Artian Geometry & Quantum Traction Theory

Abstract.

Quantum Traction Theory (QTT) is a ground-up ontological reconstruction of classical mechanics, quantum mechanics, and general relativity from a small set of foundational axioms. The framework introduces an absolute background clock distinct from laboratory time, a real-valued internal dial replacing the imaginary unit as a primitive with clear physical  explanation, quantum capacity, and bundled existence saturating one modular circle at every world-cell address. From these primitives, the standard structures of contemporary physics are derived rather than postulated.

Axioms.

A1 — Two-clock cosmological geometry: an absolute background tick alongside the laboratory clock, related by a smooth positive lapse.
A2 — Law of Endurance: an inverse-square endurance flux that produces Newtonian gravity in the infrared limit, with the framework's micro-length identified with the Planck length.
A3 — Law of Creation: a uniform creation rate that mimics a cosmological-constant term.
A4 — Internal S¹ dial at every address; the imaginary unit i is identified with the quarter-turn J on the real two-component dial (J² = −1). U(1) gauge structure and integer charge quantization follow.
A5 — World-cell decomposition with visible–hidden factorization at every address. (reality dimension in Artian Geomtery) 
A6 — Per-address capacity ceilings on energy, power, and action throughputs. (quantum capacity)
A7 — Law of Bundled Existence: a saturated modular-charge budget of one full angular modular period at every world-cell address.

Derivations within the framework.

The framework recovers, from these axioms: Newton's law of gravitation; Maxwell's equations and minimal coupling; the Schrödinger equation; integer charge quantization and the Dirac condition; the Einstein field equations from the Law of Endurance combined with the Unified Equilibrium Law; Stern–Gerlach quantization; the de Broglie–Planck relations; flux quantization and the Josephson relation; the Pancharatnam–Berry geometric phase; the Tsirelson ceiling on Bell-CHSH correlations; and a parameter-free expression for the fine-structure constant. The Unified Equilibrium Law E_P = m_P c² = ℏω_P = ρ_(4)(4πℓ_P⁴) packages mass, frequency, and four-density as four equivalent faces of the Planck four-cell capacity unit.

Additions in version 6.

Access Law (a finite-throughput restatement of the uncertainty principle); QTT Fourier Frontier; Path Phase Law; Artian Geometry; operational definitions of observation and measurement; and a Quantum Capacity formulation addressing surface-brightness limit anomalies.

On scope and approach.

QTT is offered as a foundational reconstruction, not as a corrective patch to existing theories. Rather than adopting the imaginary unit, the cosmological constant, or measurement-induced collapse as primitives, the framework derives them as consequences of more elementary structures (the real dial, the creation rate, the bundled address). The reconstruction is deliberate; readers familiar with the standard package of general relativity plus quantum field theory should expect the formulation to be unfamiliar in places. The mathematical claims are stated to professional standard, and specific structural identifications and quantitative predictions derived from this framework appear as separate paper-track preprints listed below.

Not every equation that appears in a QTT manuscript is novel, and most are not. This is by design: a structural-reconstruction programme must recover the established formulae of physics in their established regimes, and the equations that do this work are not where the contribution lies. The contribution lies in what those equations mean once they are derived from QTT primitives rather than postulated. A representative case is the relation between Newton's constant G and Planck-scale quantities. Treated as a rearrangement of Planck units, the expression is dimensional bookkeeping. Treated structurally, the same expression is forced by Axiom 2 (the Law of Endurance) acting through the Universal Endurance Law (UEL); the numerical shadow coincides with the Planck-unit form, but the underlying derivation is independent of, and prior to, the Planckian phrasing. This is the canonical "identical-equation, non-equivalent-theory" situation familiar from Newton–Cartan gravity, where shared equations encode structurally distinct theories.

Reading guidance. QTT is a structural reconstruction of classical mechanics, general relativity, and quantum theory from a small axiomatic base, not a competing modification of any of these. As a consequence, isolated objections raised against early sections of the manuscript — most commonly, that the two-clock structure of Axiom 1 appears to threaten Lorentz invariance — are answered structurally rather than locally, by tracing the relevant derivation through to its lab-scale projection. The two-clock substrate, the recovery of GR, the emergence of the local Lorentz group, and compatibility with current SME bounds (Kostelecký et al.) are addressed. The framework asks readers to follow the global chain before adjudicating its local symmetry behaviour; the appearance of conflict is, in every case examined to date, an artefact of partial reading. 

Status of the framework manuscript. QTT is an active and evolving programme. The framework manuscript is maintained under version control, and acknowledged errata are published as separate Zenodo records linked from the framework's main record. As one example, an error identified in the framework manuscript (v6, p. 201, eq. 601, in which a velocity-vs-geometry conflation produced a failed internal test) has been corrected and the correction archived ¹. The present paper does not rely on any equation currently under revision, and all load-bearing inputs cited from the framework manuscript have been verified against the latest version at the time of submission.

Status and related preprints.

This manuscript is openly archived as a long-form work-in-progress and is under continuous development; new versions are published as the framework expands. Paper-track preprints derived from this framework, intended for peer review and citing this manuscript at every load-bearing step:

— Quantum Traction Theory neutrino mass-ratio prediction: doi:10.5281/zenodo.19960814
— A modular-charge fifth face of the Unified Equilibrium Law: doi:10.5281/zenodo.19975260

Project website and blog: https://www.QuantumTraction.org