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[6] ai.viXra.org:2606.0077 [pdf] submitted on 2026-06-28 09:15:50
Authors: Ginanjar Utama
Comments: 13 Pages.
The preceding paper in this sequence connected matter-first spin networks to the simplicity-constrained EPRL vertex: matter-line frames generate spacetime-algebra bivectors, the EPRLmap selects a ray in the bivector invariant plane, and the Lorentzian four-simplex amplitude can be evaluated as a nite-cuto tensor network on K5. That result was kinematical and vertex-local. This paper asks the next question: when curvature is present, can the matter determinant see it, and can it back-react on the spin-foam flatness tendency? We build a finite hinge-link model in which several four-simplices meet around an internal triangle. The Regge decit ϵh = 2π −Pσ⊃h Θσh is represented as a rotation in the two-plane normal to the hinge,with spin lift Uspin(ϵh). The first exact result is the holonomy obstruction det(I − Uspin) = 16 sin^4(ϵh/4), which vanishes in the flat sector, modulo the expected spinorial 4π periodicity. A finite graph Dirac operator on the hinge link reproduces the same obstruction and develops a curvature-induced spectral gap. Integrating out fermions therefore suppresses the near-at zero-modesector in a one-hinge toy model, opposing the gravitational atness preference. For two hinges,disconnected link graphs factorise exactly, whereas edge-sharing link graphs have a non-zero determinant interaction; matter propagation then induces a curvature-curvature correlation between neighbouring defects. Finally we add a chiral Spin(4) = SU(2)+ × SU(2)− split. A single finite hinge determinant is phase-trivial, arg det(Dχ + m) = 0, so it can bias chiral variances but cannot by itself generate orientation-sign flow. The parity-odd channel in four dimensions is instead the Pontryagin pairing tr(γ5Σ1Σ2) ∼ B1 ∧ B2, non-zero only for transverse hinge planes. The result is not a continuum limit or a derivation of the full spin-foam measure. It is a controlled finite-complex mechanism: fermion determinants are holonomy-sensitive functionals of Regge decits and can induce matter-mediated curvature correlations on spin-foam hinge links.
Category: Quantum Gravity and String Theory
[5] ai.viXra.org:2606.0074 [pdf] submitted on 2026-06-27 03:56:08
Authors: Ginanjar Utama
Comments: 9 Pages.
A previous paper proposed a matter-first route to loop quantum gravity: interaction vertices define the graph, fermion-line segments carry local SL(2,C) frames, and geometry is reconstructedfrom the resulting spacetime-algebra comparators. Its central open gap was the relation betweenthose matter-built bivectors and the simplicity-constrained boundary data of spin-foam dynamics. This paper closes that kinematical gap and adds a finite-cutoff vertex algorithm. First, we express the EPRL linear simplicity constraint in the invariant plane of the bivector classification B^2 = s + pI: up to the standard sign and normalisation conventions for SL(2, C) Casimirs, the EPRL embedding Y_γ : j → (ρ, k) = (γj, j) selects a ray p/s = 2γ/(γ^2 − 1). Second, we sharpen the closure bridge: the area-vector closure condition at a tetrahedron is equivalent to the Minkowski polygon inequality, and this is exactly the condition that the four-valent intertwiner space be non-empty. Thus classical closure and quantum admissibility are two presentations of the same Gauss constraint. Third, we construct the Lorentzian vertex from the same data: the boost sector is represented by principal-series generators certied by the so(1, 3) algebra and Casimirs, and the node booster B^γ_4 is evaluated as a radial boost integral. Finally, by absorbing each booster and intertwiner into a rank-four node tensor, the finite-cutoff EPRL four-simplex amplitude becomes a tensor-network contraction on K_5 rather than an explicit state sum. The result is not a continuum limit; it is a reproducible bridge between the matter determinant,bivector simplicity, and a computational Lorentzian EPRL vertex.
Category: Quantum Gravity and String Theory
[4] ai.viXra.org:2606.0064 [pdf] submitted on 2026-06-25 10:42:25
Authors: Ginanjar Utama
Comments: 10 Pages.
