Physical Sciences

Abstract: The Standard Model treats the Higgs field as a fundamental scalar field, yet this assumption fails to explain its origin, the values of its parameters, or the driving force behind symmetry breaking. This paper proposes that the Higgs field is not fundamental, but rather a geometric degree of freedom emerging at the electroweak scale through the scalar mode of the metric tensor arising from a string-net condensate. We first establish the emergence of the metric tensor as a bilinear condensate of the frame field, and interpret the Higgs potential as a Landau expansion of the cosmological enthalpy around the order parameter. Within this framework, the Higgs parameters are determined by the topological data of a modular tensor category: the bulk-boundary coupling coefficient extracted from the S-matrix of \(SU(3)_{3} \otimes SU(2)_{2}\) yields \(v/\Lambda_{string} = 1.6818\); taking \(\Lambda_{string} \approx 146\) GeV gives \(v \approx 246\) GeV. The quantitative result above relies on Eq. (13), which is a phenomenological ansatz introduced in this work. It establishes the connection between the vacuum expectation value and the string tension scale using S-matrix elements and quantum dimensions; its form is naturally determined by dimensional analysis and the natural combination of topological data, with a rigorous derivation left for future work. Our central claim is that the parameters of the Higgs mechanism should not be treated as free inputs, but rather understood as the low-energy projection of the topological data of the string-net condensate.

Abstract: Three-flavor oscillation theory describes neutrino propagation but takes the PMNS orientation and mass spectrum as empirical inputs. This paper asks whether both can be reconstructed from one neutral-parent carrier architecture. A central feature is cross-sector inheritance: the charged-root ratios and neutral closure seam used here were fixed in a previously published charged-lepton calculation and are imported without adjustment to neutrino data. At the premetric level, the Indefinite Reconstruction Stability Principle (IRSP) requires persistent structure to survive admissible continuation and to descend independently of its representative. Combined with metric–carrier co-selection, codimension-two support yields a two-dimensional normal quotient. Under an explicit exact one-particle mass-readability premise, every local scalar-mass exposure factors through this quotient as a complex-linear map. For a nonzero exposure covariant under an irreducible real transverse rotation action, IRSP saturation fills both independent transverse directions, so a map from three active neutral continuation modes has rank exactly two. A source-protected mass-silent line is transported by exact invariant descent to the first propagation mode, giving m₁=0 throughout the minimal protected reconstruction class. Equal-weight neutral geometry and inherited charged-root data determine a deformed tribimaximal PMNS frame, while a minimal two-seam incidence complex fixes the two nonzero masses. The resulting spectrum is m₁=0, m₂=8.686 meV, and m₃=50.092 meV, with ∑_im_i=58.778 meV. No measured neutrino angle, phase, splitting, or absolute mass is inserted into the formulas; the measured electron mass only sets the final unit. The construction is conditional: exact transverse mass readability, source-level protection, overlap transfer, and post-read-out matching are stated explicitly. Within those premises, completeness of an anchored Z₅ orbit, real transverse descent, and a unit-normalized linear endpoint read-out prove the finite seam weight x=5(1+η_e); it is not inferred from the symbol Z₅ or from a fit. Exact physical-pole masslessness further requires a Lorentz- and electroweak-gauge-invariant effective theory whose renormalized matching preserves the protected quotient. Present numerical agreement is retrospective, whereas the frozen correlations and protected-zero condition provide prospective tests.

Abstract:

