Rendered Frame Theory I: Supreme Unification via Temporal Compression and NexFrame Modulation
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2026
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| _version_ | 1866902070946168832 |
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| author | S.Grinstead, Liam |
| author_facet | S.Grinstead, Liam |
| contents | <p><strong>Rendered Frame Theory (RFT)</strong></p> <p><strong>Authored by Liam.S.Grinstead</strong></p> <p>introduces a unified cosmological expansion law based on Observer‑indexed harmonic fields arising from a consciousness‑coupled cosmological manifold.</p> <p>The Supreme Unification Kernel blends early‑ and late‑universe frame parameters through a dynamic sigmoidal handover at \(z = 2.5\), and incorporates a NexFrame hyperdimensional gradient modulation term.</p> <p>Numerical verification demonstrates that the unified expansion law simultaneously satisfies high‑redshift cosmic age (568.92 Myr at \(z=13.67\)), the local Hubble rate (70.00 km/s/Mpc), BAO transition stability, and baryonic‑only galactic rotation curves. This deposit includes the full Python implementation of the Supreme Kernel and supporting documentation.</p> <p>Python script for a dashboard Verification: </p> <p>- - - </p> <p>import numpy as np import matplotlib.pyplot as plt</p> <p>MASTER PARAMETERS (Supreme Unification)</p> <p>p1_e, p2_e = -0.5976, 4.8900 p1_l, p2_l = -3.1239, 3.1852 nex_c = 0.0631 t_z = 2.5 H0, tau_b = 70.0, 1.0</p> <p>1. UNIFIED HUBBLE ENGINE</p> <p>def H_FINAL_PLOT(z): s = 1.0 / (1.0 + np.exp(-5.0 * (z - t_z))) p1 = p1_e * s + p1_l * (1.0 - s) p2 = p2_e * s + p2_l * (1.0 - s) tau = tau_b * (1 + p1 * z + p2 * np.log(1.0 + z)) grad = nexframe_gradient_kernel(z) return np.maximum(H0 * (1.0 - (tau - 1.0)) * (1.0 + nex_c * grad), 1.0)</p> <p>2. INITIALIZE DASHBOARD</p> <p>fig, axes = plt.subplots(2, 2, figsize=(16, 12)) ((ax1, ax2), (ax3, ax4)) = axes</p> <p>PANEL A: SUPREME HUBBLE FLOW</p> <p>z_h = np.linspace(0, 5, 100) h_vals = [H_FINAL_PLOT(z) for z in z_h] ax1.plot(z_h, h_vals, ‘m-’, linewidth=3, label=‘Supreme Unification Flow’) ax1.errorbar(0, 73.04, yerr=1.04, fmt=‘sr’, label=‘SH0ES H0’) ax1.set_title(“Dynamic Expansion History”, fontsize=14) ax1.set_xlabel(“Redshift z”); ax1.set_ylabel(“H(z) [km/s/Mpc]”) ax1.legend(); ax1.grid(True, alpha=0.3)</p> <p>PANEL B: GALACTIC ROTATION (BARYONIC ONLY)</p> <p>r = np.linspace(1, 50, 100) v_vals = [v_rft(ri) for ri in r] ax2.plot(r, v_vals, ‘g-’, linewidth=2.5, label=‘RFT Modified Dynamics’) ax2.set_title(“Rotation Curves (No Dark Matter)”, fontsize=14) ax2.set_xlabel(“Radius [kpc]”); ax2.set_ylabel(“Velocity [km/s]”) ax2.legend(); ax2.grid(True, alpha=0.3)</p> <p>PANEL C: PULSAR HARMONICS</p> <p>t_p = np.linspace(-5, 30, 1000) intensity = simulate_pulsar_echoes(t_p) ax3.plot(t_p, intensity, ‘r-’, linewidth=1.5) ax3.fill_between(t_p, 0, intensity, color=‘red’, alpha=0.15) ax3.set_title(“Quantized Pulsar Echoes”, fontsize=14) ax3.set_xlabel(“Time [ms]”); ax3.set_ylabel(“Intensity”) ax3.grid(True, alpha=0.3)</p> <p>PANEL D: GALAXY MATURITY</p> <p>z_m_range = np.linspace(10, 20, 50) ax4.plot(z_m_range, smd_rft(z_m_range), ‘b-’, linewidth=2.5, label=‘RFT Accelerated Growth’) ax4.plot(z_m_range, 8.0 - 0.6*z_m_range, ‘r–’, label=‘LCDM Baseline’) ax4.set_title(“JWST: Stellar Mass Maturity Solution”, fontsize=14) ax4.set_xlabel(“Redshift z”); ax4.set_ylabel(“log10 SMD”) ax4.legend(); ax4.grid(True, alpha=0.3)</p> <p>plt.tight_layout(rect=[0, 0.03, 1, 0.95]) plt.suptitle(“Rendered Frame Theory: Unified Evidence Dashboard”, fontsize=20, weight=‘bold’) plt.show()</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19229675 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Rendered Frame Theory I: Supreme Unification via Temporal Compression and NexFrame Modulation S.Grinstead, Liam Rendered Frame Theory Cosmology Hubble Tension JWST Early Galaxy Maturity Temporal Compression NexFrame Kernel High‑Dimensional Modulation Unified Expansion Law Cosmic Age Rotation Curves <p><strong>Rendered Frame Theory (RFT)</strong></p> <p><strong>Authored by Liam.S.Grinstead</strong></p> <p>introduces a unified cosmological expansion law based on Observer‑indexed harmonic fields arising from a consciousness‑coupled cosmological manifold.