Loop quantum gravity (LQG) is usually formulated as a quantisation of geometry, while operational measurements of length, time, and orientation are made through relations among matter fields. Penrose’s combinatorial spacetime and Altaisky’s recent locally Lorentzian matter-spin-network construction suggest a matter-first route: interaction events form the vertices of a graph, fermion-line segments form its edges, and geometry is reconstructed from the relations carried by those lines. We develop this kinematical proposal into an induced dynamical model with a computable discrete field equation. In the spacetime algebra Cl(1, 3), the SL(2, C) interaction vertices become versors; their sandwich action transports the matter-built tetrad, agrees with both the Hermitian-matrix and Ruehl Lorentz maps, and sends elementary areas to simple grade-two blades. Loop curvature is the bivector logarithm of a holonomy and is classified by the scalar and pseudoscalar invariants of B2; the generic loxodromic case is handled by a closed-form commuting elliptic—hyperbolic split. Because the discrete Grassmann matter action is bilinear, its path integral is the exact fermion determinant Z = det D. On an oriented graph Dirac operator, gauge invariance reduces Z to a functional of cycle-space holonomies, whileloops that share interaction events fail to factorise. The connected non-factorising determinant defines the interaction part of the effective action. Varying Seff = − log | det D| gives a local, gauge-covariant stationarity condition relating each independent cycle connection to the fermion propagator. Flat geometry solves the homogeneous equation as a Lorentzian saddle, and fixed boundary holonomies source curvature in the remaining cycles. We demonstrate the construction on the tetrahedral S^2 toy universe and on the K5 four-simplex 1-skeleton. The resulting equation is induced, Sakharov-style, and no continuum limit to Einstein gravity is claimed.
Category: Quantum Gravity and String Theory
[3] ai.viXra.org:2606.0055 [pdf] submitted on 2026-06-22 18:38:02
Authors: Nigel B. Cook
Comments: 5 Pages.
We present a unified analytic framework in which weak-interaction radioactive decay and neutrino flavour oscillations arise as two branches of a single exponential—oscillatory duality. The key mathematical observation is that multiplying by i in the exponent converts oscillatory behaviour into exponential damping.
Category: Quantum Gravity and String Theory
[2] ai.viXra.org:2606.0041 [pdf] submitted on 2026-06-16 20:39:51
Authors: Hongshu Zhu
Comments: 9 Pages. (Note by ai.viXra.org Admin: Author name is required in the article after article title; and please cite and list scientific references)
This comprehensive manuscript proposes a profound paradigm shift in theoretical physics, offering a unified geometric framework that bridges the genesis of the universe, the mechanics of elementary particles, and the horizon of applied aerospace engineering. Diverging from the traditional Big Bang singularity, this hypothesis posits that the universe originated from the spatiotemporal topological collapse of a fourth spatial dimension, leaving behind microscopic "black hole-white hole" dual rotating oscillators—the geometric and fluid essence of all elementaryparticles. Within this Topological Fluid framework, the four fundamental forces(gravity, electromagnetism, strong, and weak interactions) are unified seamlessly asdistinct manifestations of fluid dynamics, and the classical mass-energy equivalence(E = mc2) acquires a pure geometric derivation.Advancing into applied physics, we define the mechanism of Topological Phase Locking, whereby extreme high-frequency electromagnetic resonance aligns the spatial emissions of these microscopic dipoles. By integrating this mechanism with the Ginzburg-Landau theory of superconductivity to eliminate thermal topological friction, we introduce the Non-Minimal Topological Coupling Lagrangian. This novel field-theory formalism proves that electromagnetic resonance within a macroscopicquantum coherent state forces a renormalization of the effective gravitational constant (Gef f < 0). This directly derives the Gravitational Meissner Effect—the absolute expulsion of the background gravitational spatial flux. Ultimately, this manuscript delineates a rigorous, propellantless geometric pathway for macroscopic topological thrust, the elimination of inertial mass, and Faster-Than-Light (FTL)metric traversal, offering theoretical alignment with contemporary anomalous aerodynamic observations.
Category: Quantum Gravity and String Theory
[1] ai.viXra.org:2606.0018 [pdf] submitted on 2026-06-07 17:14:13
Authors: Nigel B. Cook
Comments: 10 Pages. (Note by ai.viXra.org Admin: An abstract labeled as such is required in the article; please cite and list scientific references)
There are three roads to the same mechanism for quantum gravity given in 2011 vixra paper 1111.0111. This paper extracts them from that paper and compares them. Illustrations are appended. Paper was checked using Microsoft Copilot AI system for mathematical accuracy.
Category: Quantum Gravity and String Theory