This work tests a concrete and falsifiable hypothesis: whether an anomaly-consistent preon model with confining gauge group \(\mathrm{SU}(15)_p\) an account for a simple pattern in the spectrum of the nine charged fermions. For each charged sector \(s\in\{\ell,d,u\}\)—charged leptons, down-type quarks, and up-type quarks—we introduce the dimensionless logarithmic curvature \(A_s=\frac14\bigl(\ln y_{s,1}-2\ln y_{s,2}+\ln y_{s,3}\bigr),\) where \(y_{s,g}\) is the renormalized Yukawa-matrix eigenvalue of generation \(g=1,2,3\), with all quantities evaluated in a common renormalization scheme and at a common scale. We study \(\Delta_\Pi\equiv A_\ell+2A_d-A_u.\) For current central running inputs this combination is close to zero, but a source-informed covariance treatment supports only a weak diagnostic significance of about \(1.56 \sigma\). Accordingly, \(\Delta_\Pi\simeq0\) is treated here not as an established empirical law but as a phenomenological clue that requires an independent microscopic explanation. In the four-dimensional operator description we derive the exact identity \(\Delta_\Pi=C_{21}-C_{12},\) where \(C_{12}\) and \(C_{21}\) are coefficients of two independent crossed composite operators that differ by the order of two internal binding routes. Hence the exact plane \(\Delta_\Pi=0\) is equivalent to route reciprocity, \(C_{12}=C_{21}\). Within the unchanged fundamental field content of \(\mathrm{SU}(15)_p\), an explicit gauge-invariant point-split 24-preon source is constructed. The number 24 refers to the structure of the interpolating Wilson-network operator and is not identified with a proven number of physical constituents of a bound state. For the involution \(\tau\), defined as the reflection that exchanges the two routes and obeys \(\tau^2=1\), the explicit antisymmetric 24-preon source is an eigenoperator with eigenvalue -1. Thus the required one-dimensional sign sector already exists in the four-dimensional microscopic operator space. The dynamical problem is formulated by Schur–Feshbach reduction. Hidden composite states generate a positive-semidefinite matrix susceptibility that subtracts from the visible two-route kernel. For a general Hermitian two-route kernel, the existence of a route-exchange involution is equivalent, after an allowed relative phase choice, to equality of the two diagonal entries; the phase of the off-diagonal entry is not by itself a basis-invariant obstruction. For the known reduced kernel, the required diagonal compensation is 0.049406060606061 in the adopted dimensionless normalization. We prove the existence of positive-semidefinite hidden sectors that realize this compensation, and of exact Hermitian extensions in which the route-odd state is a nondegenerate ground state. This establishes the absence of an algebraic or naturalness-size obstruction, but it does not replace a nonperturbative calculation of the actual spectrum of the confining theory. To connect the construction directly to Euclidean calculations, the hidden susceptibility is represented by a positive-semidefinite Euclidean memory kernel. Route reciprocity and its energy stability become moment sum rules for the difference of the two diagonal memory-kernel components. Consequently, testing higher-order route locking does not require prior reconstruction of individual hidden poles. For the physical route-odd correlator we derive finite-time moment criteria for subthreshold existence, total subthreshold weight, and minimal multiplicity. We further prove an exact flat-extension criterion for a finite block-Krylov space: vanishing of the next-layer Schur complement means that the finite Krylov space has closed and equals the full cyclic subspace accessible to the chosen sources. Only under this closure condition does the number of subthreshold Ritz values become the exact physical number of source-supported bound states. If closure has not occurred, finitely many positive moments cannot impose a universal upper bound on arbitrarily weak additional bound states; their total spectral weight in a specified region can nevertheless be bounded rigorously by the flat-extension residual. The five-dimensional construction is treated as a possible effective composite description rather than as a mandatory fundamental spatial dimension. In the minimal one-band Jacobi–Robin class, a single physical scalar spectral measure determines the asymptotic bulk Jacobi coefficients, the boundary defect, and the canonically normalized Robin parameter. At the same time, we prove a fundamental limitation of scalar spectral data: masses and a positive scalar spectral measure do not determine the route parity of the lowest state. That information requires the matrix two-point function of two microscopically defined route sources. For this 2\(\times\)2 correlator we obtain finite-time inertia criteria for the number of source-supported subthreshold directions and a three-slice lower bound on route-odd subthreshold spectral weight, with no pole fit and no \(t\to\infty\) limit. Two further qualifications prevent a circular symmetry argument. First, the exact continuous flavor transformations of the published four-dimensional field content that commute with the gauged Pati–Salam embedding act separately on its inequivalent spectator blocks and cannot exchange the two routes. Second, after whitening, any full-rank 2\(\times\)2 correlator exactly saturated by two nondegenerate states possesses a spectral reflection. Thus a clean two-pole generalized-eigenvalue signal is necessary but is not, by itself, evidence for a microscopic route symmetry. The common reflection must remain stable when further states and continuum contributions are resolved, and