The Papers
A Unified Framework for Emergent Particle Structure, Cosmology, and Gravitational Phenomena
The Axis Model introduces a geometric foundation in which particles, interactions, and cosmological structure arise from quantized internal vector displacements stabilized by a universal scalar field. In this framework, electric charge, inertial mass, spin, and the effective flow of time emerge from scalar-projected composite configurations rather than being assumed as intrinsic. The construction is developed within a controlled effective field theory (EFT) and remains compatible with standard field-theoretic methods. Built within a scalar–coherent effective field theory formalism, the program recovers Standard Model and General Relativity behavior in their established domains. It makes a comprehensive set of falsifiable predictions for phenomena including gravitational lensing, neutrino mass bifurcation, and large-scale CMB anomalies. In this context “unified” means a single scalar–vector EFT that supplies cross-sector interface relations (normalization, gauge structure, and emergent-gravity closures) and reduces to SM+GR in the stated limits; it is not a claim of a complete UV-final theory.
Abstract · Full Paper PDF · Colab Notebooks
A Geometric Origin for the Standard Model Fermion Sector
This paper presents a geometric framework for organizing the Standard Model fermion sector within the Axis Model. Rather than modifying the Standard Model gauge structure, it treats fermions as ordinary Dirac fields whose masses and mixings are shaped by an underlying morton geometry — scalar-stabilized internal configurations governed by winding, curvature, and overlap structure. Using four measured inputs — the electron mass, the charged-lepton mass ratios, and the Cabibbo angle — the framework generates fixed post-calibration outputs including charged-sector mass hierarchies, quark mass anchors with QCD dressing, CKM magnitude tables, neutrino mass scales, and PMNS benchmarks. The quark masses fall near current reference values at the percent level for most flavors, the rank-2 CKM correction lifts ∣Vub∣ to the observed order of magnitude, and remaining tensions are localized primarily in the third-row sector. In the lepton sector, the minimal construction yields a CP-conserving baseline, while a controlled neutral-sector extension produces experiment-scale leptonic CP violation. A fully reproducible numerical pipeline accompanies the analysis.
Abstract · Full Paper PDF
Quantum Completion of the Axis Model: Gauge Structure, BRST Invariance, and Renormalization Stability
This paper develops the full quantum field-theoretic formalism of the Axis Model. Gauge fields arise as scalar-filtered projections of internal vector displacements, and BRST quantization ensures unitarity and gauge consistency. It provides a complete first-principles construction of the SU(2)L × U(1)Y sector and shows that the W and Z masses and the Weinberg angle emerge without a fundamental Higgs doublet. Anomaly cancellation is shown via scalar-bundle triviality, and renormalization-group analysis establishes stability of the EFT up to the scalar coherence scale (∼105 GeV).
Abstract · Full Paper PDF
Quantum Consistency and Renormalization of the Axis Model Effective Field Theory
This paper develops the ultraviolet and quantum-field-theoretic structure of the Axis Model. It constructs a pre-geometric SU(2) ultraviolet parent for the Axis U(1)Z, performs single-threshold matching at μ = Λq , and runs the complete two-loop renormalization-group equations across the threshold. The analysis demonstrates that the apparent Abelian Landau-pole artifact disappears once the Abelian basis terminates at Λq , establishing quantum consistency and renormalization-group stability of the effective theory.
A BRST-invariant gauge fixing and anomaly-free scalar-bundle structure are proven, and the emergent electroweak mass matrix is shown to arise from a composite orientation stiffness Zχ with veff = Zχ · v. Within its predictive window (ΛΦ ≈ 10⁵ GeV – Λq ≈ 10¹⁶ GeV), the Axis EFT remains perturbative, vacuum-stable, and fully reproducible through the accompanying notebooks.
Abstract · Full Paper PDF
Quantum Gravitational Extension of the Axis Model: Emergent Spacetime and the Einstein–Hilbert Limit
This paper develops the quantum gravitational extension of the Axis Model, in which spacetime geometry, curvature, and gravitational dynamics emerge from scalar-filtered internal field configurations. The metric gµν(x) is a composite operator built from internal displacement fields and a complex scalar field Φ(x) that enforces coherence. We define scalar-coherent projection operators, construct the emergent vierbein and metric, and quantize the theory via a path integral over non-geometric degrees of freedom. In scalar-coherent domains, a one-loop effective-action calculation produces the Einstein–Hilbert term, and the graviton appears as a massless spin-2 excitation of the coherent field ensemble. Predictions include environment-dependent G(Φ), suppression of curvature and gravitational-wave amplitudes in decoherent regions, and non-singular black-hole interiors.
Abstract · Full Paper PDF
Quantifying Emergent Gravity in the Axis Model: The One-Loop Map to Geff(x)
This paper derives a local, one-loop expression for the effective Newton coupling Geff within the Axis Model’s scalar-coherent framework. It shows how gravity emerges as a state-dependent phenomenon: fully coherent regions reproduce general relativity, while partially decoherent domains within the EFT window predict a smooth, measurable weakening of gravity.
The work establishes gauge and BRST independence, boundedness, and causal consistency of the resulting equations. It also outlines falsifiable weak-field predictions—environment-dependent lensing, time-delay, and gravitational-wave signals—and provides a fully reproducible notebook that regenerates all figures and calculations.
