Universal Baseline Level (UBL) Numerical Verification and Reproducibility Script

Abstract

This file contains the complete SageMath verification script and numerical output used to reproduce all calculations in the Universal Baseline Level (UBL) framework. It includes the exact constants, code, computed values, and scale table results. This supplemental document ensures full reproducibility of the mathematical results presented in the associated UBL paper. This document is one entry in a series of UST documents. Each document in the series is an independent work, and the versions published on Zenodo are separate standalone papers, not duplicates or revisions of one another. If you have questions or want to discuss the work, you can contact me directly at dustin@unifiedsubstratetheory.com SageMath Code: # Universal Baseline Level (UBL) Verification Script # This script reproduces all numerical results in the UBL paper # using only standard physics constants and definitions. # Load constants c = 299792458 # speed of light (m/s) hbar = 1.054571817e-34 # reduced Planck constant (J·s) G = 6.67430e-11 # gravitational constant (m^3 kg^-1 s^-2) Lambda = 1.11e-52 # cosmological constant (m^-2) import math # 1. Planck energy density rho_planck = c**5 / (hbar * G**2) # 2. Vacuum energy density from cosmological constant rho_vac = Lambda * c**2 / (8 * math.pi * G) # 3. Universal Baseline Level (UBL) UBL = rho_vac / rho_planck # 4. log10(UBL) log10_UBL = math.log10(UBL) # 5. UBL scale table verification densities = { "Planck": 5.16e96, "GUT": 1e88, "Electroweak": 1e56, "QCD": 1e31, "Atomic": 1e16, "Biological": 1e-3, "Cosmic Vacuum": 6e-27 } UBL_table = {} for name, rho in densities.items(): u = rho / rho_planck UBL_table[name] = (u, math.log10(u)) # 6. Effective Higgs cutoff Lambda_eff = UBL**(1/4) * math.sqrt(c**5 / (hbar * G)) # 7. Electroweak vs gravitational hierarchy UBL_EW = 1e-40 ratio_hierarchy = UBL_EW / UBL # 8. QCD scale step difference UBL_QCD = 1e-65 step_QCD = math.log10(UBL_QCD) - math.log10(UBL) # Print results print("Planck energy density:", rho_planck) print("Vacuum energy density:", rho_vac) print("UBL:", UBL) print("log10(UBL):", log10_UBL) print("\nUBL Scale Table:") for k,v in UBL_table.items(): print(k, "=> UBL:", v[0], " log10:", v[1]) print("\nEffective Higgs cutoff (Lambda_eff):", Lambda_eff) print("EW/Gravity hierarchy ratio:", ratio_hierarchy) print("QCD step difference:", step_QCD) SageMath Output: Planck energy density: 5.15484850640341e96 Vacuum energy density: 5.94728569105370e-27 UBL: 1.15372657094887e-123 log10(UBL): -122.93789710521712 UBL Scale Table: Planck => UBL: 1.00099934917393 log10: 0.00043379511142230905 GUT => UBL: 1.93992121932932e-9 log10: -8.71221590651579 Electroweak => UBL: 1.93992121932932e-41 log10: -40.71221590651579 QCD => UBL: 1.93992121932932e-66 log10: -65.7122159065158 Atomic => UBL: 1.93992121932932e-81 log10: -80.7122159065158 Biological => UBL: 1.93992121932932e-100 log10: -99.7122159065158 Cosmic Vacuum => UBL: 1.16395273159759e-123 log10: -122.93406465613215 Effective Higgs cutoff (Lambda_eff): 3.41850751361282e12 EW/Gravity hierarchy ratio: 8.66756496019296e82 QCD step difference: 57.93789710521712 Interpretation: These results confirm: - ρPlanck and ρvac match known physics - UBL ≈ 10^-123 is the exact ratio of those two densities - The UBL scale table is numerically correct - The Higgs cutoff suppression, hierarchy ratio, and QCD step match the UBL paper - All results derive solely from c, ħ, G, Λ