A BRST-consistent effective field theory in a scalar-coherent framework deriving particle structure, gauge dynamics, and an emergent-gravity limit from a single master Lagrangian, with full RG analysis, anomaly checks, and testable predictions.
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The Axis Model is a geometric preonic theory in which Standard Model particles and interactions emerge from a simple internal geometry, with gravity appearing as an environment-dependent, emergent limit.
The Standard Model and General Relativity are the twin pillars of modern physics yet they rest on incompatible foundations. One is quantum and particle-based, the other geometric and gravitational. Neither explains why fundamental parameters take the values they do. The Axis Model explores whether these two pillars can instead emerge together from a common underlying structure.
This research program develops a BRST-consistent effective field theory where particle interactions and gravity both arise as projections from a scalar-stabilized geometric background. A single master Lagrangian yields gauge dynamics, mass structure, and a one-loop Einstein–Hilbert term with a local gravitational coupling Geff(x). The framework stays within an explicit EFT window and matches all standard quantum field theory constraints including anomaly cancellation, renormalization-group consistency, and predictive control.
The Framework in Brief
This theory derives both gravity and the Standard Model from tri-vector composites stabilized by a scalar field. Particle structure, gauge dynamics, and gravitational geometry derive from a single master Lagrangian. Observables arise as scalar-coherent projections of internal vector displacements, a mechanism that reproduces the Standard Model’s SU(3) × SU(2)L × U(1)Y sector and recovers general relativity in the low-energy limit. Supported by interlocking papers with reproducible computational notebooks, the model provides a complete renormalization-group analysis, ensures anomaly cancellation, and delivers falsifiable predictions for fermion mass hierarchies, CKM/PMNS mixing, and testable signatures in lensing, neutrinos, gravitational waves, and cosmological structure.
From four geometric inputs the suite reproduces the full SM fermion spectrum and CKM/PMNS matrices; dynamically generates the electroweak sector with W/Z masses from a composite orientation scale (veff = Zχ·v); and fixes |Vub| via a parameter-free rank-2 overlap. The framework is UV-extended to a pre-geometric SU(2) parent for the Axis U(1)Z, removing the Abelian Landau-pole artifact and establishing two-loop renormalization consistency across the Λq threshold. The quantum completion is BRST-invariant, anomaly-free, and RG-stable up to the scalar-coherence cutoff (~10⁵ GeV), consistent with (g-2) and dilepton-compositeness bounds. The gravitational extension derives the Einstein–Hilbert term at one loop and predicts environment-dependent G(Φ) with lensing/GW attenuation, providing falsifiable departures from GR.
Developed across six openly published papers with reproducible notebooks, this framework demonstrates:
Emergent Einstein equations — A one-loop effective action generates GR terms in coherent domains.
Derivation of SM parameters — All 19 fermion masses and mixing angles arise from 4 geometric inputs (74% within 1% of experiment).
Quantum consistency — BRST invariance, two-loop RG stability, and resolution of the U(1) Landau pole.
Testable predictions — Environment-dependent lensing signatures and gravitational wave attenuation in decoherent media.
The model operates within an explicit EFT window (10⁵–10¹⁶ GeV), where scalar coherence determines which field configurations project into observable spacetime.
The Papers
A Unified Framework for Emergent Particle Structure, Cosmology, and Gravitational Phenomena
The Axis Model introduces a new foundation for physics where particles, forces, and cosmological structure arise from quantized vector displacements stabilized by a scalar field. In this framework, electric charge, inertial mass, spin, and even the flow of time are not assumed as fundamental, but emerge from the projected geometry of coherent bound states. Built upon a single master Lagrangian, the model recovers the Standard Model and General Relativity 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.
Abstract · Full Paper PDF · Colab Notebooks
A Geometric Origin for the Standard Model Fermion Sector
This paper derives the full fermion sector of the Standard Model from the geometric framework of the Axis Model. All observable particles are modeled as scalar-stabilized tri-vector composites, whose internal configurations of quantized vector displacements generate gauge groups, mass hierarchies, mixing angles, and CP-violating phases. Once calibrated to {me, mµ/me, mτ/me, θC}, the framework predicts all other fermion masses, CKM/PMNS mixing matrices, and CP phases with high accuracy: 74% of observables within 1% of experiment, 95% within 5%, and all 29 predictions within 10%. Companion notebooks implement the full calibration → prediction pipeline for computational transparency.
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).
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.
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.
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.
Technical Q&A
This section provides formal answers to detailed questions from colleagues and reviewers, serving as a transparent record of the model's ongoing technical validation.
General Q&A
This section offers a plain-language entry point for curious readers, students, and science writers. It introduces the big questions the Axis Model addresses, without requiring detailed background in particle physics or quantum field theory.
A summary of the current scientific status of the Axis Model, with context on reproducibility, predictions, and future tests.