Abstract · Full Paper PDF
Ab-initio Electroweak Normalization and Mixing from a Coherent Pre-Geometric Background
This paper develops a first-principles derivation of the electroweak couplings gL, gZ , the weak mixing angle, the photon direction, and ultimately the electromagnetic coupling e directly from a single coherent background of the Axis Model. Rather than treating these parameters as empirical inputs, the construction shows how they arise from the stiffness of a self-dual geometric background and a fixed internal projection onto the electroweak subgroup.
The paper also accounts for optional kinetic mixing in the neutral sector, defines a consistent Abelian matching scheme at the UV crossover scale, and reports the hadronic vacuum-polarization contribution required in the running of α(0). A reproducible notebook accompanies the analysis, allowing readers to regenerate all RG flows, boundary conditions, and numerical predictions.
Abstract · Full Paper PDF
Ab-initio SU(3)C Normalization and Strong-Sector Running in the Axis Model
We fix the SU(3)C boundary coupling at a universal matching scale from a coherent pre-geometric background (Axis Model Scenario B) and evolve it to the Z pole using standard two-loop QCD running with threshold matching. The canonical product–UV reference background underpredicts the observed strong coupling, which we interpret as evidence for a reduced effective color projector weight induced by ultraviolet vacuum anisotropy (“kernel tilt”), not an infrared tuning parameter. An inverse RG audit isolates the required effective color weight, and Appendix C gives a minimal microscopic existence demonstration: a symmetric color-triplet kernel with one coherence/locking mode generates the needed reduction via tilt of the stiff coherence axis. Reproducibility is supported by a deterministic driver and machine-readable ledger outputs.
Abstract · Full Paper PDF
Internal-Orientation Interpretation of Vacuum Kernel Anisotropy: Projector Weights as Orientation Fractions in the Axis
Model
This paper provides a dynamical interpretation of the vacuum anisotropy (projector-weight suppression) used in strong-sector and electroweak normalization within the Axis Model Scenario B framework. Without introducing new degrees of freedom or modifying the effective field theory, renormalization-group evolution, or matching conditions, the work reinterprets the static anisotropic kernel used at matching as the effective energy of an internal orientation mode with conserved angular momentum. Stationary tilted solutions coincide with the kernel eigenvectors, giving a direct consistency check between the dynamical picture and the static normalization ledger, and sector projector weights emerge as geometric orientation fractions rather than ad hoc suppressions. Practical issues of averaging, finite-window response, damping, stability, and falsifiability are treated explicitly, while microscopic derivations of the kernel anisotropy and the precession scale are deferred.
Abstract · Full Paper PDF
Microphysical Reduction of Vacuum Kernel Tilt and Internal Precession in the Axis Model
This paper completes the microphysical foundations of vacuum anisotropy in the Axis Model by deriving the parameters that govern internal orientation and projector-weight suppression in Scenario-B normalization.
Previous work introduced an internal-precession interpretation in which reduced projector weights arise as time-averaged orientation fractions of a coherent internal degree of freedom. While that interpretation successfully explained phenomenology, several key elements were left open: the microscopic origin of the anisotropic kernel, the dynamical timescale controlling the averaging procedure, and the identification of the internal direction probed by gravity.
Here we close those gaps at quadratic order.
Starting from a generic collective-coordinate Lagrangian for the coherent branch, containing light internal coordinates and heavy locking or mediator modes, we perform a controlled quadratic reduction. Integrating out the heavy sector via a Schur-complement construction yields an effective light-sector kernel and inertia. Canonical normalization then fixes the physical meaning of the anisotropy parameters and removes basis ambiguities.
Abstract · Full Paper PDF
Non-Abelian Gauge Structure from Coherence-Gated Internal Symmetries: A Projection Mechanism and a Kernel-to-Coupling Map
Published in AIP Advances (2026)
DOI: https://doi.org/10.1063/5.0323640
This result formalizes the origin of gauge structure in the Axis Model as a geometric consequence of coherent-domain projection, rather than a model-dependent assumption.
This peer-reviewed work establishes a concrete effective-theory mechanism by which non-Abelian SU(2) gauge structure emerges from scalar-coherent internal symmetries within the Axis Model framework. We show that, on coherence-preserving domains, a rank-2 internal sector induces a fully gauge-covariant connection in the Wilczek–Zee sense, with the associated Yang–Mills structure arising as a geometric consequence rather than a postulated input. The paper further derives an explicit kernel-to-coupling map, linking microscopic quadratic response to the normalization of the emergent gauge sector via a computable projector weight. This provides a quantitative interface between internal kernel geometry and low-energy gauge dynamics. The construction is minimal, parameter-controlled, and compatible with standard effective field theory matching procedures. Reproducible computational artifacts accompany the analysis, yielding a concrete benchmark for emergent non-Abelian gauge structure within the broader Axis Model program.
Abstract · Full Paper PDF
Kernel Universality and Sector-Projection Consistency in the Axis Model: A Sector-by-Sector Identifiability and Existence Analysis with No New Inputs
This paper clarifies the role of the scalar-coherent kernel used across multiple sectors of the Axis Model. It shows that the kernel itself is not an observable: all sectoral results depend only on projector-restricted contractions of the inverse kernel on scalar-coherent domains. As a result, constraints from different sectors do not over-determine the kernel but require only mutual compatibility. No new parameters, fits, running, or predictions are introduced; the paper serves as a logical consistency and scope-clarification note for the Axis Model suite.
Abstract · Full Paper PDF
