Published May 19, 2026
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The Theory of Nothing: From ∅ to the Standard Model -- A zero-parameter Fibonacci K-theoretic derivation of 45 dimensionless observables
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Description
The Theory of Nothing: From the Empty Set to the Standard Model derives the Standard Model and twelve Planck-2018 / DESI cosmological observables from a single combinatorial primitive -- the Fibonacci substitution sigma: A -> AB, B -> A -- with no continuous parameters, no fitted constants, and no Lagrangian input.
Main structural results:
3+1-dimensional spacetime is the Zeckendorf decomposition of the admissibility level ell = 4.
The Standard Model gauge group G_SM = SU(3) x SU(2) x U(1) is the centraliser of the Fibonacci two-block VEV; SU(5) is the unique rank-4 grand-unified pair compatible with C(G) = 588 and H(G, V) = 91.
The cosmological-constant integer N_CC = L_4^2 * dim G_SM = 588 and the hierarchy integer N_hier = dim SU(5) * rank - dim 5 = 91 are mixed Hopf invariants pq of explicit doubly-twisted Hopfions Phi_{p, q} on S^3.
Closed-form polynomials in generation index g in {1, 2, 3} and gauge index m in {-1, 0, +1} produce the leading Z[phi] addresses for all nine charged-fermion masses and three gauge couplings; the polynomial coefficients lie in the 9-atom basis B = {F_3, F_4, F_5, F_6, F_7, L_3, L_4, L_5, 23}.
Bergman corrections -- saddle-mode residuals of the sigma-equivariant Faddeev-Skyrme energy minimiser -- refine each leading address; every two-term gap Delta n = n_2 - n_1 lies in the 8-element atomic family A = {2, 3, 4, 5, 6, 7, 8, 10}.
The Mobius parity det M_sigma = -1 manifests in six independent but mutually equivalent ways: the Z/2 grading of K_0(A_sigma), the Galois involution tau: phi <-> psi, KO-dimension 5 of the Hopfion spectral triple (J^2 = -1, JD = DJ, J*gamma = -gamma*J), the Lucas-Binet sign convention, the Mobius-band orientation, and mapping-torus orientation reversal.
Structural consequences include m_{nu_1} = 0 (forcing normal ordering, sum m_nu ~ 58.8 meV), Strong-CP angle bar-theta = 0 with non-perturbative residual at most phi^(-588) ~ 10^(-123) (no axion required), and three generations from the C_3 torsion of the Hopfion class group at admissibility level ell = 4.
Headline numbers: 45 dimensionless observables (charged fermions, gauge couplings, bosons, CKM, PMNS, neutrino mass-squared splittings, twelve Planck-2018 / DESI cosmological parameters, two CCH absolute ratios) reproduced from sigma alone. Aggregate RMS fractional error 0.063%, maximum 0.275% (sin^2 theta_W^eff), 41/45 within PDG / Planck / CODATA 1 sigma at k = 2 Bergman truncation. Per-sector RMS: fermions 0.021%, gauges 0.123%, bosons 0.046%, CKM 0.030%, PMNS 0.011%, neutrino splittings 0.013%, cosmology 0.075%.
Reproducibility: the single companion script framework_verifier.py (Python standard library only; runtime under 1 second) re-derives every claim in the monograph: 43/43 structural theorem tests, all 44 numerical predictions, the 38/38 Mobius-class selection rule, the Hopf-invariant identities N_hier = L_4 F_7 = 91 and N_CC = L_4^2 dim G_SM = 588 via numerical integration on S^3, the KO-dim 5 sign relations, the psi-mode / Lucas-Binet duality, the atomic Delta n classification by sector, and three open-problem audits (third Bergman atom for the four 1-sigma outliers, Strong-CP suppression bound, absolute neutrino spectrum). No external data files; PDG 2024 / Planck 2018 / CODATA 2022 reference values are hard-coded as comparison anchors only.
Contents: eighteen Parts plus five Appendices. Foundations (sigma-uniqueness from the empty set); the Mobius parity of sigma; 3+1-dimensional spacetime from the Zeckendorf decomposition; algebraic structure of A_sigma and the 9-atom basis; the doubly-twisted Hopfion spectral triple; the sigma-equivariant action principle; uniqueness of the admissibility level ell = 4; the Higgs-quartic mechanism; the SU(5) grand-unified group; the tight-binding 588-theorem; the hierarchy 91-theorem; structural primitives; Bergman corrections; cosmology and the hierarchy; special structural identities (three generations, m_{nu_1} = 0, bar-theta = 0, spinorial matter); the 45-observable catalogue; the Master Theorem; and synthesis & outlook. Appendices: compact catalogue table, notation, theorem index, the companion script, and the bibliography.
Files in this record:
theory_of_nothing.pdf (or .tex source) -- the monograph
framework_verifier.py -- single companion script (Python standard library only, runtime < 1 second, emits an eight-part deterministic report)
To reproduce all numerical claims:
python framework_verifier.py
Files
The Theory of Nothing.pdf
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2026canonical date of creation