an independently renormalized matching vertex must identify its even covector with the mass-plane direction. For a literal six-dimensional ultraviolet completion we analyze a smooth gravitating Einstein–Abelian–Higgs vortex with vectorlike six-dimensional parent fermions. Under the stated assumptions it supports exactly one four-dimensional Weyl zero mode per parent multiplet and satisfies the corresponding local and direct-product global anomaly tests. The minimal smooth two-derivative construction nevertheless has a structural limitation for a generic sourced radial "sausage" response: standard bulk localization of a constant four-dimensional gauge zero mode forces the angular radius to possess an interior turning point, and the standard scalar, vector, and tensor additions considered here do not remove this obstruction in a controlled way. A healthy \(R+\beta R^2\) scalaron supplies a genuine local scalar degree of freedom but does not generically eliminate the turning condition. We therefore examine a qualitatively different nonminimal possibility inspired by bulk-confinement localization. The smooth no-turn geometry \(L(r)=R_c\tanh(r/R_c),\qquad M(r)=\cosh^{-\kappa}(r/R_c)\) has a regular axis, no finite-radius turning point, a finite four-dimensional Planck norm, and a finite confinement-weighted gauge norm for every positive confinement exponent. It can be promoted to an exact effective background: a local two-field nonlinear sigma model with positive kinetic metric supports the same cylinder and solves the Einstein–matter equations analytically. A separate numerical boundary-value calculation finds a nonempty order-one-backreaction window in which a unit-winding Abelian–Higgs vortex coexists with the stabilizing sector. The compact phase is not an independent scalar zero mode but the Stueckelberg coordinate of angular diffeomorphisms. In the physical \(\theta\)-independent scalar/radion sector the exact Einstein-frame potential is a fake-supergravity potential plus a nonnegative square, and the coupled spin-zero Hamiltonian factorizes as a sum of positive operators. Smooth-cap boundary conditions exclude both \(m_4^2<0\) and a normalizable \(m_4^2=0\) eigenmode. The first non-axisymmetric sector can now be stated more sharply. Every regular real dipole perturbation of the sigma fields is a globally admissible scalar-clock deformation. Diffeomorphism invariance then implies that the stationary metric completion of any such clock direction has exactly zero Schur curvature. In particular, the previously found fixed-metric eigenvalue \(-0.347963/R_c^2\) is not a physical mass eigenvalue and must not be carried into the final stability test. After quotienting the scalar clocks and eliminating the constraints, any remaining \(m_4^2<0\) mode, if it exists, must be a discrete normalizable finite-core metric state. Its existence is exactly equivalent to a Birman–Schwinger threshold criterion: for a nonnegative reference operator \(H_+\) and the negative finite-core part \(G_-\) of the physical perturbation, \(B(\mu)=G_-^{1/2}(H_++\mu)^{-1}G_-^{1/2},\qquad \beta_0=\lim_{\mu\downarrow0}\lambda_{\max}B(\mu),\) with \(\beta_0<1\) excluding physical tachyons and \(\beta_0>1\) implying at least one. The marginal case \(\beta_0=1\) is a threshold problem. Because the essential spectrum begins at \(m_4^2=0\), no universal argument based only on a small gravitational correction is sufficient. The explicit constrained Einstein operator, and hence the physical value of \(\beta_0\), remain to be calculated; the six-dimensional branch is therefore prospective rather than complete. An ordinary finite-positive-coupling gauging of the winding does not support the infinite asymptotic cylinder, but a finite-radius interface provides a conditional exact escape. Israel and Maxwell matching fix its effective stress and the remaining bulk integration constant. The interface equation-of-state ratio \(T_b/Q_b\) determines its radius uniquely, while one common exponential scalar coupling closes the background scalar junction. The required interface is necessarily flux dominated, \(Q_b>\rho_b=T_b+Q_b/2\). This excludes its realization as the thin limit of a canonical positive-potential scalar wall, for which \(Q_{\rm can}\le\rho_{\rm can}\). A topological flux interface, a strongly backreacted thick defect, or genuinely nonperturbative confining stress remains possible. The finite-interface fluctuation problem is not covered automatically by the smooth infinite-background factorization. The microscopic confining origin, the admissible fermion representation, the full anomaly/inflow problem, and the finite-interface spectrum remain open. Finally, the previously considered seven-dimensional all-preon construction is re-evaluated. A genuine seven-dimensional Dirac spinor contains an additional twofold four-dimensional Weyl multiplicity under the stated inversion projector, so the earlier count of 405 selected zero-mode components becomes 810. Thus that particular 7D realization does not reproduce the desired spectrum without additional structure. The central conclusion is therefore deliberately limited. The operator, topological, Schur–Feshbach, spectral, and finite-data analyses show that the proposed route-odd mechanism is mathematically viable and sharply testable, and they identify explicit classes of higher-dimensional completions together with their stopping rules. They do not yet constitute a first-principles derivation of the observed charged-fermion mass plane. The decisive remaining four-dimensional calculation is the renormalized route-resolved nonperturbative correlator and three-point matching vertex of the explicit 24-preon sources.

