Zero Operator Theory: Ab Initio Derivation of 41 Physical Quantities as a Proposed Resolution to the Naturalness and Hierarchy Problems
Year: 2026
Type: article
Abstract: The Zero Operator Theory (ZOT v3.6) proposes a rigorous resolution to the long-standing Naturalness and Hierarchy problems in modern theoretical physics by replacing the classical assumption of a continuous space-time continuum with a discrete, causal-informational quantum vacuum termed the Emergent Compressed Vacuum (ECV). The model operates under an over-constrained framework with zero free degrees of freedom ($\text{DOF} \equiv 0$). Unlike conventional theories that depend on the empirical fine-tuning of dozens of arbitrary free parameters, ZOT establishes a strictly irreversible, unidirectional causal sequence—governed by a Directed Acyclic Graph (DAG)—derived from only two irreducible native seeds: the Constant of Motion ($C_{\text{ZOT}} = 518500.0$) and the Thermodynamic Exponent ($\gamma = 0.383002$). The cornerstone of the architecture is its Global Interlocking Index ($GII = 316.2$), wherein the Universal Vacuum Dressing Formula (CILP-ECV) serves as an elastic impedance response bridge between the sub-Planckian informational mesh and observable physical phenomena. Through this mechanism, the theory achieves the ab initio derivation of more than 41 fundamental constants and physical quantities (structured around a 41-observable primary Master Matrix and extended analytically to 49 quantities in Appendix A) without post-hoc tuning or slack variables. This single causal chain unifies:1. The SI metrological sector ($c, \hbar, G, e_q, k_B$);2. The electroweak sector ($v_{\text{dressed}} \approx 237.15\text{ GeV}$, $m_H \approx 125.28\text{ GeV}$, dressed $W^\pm/Z^0$ gauge boson masses);3. Baryonic and flavor physics, featuring the neutron-proton mass gap ($\Delta M_{n-p} \approx 1.293856\text{ MeV}$) derived from electron Dirac spinor geometry, and the muon anomalous magnetic moment ($a_\mu \approx 0.00116592$);4. The active neutrino mass scale ($m_\nu \approx 0.080536\text{ eV}$);5. Dark sector and cosmological parameters, including the single-step holographic dark matter fraction ($\Omega_{\text{DM}} = \gamma - c_{\text{top}} \approx 0.251415$), the dark energy density ($\rho_{\text{DE}} = 6.4 \times 10^{-11}\text{ eV}^4$), and the periodic table upper ceiling ($Z_{\text{limit}} = 128.993, A \approx 310$). Because the system is strictly over-constrained, each derivation acts simultaneously as a boundary condition and a consistency test for all others. A Jacobian Sensitivity Matrix computed to 50 decimal digits confirms a finite condition number ($\kappa \approx 1478.78$) and an extremely tight MCMC viable parametric volume ratio ($V_{\text{viable}}/V_{\text{prior}} < 1.4 \times 10^{-12}$). This mathematical rigidity turns the model's extreme Popperian falsifiability into its primary epistemological strength: minor shifts in baseline empirical data would collapse the interlocking chain, whereas increasing metrological precision continuously confirms the model without requiring manual recalibration. This technical manuscript was translated from Brazilian Portuguese into English with the assistance of Google AI technology (Gemini), operating within a Human-in-the-Loop (HITL) framework. All mathematical derivations, LaTeX syntax, unit mappings, and canonical terms of the Zero Operator Theory (ZOT v3.6) were rigorously verified and audited to ensure full technical accuracy and alignment with international publication standards. List of the 41 Master Observables Derived *Ab Initio* by ZOT v3.6 Sector 1: Metrology and Fundamental SI Constants1. Base Speed of Light ($c_{\text{bare}}$)2. Projected Speed of Light $c$3. Reduced Planck Constant $hbar$4. Planck Constant $(h$5. Gravitational Constant $G$6. Boltzmann Constant $k_B$7. Vacuum Permeability $mu_0$8. Vacuum Permittivity $varepsilon_0$9. Characteristic Vacuum Impedance $(Z_0$10. Rydberg Constant $R_\infty$11. Avogadro Constant $(N_A$12. Faraday Constant $F$13. Stefan-Boltzmann Constant $sigma_{\text{SB}}$ Sector 2: Couplings, Mixing Angles, and Electroweak Unification14. Inverse Fine-Structure Constant $alpha^{-1}$15. Fine-Structure Constant $alpha$16. Strong Coupling Constant at $(Z$ Scale $alpha_s(M_Z)$17. Weak Mixing Angle / Weinberg Angle $sin^2\theta_W$18. Electrospherical Golden Angle $psi$19. Fermi Coupling Constant $G_F$ Sector 3: Baryons, Leptons, and Flavor Physics20. Yang-Mills Mass Gap / QCD Scale $mu_{\text{vac}}$21. Proton Rest Mass $M_p$22. Neutron Rest Mass $m_n$23. Neutron-Proton Mass Gap $Delta M_{n-p}$24. Electron Rest Mass $m_e$25. Proton-to-Electron Mass Ratio $M_p/m_e$26. Muon-to-Electron Mass Ratio $m_\mu/m_e$27. Tau-to-Electron Mass Ratio $m_\tau/m_e$28. Muon Anomalous Magnetic Moment $a_\mu$29. Electron Anomalous Magnetic Moment $a_e$30. Active Neutrino Rest Mass $m_\nu$31. Active Neutrino Mass Difference Scale $Delta m^2_{31}$ Sector 4: Electroweak Sector and Higgs Boson 32. Dressed Higgs Vacuum Expectation Value $v_{\text{dressed}}$33. Higgs Boson Mass $m_H$34. Dressed $W^\pm$ Boson Mass $m_W$35. Dressed $Z^0$ Boson Mass $m_Z$36. Top Quark Mass $m_t$ Sector 5: Dark Sector, Cosmology, and Astroparticle Phenomenology 37. Dark Matter Density Fraction $\Omega_{\text{DM}}$38. Dark Energy Energy Density $rho_{\text{DE}}$39. Dark Energy Fraction $Omega_{\text{DE}}$40. MOND Critical Acceleration $a_0$41. Periodic Table Upper Ceiling / Nuclear Charge Limit $Z_{\text{limit}}$ Note: This document is the official English translation of the original article in Brazilian Portuguese, available at DOI: https://zenodo.org/uploads/22832916 "This study is part of the overarching compendium of the Zero Operator Theory (ZOT) framework. For further details regarding canonical terminology, analytical derivations, and an in-depth exploration of the theoretical structure, readers are invited to consult the complete repository of works deposited under the author's name: Bartolome, Ricardo on Zenodo."
Author: Bartolome, Ricardo
Institution: Universidade Cidade de São Paulo
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213753029
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