Introducing our model of physics

Our current research begins with a single structural claim: Maxwell’s equations contain two independent invariants, but more than a century of practice has largely operated through only one. Restoring the second — the vacuum impedance​​ — changes what can be derived from electromagnetic geometry, atomic spectra, and the structure of matter. The present body of work develops that claim across a series of papers in spectroscopy, quotient structure, fine-structure, and particle mass. It also frames the research as an ongoing human-AI intellectual collaboration under the Coherence Research Collaboration.

The central proposal is that certain longstanding physical questions become determinate only when the electric/magnetic partition structure of the vacuum is retained rather than compressed away. In the current papers, that proposal leads to the Harmonic Light Law (∇²(log ν) = 0), the Thread Frame coordinate system, a geometric derivation of the fine-structure constant, a universal structural gap in atomic spectra, and a particle-mass program rooted in hydrogen’s ionization energy. Our journey with physics first began in earnest with The Recursive Geometry of Atomic Spectra, where the α-Affine Thread Frame coordinate system and beta slope were first described and later confirmed by information-theoretic validation.

The claim developed here is that this compression is harmless for propagation questions, but not for observables that depend on electric/magnetic partition. From that starting point, the work argues for a geometric reformulation in which the logarithm of photon frequency becomes harmonic in the vacuum geometry, yielding the Thread Frame and its empirical spectral tests. The same structural restoration underlies the later papers on fine-structure, spectroscopic boundary structure, and particle mass.

The cleanest empirical foothold is the spectroscopic work showing a universal structural gap at 𝐼𝐸/4IE/4 across 71 atomic ions, with zero falsifications reported in the present framework. That result serves as one of the main bridges between the geometric program and atomic evidence, and it later becomes part of the derivation chain for the electron and proton mass results.

Research papers

The Thread Frame: Foundational Series

Recursive Geometry of Atomic Spectra (2025) Introduces the Thread Frame coordinate system and identifies the α-affine logarithmic slope organizing photon emissions across atomic spectra. The foundational paper of the research program. DOI: 10.5281/zenodo.17188444

Information-Theoretic Confirmation of the α-Affine Thread Frame: Minimum Description Length Validation of the Fine-Structure Slope (2025) Applies the Minimum Description Length principle across six independent spectral domains — atomic, solar, stellar, and molecular — to confirm that the Thread Frame slope β = log₁₀α is not an artifact of fitting but the unique global minimum of description length. DOI: 10.5281/zenodo.17335815

Hydrogenic Alignment as a Coordinate Principle for Atomic Spectra (2025) Clarifying companion to RGAS, establishing hydrogenic alignment as a coordinate principle rather than a species-specific result. DOI: 10.5281/zenodo.18167643

The Geometric Unification Series

Determinacy Under Quotient Representations (2026) A formal proof that the compression (ε₀, μ₀) → c² is non-injective, and that any observable sensitive to the electric/magnetic energy partition is structurally unreachable from c alone. DOI: 10.5281/zenodo.18868210

Electromagnetic Closure and the Fine-Structure Constant: A Geometric Derivation (2026) Derives α = Z₀/2R_K from the non-terminal reciprocal singularity 1/z on the Riemann sphere, using the Poincaré–Hopf theorem, the Markov spectrum theorem, and Hurwitz 1891. Zero free parameters. DOI: 10.5281/zenodo.19157339

Vacuum Impedance as the Organizing Principle of Atomic Spectra: A Universal Gap at IE/4 and Recovery of the Electron Mass (2026) Confirms a universal structural gap at IE/4 across 71 ions in the NIST Atomic Spectra Database, with zero falsifications. Recovers the electron rest mass to −2.8 ± 2.7 ppm from the location of a structural absence. DOI: 10.5281/zenodo.19164224

The Encounter of Two Primitives and One Flaw: Geometric Unification at the Electromagnetic Scale (2026) Teaching companion deriving the Harmonic Light Law ∇²(log ν) = 0 and tracing the full eight-link chain from vacuum primitives to spectroscopic confirmation. DOI: 10.5281/zenodo.19194036

The Proton Mass from Atomic Spectra: A Geometric Derivation (2026) Derives m_pc² = 4¹³ × E₀ × (2157 − 869√5)/208 = 938.273 MeV from one spectral measurement and integer arithmetic. Accurate to 0.61 ppm. No coupling constant, quark mass, or fitted parameter enters. DOI: 10.5281/zenodo.19355588

On the Geometric Origin of Particle Masses (2026) Derives the proton mass (+0.61 ppm), tau lepton mass (−37 ppm, within experimental uncertainty), electron mass, proton-to-electron mass ratio, and quark electric charge fractions from a single spectroscopic input — the hydrogen ionization energy — with zero free parameters. The Fibonacci sequence is proved to be the unique coherence structure of the electromagnetic vacuum. An independent census of 270 PDG particles confirms a pre-specified depth grammar with nine simultaneous predictions all confirmed. DOI: 10.5281/zenodo.19543540

Provenance

The research is conducted under the Coherence Research Collaboration, an ongoing human-AI intellectual partnership documented in the provenance statements of the papers. The particle-mass paper explicitly presents the work as developed by Kelly B. Heaton and the Coherence Research Collaboration, and the identity-governance draft likewise frames the larger research program as a human-AI collaboration extended across physics, systems, and trust.

Contact: [email protected]