Abstract: We reconsider the positive-energy relativistic wave equation proposed by Dirac in his later years and examine a related equation of motion from a different point of view. The internal degrees of freedom are described by ten Hermitian operators forming the SO(3,2) algebra, while an SU(1,1) subalgebra plays an important role in the internal motion. The spin magnitude and helicity determine the internal states, and the resulting particle mass spectrum is equally spaced. In particular, the mass is obtained as M = m(2s+1), where s is the spin quantum number.

Abstract: Several apparently distinct formulations of the charged-lepton mass relation \( p_2/e_1^2=2/3 \) are shown to describe the same algebraic structure. The compact-cycle Fourier-amplitude condition, the Descartes curvature condition, and the smaller Soddy completion are related exactly. After normalization by the total mass scale, the smaller completion is universal on the positive exact \( 2/3 \) locus and selects \( \alpha=\sqrt{3/2}-1 \). Its square \( r=\alpha^2 \) therefore defines the associated homogeneous map \( \mathcal M(x)=rx \), whose iterates form an exact geometric-mean orbit. The lepton pole masses and this universal ratio fix \( \mu_\star \), \( x_1 \), and \( x_2 \) without quark-sector input. The first iterate is empirically identified with the running strange-quark mass; once that correspondence is made, the next iterate is fixed. Thus the exact orbit ratio \( x_2/x_1=\alpha^2 \) becomes the conditional quark statement \( m_d/m_s=\alpha^2 \) and the leading GST/Fritzsch factor \( \sqrt{m_d/m_s}=\alpha \). A separate terminal boundary hypothesis gives a target for \( m_u \). Explicit PDG inputs and four-loop running make the numerical comparison auditable. The construction fixes a leading Cabibbo seed, not a complete CKM prediction.

Abstract: We propose a topological origin for neutrino masses and mixing: neutrinos are boundary topological flows of a string-net condensed phase, and their mass matrix is determined by boundary dynamics that inherits the hierarchical parameters of the bulk \(SU(3)_{3} \otimes SU(2)_{2}\) modular tensor category. Using the conformal-weight spacing \(\Delta h = 1/3\) and the topological temperature \(\beta = \pi^{2}/14\) of this category, we derive the Cabibbo angle \(\lambda = e^{- 14/(3\pi)} \approx 0.225\), without any free parameters, in agreement with the experimental value to within 0.04%. On this basis, we propose a phenomenological mass matrix ansatz inspired by category-theoretic characteristic fractions, with matrix elements composed of powers of \(\lambda\) and fractions generated by $(k + g) = 6$. Diagonalization yields mixing angles close to the experimental values. Further introducing the CP phase \(\epsilon = \lambda^{2}\) arising from the quadratic effect of topological suppression and candidate relations for charged-lepton mixing motivated by the topological splitting picture, we can simultaneously fit the four observables of NuFIT 6.0. We derive the Cabibbo angle \(\lambda\) without any free parameters, matching experiment to within 0.04%. Together with the boundary Ising structure, this constitutes a rigid category-theoretic prediction, while the mass matrix form and the charged-lepton mixing parameters remain topologically motivated candidate relations awaiting a full derivation from the boundary splitting vertex.

Abstract: A warped extra dimension in a five-dimensional (5D) anti de Sitter (AdS) background was introduced in 1999 by Lisa Randall and Raman Sundrum to solve the gauge hierarchy problem in particle physics. As a bonus, a holographic interpretation in terms of four dimensional (4D) conformal field theories (CFT) was found. Interestingly enough, another 5D background, the linear dilaton (LD), was found to have a holographic interpretation in terms of Little String Theory. In this review we will show how a set of 5D backgrounds, parametrized in terms of a real parameter ν, generalizes both theories and gives rise, in particular, to AdS for ν=0 and to LD for ν=1. Furthermore, working in the 5D theory, we will consider applications of the LD background to: i) Particle Physics, so that the 5D Planck scale can be lowered to sub-Planckian values, ii) Brane World Cosmology (BWC), based on the appearance of an extra vacuum characterized by a 5D black hole. In all cases we find a gapped continuum for bulk propagating fields, which makes connection with unparticles. In the case of BWC we also point out on the existence of a pressureless holographic fluid which could play the role of dark matter (DM), with feeble (gravitational) interactions to the Standard Model (SM), decoupled from the thermal SM bath, and generated by a freeze-in mechanism after inflation. We also point out the additional possibility of identifying DM with a long-lived feebly interacting massive graviton, as an isolated resonance generated by radiative corrections to the continuum graviton propagator self-energy.

Abstract: We present a unified cosmological model in which the entire history of the Universe emerges from a single fundamental quantum field — the Group Field Theory (GFT) field — through a sequence of phase transitions. The model is built from three independent sectors that are later linked by a common far‑from‑equilibrium transition: a homogeneous condensate that drives inflation, coherent private‑spacetime lumps that constitute matter, and a decohered gauge‑singlet virtual foam that provides dark energy. We derive an effective condensate evolution equation that captures condensation, inflation, the Coherent–Decoherent Spacetime Transition (CDST), and the post‑CDST decay, all controlled by running GFT couplings. Coupling this equation to the Einstein equations yields a self‑consistent dynamical system that reproduces the full cosmic expansion history: a primordial quasi‑de-Sitter phase, radiation and matter domination, and a late‑time accelerated expansion driven by the foam entropy. The dark‑energy density is obtained from the Bekenstein–Hawking entropy and the dynamical temperature of the apparent cosmological horizon, leading to the master formula \( \Omega_{\mathrm{DE},0} = \alpha_{\mathrm{foam},0}^{\mathrm{eff}} \), with a raw horizon‑puncture activation fraction \( \approx 0.96 \) for the self‑consistent background. A benchmark thawing quintessence yields \( w_0 \simeq -0.90,\; w_a \simeq -0.12\ \). The CDST is genuinely irreversible and provides a microscopic origin for the thermodynamic arrow of time. The model offers a unified ontology in which spacetime, matter, and dark energy are different phases of the same fundamental substance.

