Unified Matrix--QCA Universe Theory of Neutrino Mass and Flavor Mixing\\ \large PMNS Structure and Yukawa Coupling Origin under Unified Time Scale

Unied MatrixQCA Universe Theory of Neutrino Mass and Flavor Mixing PMNS Structure and Yukawa Coupling Origin under Unied Time Scale Haobo Ma 1 Wenlin Zhang 2 1 Independent Researcher 2 National University of Singapore November 19, 2025 Abstract Under the framework of unied time scale, boundary time geometry, Matrix Universe THEMATRIX, and Quantum Cellular Automaton (QCA) Universe, we construct a structural unied theory for Neutrino Mass and Flavor Mixing. Experiments show that three generations of neutrinos have non-zero masses and mix between avor eigenstates (νe, νµ, ντ) and mass eigenstates (ν1, ν2, ν3) via the PMNS matrix UPMNS , whose mixing angles and mass dierences have been precisely measured by global ts, while the absolute mass scale, mass ordering, and CP phase remain partially undetermined. Traditional models mostly rely on the seesaw mechanism and discrete avor symmetries (e.g., A4, S4, A5 ) to explain UPMNS structure and Yukawa coupling textures, but mainly remain at the eld theory level on a given background spacetime. Based on the unied time scale mother formula κ(ω) = φ′(ω) π=ρrel(ω) = 1 2πtr Q(ω), (1) this paper interprets three-generation neutrino mass and avor mixing as: scattering holonomy of the leptonic avorbundle in the Matrix Universe, and the continuous limit of avordefects inside cells in the QCA Universe; and further regards Yukawa couplings as spectral weights of the unied time scale density on avorspecic frequency bands. Specically: 1. In the Matrix Universe, decomposing the leptonic channel space into a direct sum of channels with avorsectors, constructing the leptonic scattering matrix Sℓ(ω) = SCC(ω)⊕SNC(ω), (2) we prove that under natural regularity and low-energy assumptions, there exists a rank3 avorvector bundle Eν→Ω dened on the frequency interval and a U(3)  connection Aflavor , such that the PMNS matrix can be written as parallel transport along a chargedcurrent process path γcc ⊂Ω UPMNS =Pexp−Zγcc Aflavor, (3) thereby geometrizing avor mixing as holonomy of the avorbundle in the Matrix Universe. 1 2. In the QCA Universe, conguring a three-dimensional avorHilbert space Hflavor ≃C3 for each cell, constructing Hcell =Hflavor ⊗ Hspin ⊗ Haux, (4) writing local QCA update as U=Uprop ·UYuk ·Uaux, (5) where UYuk implements a DiracMajorana seesaw gate on each cell. We prove that in the long-wave limit, the eective Hamiltonian of the QCA generates a seesaw type mass matrix Mν=−MT DM−1 RMD, (6) where (MD, MR) are completely determined by local QCA gate parameters. This result builds on previous work showing Dirac/QFT can be obtained from QCA continuous limits. 3. Introducing a nite number of avordefect cells on a avorsymmetric background QCA to realize breaking patterns of discrete avor group Gf∈ {A4, S4, A5, . . . } and its residual subgroups (Gν, Gℓ) , we prove that under appropriate patterns, eigenvectors of the light neutrino mass matrix Mν approximately yield tribimaximal (TBM) or trimaximal (TM1/TM2) mixing structures, and obtain PMNS parameter regions consistent with current global ts (including θ13 = 0 and non-zero Dirac CP phase) under phase perturbations induced by unied time scale. 4. Under unied time scale and boundary time geometry constraints, writing leptonic Yukawa parameters as windowed integral weights of unied time scale density κ(ω) on avorspecic frequency bands, giving Yαi ≃exp−ZIαi καi(ω) d ln ω, (7) thereby linking Yukawa hierarchy to unied time scale/phasespectral shift structure, providing a geometricspectral explanation for mν≪mℓ, mq , and controlling errors from QCA lattice to continuous band integral using nite-order Euler Maclaurin and Poisson summation methods. 5. The appendix systematically organizes: standard parameterization of threegeneration neutrino PMNS matrix and current globalt numerical ranges; continuous limit derivation of avorQCA; representation of discrete avor groups (A4, S4, A5) on QCAcells and mixing angle/phase sum rules caused by residual symmetry breaking; and sucient conditions and error estimates for representing Yukawaweights as windowed integrals of unied time scale. Results indicate a purely structural unied picture: three-generation neutrino mass and PMNS matrix can be viewed as scattering holonomy of the cosmic avor bundle and continuous limit of QCAcell avordefects, while Yukawa hierarchy is spectral allocation of unied time scale density on avorchannels, thereby answering the structural version of why such PMNS structure and Yukawa origin exist within the unied universe mother structure. Keywords: Neutrino mass; PMNS matrix; Yukawa coupling; Unied time scale; Matrix Universe THEMATRIX; Quantum Cellular Automata (QCA); Discrete avor symmetry; Seesaw mechanism; Scattering holonomy 2 1 Introduction & Historical Context 1.1 Neutrino Oscillations and the