</p> <p>The Supreme Unification Kernel blends early‑ and late‑universe frame parameters through a dynamic sigmoidal handover at \(z = 2.5\), and incorporates a NexFrame hyperdimensional gradient modulation term.</p> <p>Numerical verification demonstrates that the unified expansion law simultaneously satisfies high‑redshift cosmic age (568.92 Myr at \(z=13.67\)), the local Hubble rate (70.00 km/s/Mpc), BAO transition stability, and baryonic‑only galactic rotation curves. This deposit includes the full Python implementation of the Supreme Kernel and supporting documentation.</p> <p>Python script for a dashboard Verification: </p> <p>- - - </p> <p>import numpy as np import matplotlib.pyplot as plt</p> <p>MASTER PARAMETERS (Supreme Unification)</p> <p>p1_e, p2_e = -0.5976, 4.8900 p1_l, p2_l = -3.1239, 3.1852 nex_c = 0.0631 t_z = 2.5 H0, tau_b = 70.0, 1.0</p> <p>1. UNIFIED HUBBLE ENGINE</p> <p>def H_FINAL_PLOT(z): s = 1.0 / (1.0 + np.exp(-5.0 * (z - t_z))) p1 = p1_e * s + p1_l * (1.0 - s) p2 = p2_e * s + p2_l * (1.0 - s) tau = tau_b * (1 + p1 * z + p2 * np.log(1.0 + z)) grad = nexframe_gradient_kernel(z) return np.maximum(H0 * (1.0 - (tau - 1.0)) * (1.0 + nex_c * grad), 1.0)</p> <p>2. INITIALIZE DASHBOARD</p> <p>fig, axes = plt.subplots(2, 2, figsize=(16, 12)) ((ax1, ax2), (ax3, ax4)) = axes</p> <p>PANEL A: SUPREME HUBBLE FLOW</p> <p>z_h = np.linspace(0, 5, 100) h_vals = [H_FINAL_PLOT(z) for z in z_h] ax1.plot(z_h, h_vals, ‘m-’, linewidth=3, label=‘Supreme Unification Flow’) ax1.errorbar(0, 73.04, yerr=1.04, fmt=‘sr’, label=‘SH0ES H0’) ax1.set_title(“Dynamic Expansion History”, fontsize=14) ax1.set_xlabel(“Redshift z”); ax1.set_ylabel(“H(z) [km/s/Mpc]”) ax1.legend(); ax1.grid(True, alpha=0.3)</p> <p>PANEL B: GALACTIC ROTATION (BARYONIC ONLY)</p> <p>r = np.linspace(1, 50, 100) v_vals = [v_rft(ri) for ri in r] ax2.plot(r, v_vals, ‘g-’, linewidth=2.5, label=‘RFT Modified Dynamics’) ax2.set_title(“Rotation Curves (No Dark Matter)”, fontsize=14) ax2.set_xlabel(“Radius [kpc]”); ax2.set_ylabel(“Velocity [km/s]”) ax2.legend(); ax2.grid(True, alpha=0.3)</p> <p>PANEL C: PULSAR HARMONICS</p> <p>t_p = np.linspace(-5, 30, 1000) intensity = simulate_pulsar_echoes(t_p) ax3.plot(t_p, intensity, ‘r-’, linewidth=1.5) ax3.fill_between(t_p, 0, intensity, color=‘red’, alpha=0.15) ax3.set_title(“Quantized Pulsar Echoes”, fontsize=14) ax3.set_xlabel(“Time [ms]”); ax3.set_ylabel(“Intensity”) ax3.grid(True, alpha=0.3)</p> <p>PANEL D: GALAXY MATURITY</p> <p>z_m_range = np.linspace(10, 20, 50) ax4.plot(z_m_range, smd_rft(z_m_range), ‘b-’, linewidth=2.5, label=‘RFT Accelerated Growth’) ax4.plot(z_m_range, 8.0 - 0.6*z_m_range, ‘r–’, label=‘LCDM Baseline’) ax4.set_title(“JWST: Stellar Mass Maturity Solution”, fontsize=14) ax4.set_xlabel(“Redshift z”); ax4.set_ylabel(“log10 SMD”) ax4.legend(); ax4.grid(True, alpha=0.3)</p> <p>plt.tight_layout(rect=[0, 0.03, 1, 0.95]) plt.suptitle(“Rendered Frame Theory: Unified Evidence Dashboard”, fontsize=20, weight=‘bold’) plt.show()</p> |
| title | Rendered Frame Theory I: Supreme Unification via Temporal Compression and NexFrame Modulation |
| topic | Rendered Frame Theory Cosmology Hubble Tension JWST Early Galaxy Maturity Temporal Compression NexFrame Kernel High‑Dimensional Modulation Unified Expansion Law Cosmic Age Rotation Curves |
| url | https://doi.org/10.5281/zenodo.19229675 |