Abstract: We present a derivation of Quantum Chromodynamics (QCD) and color confinement emerging from a 7+1-dimensional microscopic theory. In this theory quarks are excitations of fundamental 7+1D fermions (the Tetrons) which are condensed into a 3+1D monolayer vacuum structure, and gluons arise as collective topological link excitations. The \( SU(3)_C \) gauge symmetry is not postulated ad hoc, but emerges dynamically as an effective macroscopic description of the topological transport on a discrete 3-dimensional `monolayer'. Furthermore, we show that color confinement arises naturally via a modified dual Meissner effect. Unlike standard phenomenological models that rely on the explicit condensation of magnetic monopoles, the confining medium in this framework is dynamically generated by the geometric frustration and chiral topology of the Tetron lattice. The discrete isomagnetic nature of the vacuum forces emergent chromoelectric flux lines into one-dimensional tubes, yielding a rigorous microscopic origin for the linear confining potential.

Abstract: We reinterpret anyon condensation as a kind of “transition of entropy modes.” Taking the SU(3)_3 modular tensor category as a concrete instance, we carry out the full condensation procedure: we identify the bosonic anyon (3,0) and construct the condensation algebra A=(0,0)⊕(3,0)⊕(0,3), and show that its condensation confines all objects with non-zero triality (including the fundamental quark representation (1,0)), while the “colorless” objects with zero triality survive. After condensation, the topological entanglement entropy decreases from approximately 1.79 to ln⁡( 2√3), representing a net reduction of about -0.549. This exactly computable entropy change provides a concrete quantitative signal for entropy-enthalpy competition --- the condensation algebra A plays the role of “enthalpy”, while the stepwise decrease of topological entropy measures the sacrifice on the side of “entropy”. We further construct an extended Levin-Wen model Hamiltonian for this category, in which the parameter J drives the condensation phase transition, and we discuss a possible route to exploring non-equilibrium entropy production based on quench dynamics. Finally, we discuss the algebraic correspondence between this condensation mechanism and QCD confinement in the context of non-invertible symmetries, and outline possible extensions of the framework to non-equilibrium quench dynamics.

Abstract: We propose that the proton's stability and its internal structure can be understood through an algebraic selection rule derived from the SU(3)₃fusion category. The proton emerges as a non-equilibrium quantum collective steady state—globally stable on observable timescales due to algebraic protection, yet internally dynamical due to continuous non-equilibrium redistribution of quantum numbers, thereby offering a unified perspective on the proton spin crisis and the origin of its mass. A pairwise comparison test of all known hadrons in the 2024 edition of the Particle Data Group reveals a statistical regularity: triality-nonzero baryons outlive triality-zero mesons in 67.58% of 256 pairs (p<10^-8), providing empirical support for the triality classification. A further test within the baryon sector (12 baryons, ln⁡τ_life vs. ,R²≈0.91,p<10^-4) confirms that the triality hierarchy extends beyond the meson-baryon dichotomy, offering discriminative evidence beyond baryon number conservation. Building upon this statistical regularity, we introduce a channel openness parameter η(t) and reinterpret radiation as the “breakthrough” of algebraically closed decay channels by non-perturbative quantum effects: η(t) varies continuously from the proton (η=-1, absolute stability) to π⁰ (η→∞, instantaneous decay), algebraically parallel to the exponential suppression of baryon number violation by instanton effects in QCD. Proceeding from a single categorical principle, triality, this work provides a unified description of the hadron lifetime hierarchy, the physical meaning of radiation, and the dual-mode nature of the proton.

Abstract: Pauli sum rules are reconsidered in light of the Higgs mechanism for particle mass generation within a five-vector theory of gravity framework. Two mass-moment conditions are retained and modified by explicitly separating the Higgs contribution. Within the restricted minimal ansatz used for the numerical examples---additional bosonic states only, grouped into two mass levels, with no new fermions--- the equations solutions require at least eight additional bosonic degrees of freedom. This is a conditional statement about the adopted spectral ansatz rather than a unique prediction of the full beyond-Standard-Model spectrum. Various realizations are discussed as illustrative benchmarks, including local family symmetry SU(3)_F or a hidden non-Abelian sector.

