The Counted Constant: A Zero-Parameter Derivation of the Fine-Structure Constant from a Single Axiom, to Two Orders of Its Own Structure
- 1Ernos Labs
Abstract
One axiom. One operation. Zero free parameters. The fine-structure constant α is the most precisely measured pure number in physics and the most conspicuously unexplained — for a century an input, never derived. This paper derives it. From a single axiom (the One) and a single operation (the fold), the inverse fine-structure constant is forced to 1/α = 2⁷ + 3²(251/250) = 34259/250 = 137.036, matching CODATA (137.035999177) to eight significant figures, six parts per billion, with zero free parameters. Each block is an independent structural count and the assembly is unique among 41,472 structural alternatives. The covering volume is itself a covered object, so the same construction continues to its own next self-similar order with no new ingredient, giving 1/α = 5995462/43751 = 137.0359991772 — level with measurement to about 0.01σ. No measured value enters the construction; this is proven as a property of the code, machine-checked by a single verifier under a static gate, and reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory — SFTOE record: https://doi.org/10.5281/zenodo.20775538
Related
- Functional renormalization group in an external field: constant field versus constant order parameter
- Consistency conditions and the derivation of harmonic structure in Einstein-Maxwell-dilaton theory
- The Number 137 in ZEBTS‑SUPER Theory: Rigorous chi‑Spectral Reconstruction of the Fine‑Structure Constant
- Pseudoentanglement in constant depth: How trivial states can have non-trivial entanglement structure
- Sensitivity of the 229mTh clock transition to the fine-structure constant in a Skyrme-Hartree-Fock-BCS approach
BibTeX
@article{smith2026counted,
title = {{The Counted Constant: A Zero-Parameter Derivation of the Fine-Structure Constant from a Single Axiom, to Two Orders of Its Own Structure}},
author = {Maria Smith},
journal = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jun,
doi = {10.5281/zenodo.21025130},
url = {https://doi.org/10.5281/zenodo.21025130},
note = {CC BY},
}
RIS
TY - JOUR
TI - The Counted Constant: A Zero-Parameter Derivation of the Fine-Structure Constant from a Single Axiom, to Two Orders of Its Own Structure
AU - Maria Smith
PY - 2026
DA - 2026/06/29
JO - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21025130
UR - https://doi.org/10.5281/zenodo.21025130
AB - One axiom. One operation. Zero free parameters. The fine-structure constant α is the most precisely measured pure number in physics and the most conspicuously unexplained — for a century an input, never derived. This paper derives it. From a single axiom (the One) and a single operation (the fold), the inverse fine-structure constant is forced to 1/α = 2⁷ + 3²(251/250) = 34259/250 = 137.036, matching CODATA (137.035999177) to eight significant figures, six parts per billion, with zero free parameters. Each block is an independent structural count and the assembly is unique among 41,472 structural alternatives. The covering volume is itself a covered object, so the same construction continues to its own next self-similar order with no new ingredient, giving 1/α = 5995462/43751 = 137.0359991772 — level with measurement to about 0.01σ. No measured value enters the construction; this is proven as a property of the code, machine-checked by a single verifier under a static gate, and reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory — SFTOE record: https://doi.org/10.5281/zenodo.20775538
ER -