute, and even derives new forms of radio communication. Caveat - We are working in **Hotswap** BINARY/TRINARY y,x = 0, p = 1, m= -1; the below is not in order, per se. In symbolics, we allow atypical presumptions to build out striking new groun…

hyperspace7.py

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

def render_5v_complex_manifold():
    # 1. Initialize Visual Canvas
    fig = plt.figure(figsize=(13, 10))
    ax = fig.add_subplot(111, projection='3d')

    # Generate a tight spatial grid across X and Z axes
    x_arr = np.linspace(-2.0, 2.0, 100)
    z_arr = np.linspace(-2.0, 2.0, 100)
    X, Z = np.meshgrid(x_arr, z_arr)

    # 2. Pre-allocate reference containers for the mesh layers
    meshes = {'r1': None, 'r2': None, 'c1': None, 'c2': None}

    # Overlay text block to track the hyper-dimensional coordinates
    coord_text = ax.text2D(0.02, 0.95, "", transform=ax.transAxes, fontsize=11,
                           bbox=dict(boxstyle="round", fc="ghostwhite", alpha=0.85))

    # 3. Instantiate the 7 Target Coordinate Markers (At X=0, Z=0, with Time P evolving)
    dot_m1_u = ax.scatter([], [], [], color='blue', s=160, edgecolor='black', zorder=20, label='m = 1 (+Y Branch)')
    dot_m1_l = ax.scatter([], [], [], color='cyan', s=160, edgecolor='black', zorder=20, label='m = 1 (-Y Branch)')
    dot_mn1_u = ax.scatter([], [], [], color='navy', s=90, marker='^', edgecolor='white', zorder=21, label='m = -1 (+Y Branch)')
    dot_mn1_l = ax.scatter([], [], [], color='teal', s=90, marker='v', edgecolor='white', zorder=21, label='m = -1 (-Y Branch)')
    dot_mi = ax.scatter([], [], [], color='red', s=160, edgecolor='black', zorder=22, label='m = i Gauge')
    dot_mni = ax.scatter([], [], [], color='orange', s=90, marker='X', edgecolor='black', zorder=23, label='m = -i Gauge')

    # Absolute zero index reference marker
    ax.scatter([0], [0], [0], color='gold', s=140, marker='*', edgecolor='black', zorder=19, label='Core Substrate Anchor')

    # Scene parameters and boundary clamps
    ax.set_xlabel('Spatial Axis X', fontsize=10)
    ax.set_ylabel('Spatial Axis Z (New Dimension)', fontsize=10)
    ax.set_zlabel('Substrate Value Y', fontsize=10)
    ax.set_xlim(-2.0, 2.0)
    ax.set_ylim(-2.0, 2.0)
    ax.set_zlim(-5.0, 5.0)
    ax.view_init(elev=25, azim=55)
    ax.legend(loc='center left', bbox_to_anchor=(1.05, 0.5), fontsize=9)

    # 4. Animated Frame Evolution (P acts as continuous cosmic time)
    def update_manifold(frame):
        # Evolve the parameter P smoothly back and forth between -2.0 and +2.0
        p = 2.0 * np.sin(frame)

        # Strip old meshes to maintain memory performance
        if meshes['r1'] is not None:
            meshes['r1'].remove()
            meshes['r2'].remove()
        if meshes['c1'] is not None:
            meshes['c1'].remove()
            meshes['c2'].remove()

        # Compute Real Branches (m^2 = +1)
        # Y = p*(x+z) ± sqrt(1 + p^2 * (1 - 2xz))
        radial_real = 1.0 + (p**2) * (1.0 - 2.0 * X * Z)
        # Ensure smooth visual transitions over negative regional transitions
        radial_real_safe = np.maximum(0, radial_real)

        Yr_pos = p * (X + Z) + np.sqrt(radial_real_safe)
        Yr_neg = p * (X + Z) - np.sqrt(radial_real_safe)

        # Compute Complex Core Branches (m^2 = -1)
        # Y = p*(x+z) ± sqrt(-1 + p^2 * (1 - 2xz))
        radial_comp = -1.0 + (p**2) * (1.0 - 2.0 * X * Z)
        mask = radial_comp >= 0

        Yc_pos = np.full_like(X, np.nan)
        Yc_neg = np.full_like(X, np.nan)
        radial_comp_safe = np.sqrt(np.maximum(0, radial_comp))

        Yc_pos[mask] = (p * (X + Z))[mask] + radial_comp_safe[mask]
        Yc_neg[mask] = (p * (X + Z))[mask] - radial_comp_safe[mask]

        # Render the newly twisted spatial manifold layers
        meshes['r1'] = ax.plot_surface(X, Z, Yr_pos, cmap='winter', alpha=0.25, rstride=5, cstride=5)
        meshes['r2'] = ax.plot_surface(X, Z, Yr_neg, cmap='cool', alpha=0.15, rstride=5, cstride=5)
        meshes['c1'] = ax.plot_surface(X, Z, Yc_pos, cmap='autumn', alpha=0.40, rstride=5, cstride=5)
        meshes['c2'] = ax.plot_surface(X, Z, Yc_neg, cmap='YlOrRd', alpha=0.25, rstride=5, cstride=5)

        # Update the 7 target marker positions exactly at coordinate crosshairs X=0, Z=0
        # Under X=0, Z=0: Y = ±sqrt(m^2 + p^2)
        y_real_val = np.sqrt(1.0 + p**2)
        y_comp_val = np.sqrt(np.maximum(0, p**2 - 1.0)) if abs(p) >= 1.0 else 0.0

        dot_m1_u._offsets3d = ([0], [0], [y_real_val])
        dot_m1_l._offsets3d = ([0], [0], [-y_real_val])
        dot_mn1_u._offsets3d = ([0], [0], [y_real_val])
        dot_mn1_l._offsets3d = ([0], [0], [-y_real_val])
        dot_mi._offsets3d = ([0], [0], [y_comp_val])
        dot_mni._offsets3d = ([0], [0], [-y_comp_val])

        # Track numerical metrics via display overlay
        coord_text.set_text(f"Current Time (P): {p:.3f}\n"
                            f"Real Mass Step (Y): ±{y_real_val:.2f}\n"
                            f"Complex Mass Step (Y): ±{y_comp_val:.2f}")
        ax.set_title(r'5-Variable Substrate: $(Y - p(x+z))^2 + p^2(x^2-z^2-1) = m^2$', fontsize=11, pad=20)

        return meshes['r1'], meshes['r2'], meshes['c1'], meshes['c2']

    # 5. Build and execute the continuous loop
    frames_timeline = np.linspace(0, 2 * np.pi, 150)
    anim = FuncAnimation(fig, update_manifold, frames=frames_timeline, interval=45, blit=False)

    plt.tight_layout()
    plt.show()

if __name__ == '__main__':
    render_5v_complex_manifold()

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