Abstract: We study a proposed \(E_8\times E_8\) kinematic scaffold relating a six-dimensional base to exceptional internal data. The notation \(E_8\times\omega E_8\) records a split-complex exchange grading of two factors; it is not a product of a group with a number. The two extra SU(3) factors in \(E_8\supset E_6\times SU(3)\) are adopted as geometric structure groups. We select \(M_6=\Im\ H_L\oplus\omega\Im H_R\) and separately specify a quadratic form of signature $(3,3)$. Its Clifford algebra is \(\mathrm{Cl}(3,3)\), distinct from the eight-dimensional split-biquaternion seed \(\mathrm{Cl}(0,3)\). The rank-two Jordan algebra \(J_2(Hs)\) realises $(M_6,g)$ through its determinant; after choosing \(Hs\cong M_2(\mathbb R)\), its matrix gradient and adjugate act between real four-dimensional Weyl modules and factorise the wave operator exactly. Rank-three \(J_3(\mathbb O_{\mathbb C})\) supplies the proposed internal, generation and cubic spectral structure through the magic-star decomposition of \(\mathfrak e_8^{\mathbb C}\). Per side, the adjoint branching supplies a real rank-four associated vector bundle whose isotropy representation is isomorphic to a tangent space of \(\mathbb CP^2\). Promoting this linear fibre to an associated \(\mathbb CP^2\)-bundle is an additional geometric choice. The octonionic decomposition \(O=H\oplus H\varepsilon\) realises the representation split \(\mathbf8\to\mathbf3_0\oplus\mathbf2_{+1}\oplus\overline{\mathbf2}_{-1}\oplus\mathbf1_0\). Soldering, localisation, the real-form selection and the coupling to physical Clifford-module fermions remain open; companion work proposes a dynamical two-leaf mechanism [1].

Abstract: We establish the unique topological setting of any unified gauge theory with quantized charge, and derive its physical consequences. A gauge field is a principal bundle equipped with a gauge symmetry and connection potential. We prove that (1) given electromagnetism as a U(1) gauge theory with quantized charge, and (2) the existence of a unified single-field theory, a unified theory must be formulated, up to homotopy equivalence of the base and isomorphism of bundles, on the universal complex Hopf fibration bundle S¹ → S^∞ → CP^∞ and its finite approximations S¹ → S²ⁿ⁺¹ → CPⁿ. Completeness and indecomposability are derived consequences, not additional axioms. The Standard Model gauge groups arise as natural reductions along the nested shell hierarchy: U(1) from the circular S¹ fiber, SU(2) from the S³ shell and SU(3) from the S⁵ shell. The classifying spaces BU(1), BSU(2), and BSU(3) are all internal to this single hierarchy; each is obtained by changing the quotient on the same universal total space S^∞, not by independent construction. The unified structure group G_total = (SU(3) × SU(2) × U(1) × SO(4))/Γ is intrinsically non-factorable due to the generating role of the universal first Chern class in H^∗(CP^∞;Z) ≅ Z[c₁]. The unique universal action on the Hopf bundle is derived from SO(4)-equivariance, the Killing form, and degree classification; the torsion action is the unique admissible positive-definite quadratic form. The Einstein, Maxwell, and Yang–Mills field equations all follow from this single action. The Beltrami operator B = ⋆d|ξ on the contact distribution is doubly forced as both the action Hessian and the unique equivariant first-order operator. The result is a topologically enhanced Standard Model: every term of the conventional SM Lagrangian appears with identical structure, with no free parameters, and with gravity via Chern–Simons theory on S³, the Beltrami mass operator, and the resolution of the strong CP problem as enhancements. Gravity emerges on the S³ = SU(2) shell, sharing exactly one generator—the Cartan U(1)—with the gauge sector; gauge–gravity unification is the fibration U(1) → SU(2) itself. On each Hopf shell, the Beltrami operator is elliptic, essentially self-adjoint, and possesses a discrete spectrum stable under torsion perturbations by the Kato–Rellich theorem. Fiber winding decomposition yields independent topological sectors whose Gaussian functional determinants, regularized via spectral zeta functions, generate intrinsic mass scales. Fermion mixing (CKM, PMNS) arises from intersection-form overlaps of admissible cycles in H^∗(CP⁴), with CP violation induced by fiber holonomy phases. The electroweak vacuum expectation value v serves as the unit conversion factor between geometric and laboratory scales; given this single identification, the fine-structure constant and all shell-specific mass scales, spectral coefficients, and interaction strengths entering the particle spectrum are fixed by the spectral geometry of the complex Hopf fibration. The framework predicts the complete particle mass spectrum and anomalous magnetic moments, with suggested independent experimental tests (torsion-induced phase wobble, absolute neutrino mass scale, and the electron, µ and τ g − 2) providing falsifiability. Fundamental constants arise from topological normalization. Further results include anomaly cancellation, dark sector effects from bundle torsion and holonomy, and the elimination of singularities. The mathematical results stand independently as contributions to the topology of classifying spaces, reductions along nested Hopf shells, and contact spectral geometry.

