What question did this study set out to answer?

The research aims to derive physical consequences from a quaternionic vacuum framework, establishing connections among geometry, mass, and nuclear binding.

March 28, 2026Open Access

Vacuum Mechanics: New Series — From Spectral Geometry to Fermion Masses, Nuclear Binding, and the Framework Boundary (Papers I-V)

Key Points

The research aims to derive physical consequences from a quaternionic vacuum framework, establishing connections among geometry, mass, and nuclear binding.
Analysis of spectral zeta functions and theorem proofs
Derivation of NLO mass-formula coefficients from Casimir energy ratios
Examination of various domains including particle masses and theoretical models
Application of numerical correlations and boundary assessments
Evaluating predictions of nuclear parameters and masses using the vacuum framework
Proven theorems regarding spectral zeta function properties
Reproduction of nine charged-fermion masses with minimal error
Identification of ratios critical to quantum mechanics and nuclear stability
New predictions for neutron lifetime and axial coupling
Establishment of a physical argument for the Yang-Mills mass gap

Abstract

Five papers deriving consequences of the quaternionic vacuum condensate framework established in Papers I-IX (Zenodo, 2026) and consolidated in Paper 10 (DOI: 10. 5281/zenodo. 19234951). Paper I (10pp) proves two theorems about the spectral zeta function of the Laplacian on S³: (1) ζᵤ (s) ∈ ℚπ² for all positive integer s, and (2) the rational-part numerators satisfy b (s) = 4ˢ + C (2s, s) /2. The unique Pythagorean decomposition 137 = 4² + 11² = dim (ℍ) ² + b₀² is established as a Gaussian integer norm. Paper II (7pp) derives all six NLO mass-formula coefficients from two Casimir vacuum energy ratios on S³: RM = E (Maxwell) /E (scalar) = 22 and RD = E (Dirac) /E (scalar) = 8. The identity RM = 2b₀ is proven from Bernoulli numbers and holds exclusively at Nc = 3. Nine charged-fermion masses are reproduced at 0. 14% RMS with zero fitted parameters. The proton charge radius rₚ = 4ℏc/mₚ = 0. 8412 fm matches muonic hydrogen to 0. 04%. Paper III (14pp) traces the master identity λₖ (S³) = dim (SU (k+1) ) across domains: periodic table orbital blocks, crystal field splitting (Δₜet/Δₒct = QK² = 4/9), five DFT functional parameters (zero fitted), gold's colour (γ = 1/√QK), the glueball mass spectrum (four ratios at 0. 05-0. 2%), and Fibonacci anyons at Chern-Simons level k = 3. A sharp framework boundary is documented via six negative probes. Paper IV (11pp) proves that the QCD colour Casimir CF = 4/3 equals (Nc+1) /Nc exclusively at Nc = 3, and traces this ratio through baryogenesis, DFT exchange, MHD turbulence (exponent gap 1/6 = 1/Nf), the She-Leveque intermittency formula, and the Abraham-Lorentz electromagnetic mass problem. A physical argument for the Yang-Mills mass gap is presented. Paper V (9pp) derives all five Weizsäcker SEMF coefficients from framework constants. The headline result aA/aV = 3/2 = 1/QK (0. 24%) connects nuclear isospin to the Koide lepton mass fraction. The axial coupling gA = 1 + 3MK = 1. 275 (0. 033%) and neutron lifetime τ = 878. 7 s (favouring bottle over beam) are new predictions. Total: 51 pages, ~180 results, 3 proven theorems, 7 sub-0. 1% predictions, zero fitted parameters beyond v = 246. 22 GeV.

Vacuum Mechanics: New Series — From Spectral Geometry to Fermion Masses, Nuclear Binding, and the Framework Boundary (Papers I-V)

Key Points

Abstract

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