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July 1, 20260 citationsOpen Access

The Forced Constants: The Charged Leptons, Quarks, Neutrinos, Mixing, and Cosmological Sector Derived from One Axiom with Zero Free Parameters

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MSMaria SmithFano Labs (China)

Key Points

  • The aim is to derive lepton and quark masses, mixing angles, and cosmological constants from a single axiom without free parameters.
  • Utilizes a cubic equation to derive charged lepton mass ratios and the Koide relation.
  • Applies forced dressing over the fine-structure constant to calculate quark ratios.
  • Establishes conditions for neutrino masses and cosmological constants from the derived relationships.
  • Derives the charged lepton mass ratios with exact correspondence to measured values.
  • Establishes a fixed mass-squared ratio for neutrinos at 3/100, predicting neutrinoless double-beta decay.
  • Calculates cosmological constants, providing a positive non-zero value and solving the ten-to-the-120 catastrophe.

Abstract

One axiom. One operation. Zero free parameters. The Standard Model carries roughly two dozen free parameters — lepton and quark masses, neutrino splittings, mixing angles, the CP phase — plus the cosmological constants. Every one is measured and inserted by hand; none is derived. This paper derives them. From the same axiom (the One) and operation (the fold) that fix the fine-structure constant, the charged leptons are the three roots of one cubic x³ − x² + (1/6)x − 1/485 = 0 whose roots sum to the One and whose squares give the measured mass ratios; the Koide relation falls out as exactly 2/3. The quark ratios follow by a single forward dressing over the forced 1/α. The neutrino is single-handed, so a Dirac mass is forbidden and a Majorana mass is forced — neutrinoless double-beta decay must occur — with mass-squared ratio fixed at 3/100. CKM mixing is the bare overlap of two fold bases; the CP phase sits at the unique self-antipodal point, the half-One, giving maximal CP violation (Jarlskog ≈ 3.1×10⁻⁵). In cosmology: dark-to-baryon 27/5, a positive non-zero cosmological constant at the binary floor 2⁻²⁰ (the 10¹²⁰ catastrophe dissolved), the Hubble calibration ratio 13/12, and the black-hole quarter 1/4. No measured value enters any construction; every result is machine-checked and reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE), companion to The Counted Constant (the fine-structure constant). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory

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Cite This Study

Maria Smith (2026) studied this question.

synapsesocial.com/papers/6a44aedf5cd2549c8bc44032https://doi.org/10.5281/zenodo.21026112
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1The Constants Are One Object: The Grand Lock of the Generators {One, 2, 3}2026
  2. 2The Smithian Fold Theory of Everything: Zero Free Parameters, Zero Axioms, One Fold — the Constants of Nature, Derived2026
  3. 3Unified Scalar-Imprint Framework: A Complete Derivation of the Fundamental Constants, Forces, and Cosmological Parameters of the Standard Model and Beyond from the Single Axiom Ω = 100/99 (Complete Series, Researches 1–20)2026
  4. 4Much Ado About Nothing: The Cosmological Constant at the Binary Floor 2^-202026
  5. 5BSM Fixed-Points: Solving the Muon g −2 and W Boson Mass Deviations with Zero Free Parameters (Python Verification Included)2026