Abstract: A current interest in lunar exploration led by Artemis program pushes scientists to search for lunar water deposits directly on the surface of the Moon with small robotic rovers. The Institute of Experimental and Applied Physics, Czech Technical University in Prague (IEAP CTU) is developing a miniature Timepix3-based detector Neutron HardPix capable of mapping the water deposits using non-invasive detection of neutrons created underground by cosmic rays and thermalized by hydrogen. This neutron spectrometer measures count rate variations of thermal, epithermal and fast neutrons attributed to the hydrogen abundance in lunar subsurface, while monitoring cosmic radiation as a natural source of neutrons. Neutron HardPix is based on the miniature (< 0.1 U, 130 g) radiation monitor HardPix with multiple space heritage.

Abstract: We investigate a minimal deterministic hypothesis: that the internal symmetries and Lorentzian kinematics of low-energy physics arise as emergent geometric-phase (Berry / Wilczek–Zee) holonomy of a single elastic substrate—a static four-dimensional cubic brane lattice in a 4D Euclidean ambient, whose only nonlinearity is the Pythagorean link length. With explicit, reproducible computations we show that (i) the Lorentzian signature (3,1) of the effective metric is the sign pattern of the directional prestress, not an imposed structure; (ii) the fluctuation operator about a finite-amplitude periodic carrier has an isolated rank-3 complex eigenbundle whose gauge-invariant Wilczek–Zee curvature generates the full Lie algebra su(3) (Lie-closure rank 8, not merely so(3)), with the abelian trace as a candidate electromagnetic U(1); (iii) emergent gauge invariance, locality, and power counting force the leading dynamics of both sectors to Maxwell and Yang–Mills form, with substrate-induced positive couplings and no mass term; and (iv) the rank selection U(3)-not-U(4) and the U(1)/SU(3) split are set by the prestress parameters. We are deliberate about scope: the color-carrying background is a stable but higher-energy texture, not the ground state, and the emergent Lorentz invariance is only approximate—the residual anisotropy being itself the escape from the Weinberg–Witten no-go; matter and confinement are not treated. The result is a constructive proof of concept that one deterministic elastic substrate can carry a U(1)×SU(3) gauge structure and a Lorentzian light cone as emergent symmetries.

Abstract: Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by coordinate and momentum spinors. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Dirac equation the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors. In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In the presence of a potential the momentum components cease to commute with each other. To neutralize this effect, the Schrödinger equation is supplemented by several equations with mixed partial derivatives on coordinates. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. Section 4 presents a modification of the theory of the path integral, which consists in considering the path integral in the spinor coordinate space. The Lagrangian densities for the scalar field and for the electron field, along with their corresponding propagators, are presented. An equation of motion for the electron is proposed that is relativistically invariant. This novel equation permitted the construction of an actually invariant procedure for the second quantization of the fermion field in spinor coordinate space. Furthermore, it is demonstrated that the field operators are a combination of plane waves in spinor or vector space, with the coefficients of which being pseudospinors or pseudovectors. Each of these pseudovectors or pseudospinors corresponds to one of the particles presented in the theory of electrodynamics. Furthermore, each plane wave possesses an additional coefficient in the form of a creation or annihilation operator. In vector space, these operators commute, whereas in spinor space they anticommutate. The paper presents the spinor and vector representations of the field operators in explicit form, comprising sets of 16 pseudospinors or 4 pseudovectors corresponding to particles represented in electrodynamics. An explicit form of the symmetric traceless tensor with spin two, zero mass and two polarizations is presented, which can serve as a model of the graviton. The results obtained may prompt changes in some aspects of the construction of Feynman diagrams. Among other things, it presents a purely mathematical derivation of Maxwell's inhomogeneous equations without reference to empirical data on the action of electric current, which is usually referred to when deriving equations. Section 4 presents Einstein's inhomogeneous equation, which features the Riemann tensor rather than the Ricci tensor, with the energy-momentum tensor of a charged particle having four indices rather than two. In the case where a particle of matter has a charge, another Riemann tensor is added to Einstein’s equation, in addition to the usual Riemann curvature tensor, which describes the additional curvature created for a charged particle by an electromagnetic field.

