The Forced Constants: The Charged Leptons, Quarks, Neutrinos, Mixing, and Cosmological Sector Derived from One Axiom with Zero Free Parameters
- 1Ernos Labs
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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BibTeX
@article{smith2026forced,
title = {{The Forced Constants: The Charged Leptons, Quarks, Neutrinos, Mixing, and Cosmological Sector Derived from One Axiom with Zero Free Parameters}},
author = {Maria Smith},
journal = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jun,
doi = {10.5281/zenodo.21025948},
url = {https://doi.org/10.5281/zenodo.21025948},
note = {CC BY},
}
RIS
TY - JOUR
TI - The Forced Constants: The Charged Leptons, Quarks, Neutrinos, Mixing, and Cosmological Sector Derived from One Axiom with Zero Free Parameters
AU - Maria Smith
PY - 2026
DA - 2026/06/29
JO - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21025948
UR - https://doi.org/10.5281/zenodo.21025948
AB - 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
ER -