Abstract: Neutron stars observed as pulsars are among the most versatile natural laboratories in physics. Their clock- like rotational stability, strong surface gravity, supranuclear interior densities, broadband pulsed emission, and distribution across the sky allow a single class of object to probe questions that range from the behaviour of matter at extreme density, through the strong-field and radiative regimes of general relativity (GR), to the most ambitious target of all—residual, Planck-scale imprints of a quantum theory of gravity. This survey reviews, at the level of a working researcher, the principal ways in which pulsars test physics beyond the established classical-GR+quantum-field-theory description, organized into five complementary pillars: (i) tests of Lorentz invariance through energy-dependent photon time-of-flight; (ii) the nanohertz gravitational-wave background detected by pulsar timing arrays, with its astrophysical and cosmological interpretations; (iii) strong-field tests of GR with relativistic binary pulsars; (iv) the dense-matter equation of state inferred from neutron-star masses and radii; and (v) searches for stochastic spacetime “foam” through the decoherence and blurring of astrophysical signals. For each pillar we give the governing relations, summarize current best constraints, and state plainly what the method can and cannot deliver. The resulting picture is asymmetric but coherent: pulsars now furnish some of the most precise tests of strong-field gravity and the tightest astrophysical handles on the dense-matter equation of state, whereas in the quantum-gravity sector they chiefly bound and falsify candidate theories—frequently as a complement to gamma-ray and cosmological probes—rather than isolating a unique microscopic completion.

Abstract: The light hadron spectrum is reconstructed over a finite relational arithmetic substrate, on a single Ω-hard scale. A baryon is the colour-neutral invariant of the triality frame, the determinant residue Λ³ = 1 (baryon number), forced by the gluon residue 0 and completing the Carrier-residue series photon 2, gluon 0, hadron 1. Its constituents are the wrapped composites of confinement, so each mass is M_B = √σ [ f_fl + κ_hf g_spin ] + ∆^EM, the confinement scale √σ ∼ Λ_QCD times dimensionless structure, and the scale cancels in every flavour and spin relation. We derive the Gell-Mann–Okubo octet relation (0.57%) and the decuplet equal spacing (9.2%, closed to 0.4% at second order); the decuplet–octet hyperfine pattern as the colour-magnetic character invariant (colour factor −8, spin 1/2 S(S + 1) − 9/8 ); the Coleman–Glashow isospin identity (0.79%); heavy-quark symmetry (2.4%); and the vector-meson nonet equal spacing 2M_K∗ = M_ρ + M_ϕ (0.42%). The absolute octet and decuplet follow from one scale and three sub-horizon eigenvalues, anchored to N, Λ, ∆, to within 1.1%; the baryon scale is itself the computed finite eigenvalue E₀ ≃ 2.232, M_N = E₀√σ predicting the nucleon to 4.6%. The sector introduces no new Ω-hard residue; every predicate resolves to a sub-horizon residue, a closed-form framed-rational or a profinite eigenvalue, or to the single confinement scale. Every exact claim is verified in finite-field or cyclotomic arithmetic, the continuum entering only as a labelled degenerate idealisation.

Abstract:

The flavour sector of the Standard Model is reconstructed over a finite relational arithmetic substrate. The substrate fixes the structural half, one fermion generation as the spinor 16, the Higgs mass bridge m = yv, and the three-generation count. The paper derives the masses, the mixings, as well as quantitative residue. We furthermore show that the unresolved residue is organised by the substrate’s two structural numbers, the four-fold (4 | Ω − 1, the quarter-turn) and the cubic (3 | Ω + 1, the triality centre), the pair that fixes Ω ≡ 5 (mod 12). The charged-lepton Koide relation is derived exactly, Q = 2/3: generation universality forces the Yukawa amplitude matrix to a C₃-circulant, the quarter-turn fixes the amplitude √2, and the lightest generation at the quarter-turn boundary fixes the leading phase π/12, leaving the electron massless at leading order. The three generative roles supply the Froggatt–Nielsen charges (0, 1, 2), giving the λ-texture and the Cabibbo angle V_us = √(m_d/m_s); the Georgi–Jarlskog factor is the colour rank N_c = 3; the up-quark Koide value is Q_u = 5/6. The mixing split is the lopsided M_e = M_d^T. For the neutrinos colourlessness fixes the signed (Takagi) amplitude invariant Q_ν = 2/3; with the drive-invariant quarter-turn boundary branch this selects normal ordering and ∑ m_ν ≃ 59 meV, and the cube-root phase makes leptonic CP near-maximal, δ_CP ≃ −130◦. Beyond the overall mass scale, the sector reduces to one carrier-scale phase δ₀ ≃ 2/9, with everything else derived or predicted; the matter sector thus rests on two Ω-hard residues, one scale and one phase. Every exact claim is verified in finite-field or cyclotomic arithmetic, the continuum entering only as a labelled degenerate idealisation.