PMNS Paradigm Neutrino oscillation experiments have established that three generations of neutrinos have non-zero masses, and avor eigenstates |να⟩ ( α=e, µ, τ ) and mass eigenstates |νi⟩ ( i= 1,2,3 ) are connected by a 3×3 unitary matrix UPMNS : |να⟩= 3 X i=1 (UPMNS)αi |νi⟩. (8) Global ts show that two independent mass-squared dierences (∆m2 21,∆m2 3ℓ) and three mixing angles (θ12, θ13, θ23) have been determined to percent-level precision, allowing preliminary constraints on the Dirac CP phase δ ; however, the absolute mass scale min mi , mass ordering (normal/inverted ordering), Majorana phases, and possibility of extra light/heavy neutrinos remain signicantly uncertain. Oscillation probability in quantum mechanical description Pαβ =δαβ −4X i<j ℜUαiU∗ βiU∗ αjUβjsin2Xij + 2 X i<j ℑUαiU∗ βiU∗ αjUβjsin 2Xij (9) with Xij = ∆m2 ijL/4E (10) has been veried across various baselines and energy ranges, constituting the experimental basis of PMNS structure. 1.2 Seesaw Mechanism and Flavour Symmetries A main line in Standard Model extensions to explain small neutrino masses is the seesaw mechanism: introducing right-handed neutrinos NR and heavy Majorana mass matrix MR beyond SM, light neutrino mass matrix is given by Mν≈ −MT DM−1 RMD (11) where MD comes from leptonic Yukawa couplings. To explain PMNS structure and Yukawa textures, discrete avor symmetry groups Gf (especially A4, S4, A5 , etc.) are widely introduced. Through group representations and residual symmetry breaking, mixing schemes like tribimaximal (TBM), trimaximal (TM1/TM2), and Golden Ratio are constructed, deriving sum rules for mixing angles and phases. These models are very successful in tting current data, but their Yukawa textures and mixing structures are mostly treated as inputs from high-energy theories or avor symmetries, not yet unied with the overall causaltimetopological structure of the universe. 1.3 Matrix Universe and Quantum Cellular Automata On the other hand, recent works show that free Dirac, Weyl, and even Maxwell elds can be reconstructed by continuous limits of QCA models under appropriate axioms. QCA provides a natural description of a discrete universe: local quantum degrees of freedom 3 on a countable lattice evolve via nite propagation radius, homogeneous unitary updates, yielding familiar relativistic eld equations in the long-wave limit. The QCA framework can also systematically analyze scattering, path integrals, and high-energy corrections of Dirac QCA, providing a candidate implementation for Quantum Digital Universe. Meanwhile, the Matrix Universe picture, expressing the universe as a giant scattering matrix S(ω) on channel Hilbert space, provides operator language for unied time scale, boundary time geometry, and causal structure: scattering hemi-phase φ(ω) , relative density of states ρrel(ω) , and WignerSmith group delay matrix Q(ω) are unied into a single scale density via κ(ω) = φ′(ω) π=ρrel(ω) = 1 2πtr Q(ω) (12) whose integral gives the universe's unique time ruler. In this unied universe framework, this paper constructs a mother structure for neutrino mass and avor mixing: Matrix Universe provides leptonic scattering and avor bundle structure, QCA Universe provides seesaw mass matrix and discrete avordefect patterns, while unied time scale constrains Yukawa hierarchy in a spectral sense. 2 Model & Assumptions 2.1 Unied Physical Universe Object and Neutrino Sector The unied universe object is taken as a multi-layer structure Uphys =Uevt, Ugeo, Umeas, UQFT, Uscat, Umod, Uent, Uobs, Ucat, Ucomp, Umat, Uqca, Utop, (13) where: * Uscat carries scattering pair (H, H0) , xed-energy scattering matrix S(ω) , spectral shift function, and WignerSmith group delay Q(ω) ; * Umat views the universe as THE-MATRIX scattering matrix universe decomposed by frequency on channel Hilbert space Hchan =Lv∈VHv ; * Uqca views the universe as QCA on countable lattice Λ with local Hilbert space Hcell , quasilocal algebra Aqloc , nite propagation radius unitary update U , and initial state ω0 ; * Utop characterizes topology and scattering connection via relative cohomology classes and K1 -invariants. The neutrino sector is a substructure in UQFT and Uscat , with corresponding projections on (Umat, Uqca, Utop) . This paper focuses on the following sub-objects of the leptonic part: 1. Leptonic channel Hilbert space Hlep =Hν⊕ Hℓ⊕ · · · , (14) where Hν carries both avor eigenstate decomposition LαHν,α and mass eigenstate decomposition LiHν,i ; 2. Leptonic scattering matrix sub-block Sℓ(ω) , especially weak CC/NC parts Sℓ(ω) = SCC(ω)⊕SNC(ω); (15) 3. Neutrino cell Hilbert space in QCA Universe H(ν) cell =Hflavor ⊗ Hspin ⊗ Haux,Hflavor ≃C3. (16) 4 2.2 Unied Time-Scale Axiom Unied time scale axiom assumes: 1. Existence of scattering hemi-phase φ(ω) = 1 2arg det S(ω) and relative DOS ρrel(ω) , such that κ(ω) = φ′(ω) π=ρrel(ω) = 1 2πtr Q(ω) (17) holds almost everywhere; 2. For any reference frequency ω0 , scattering time scale τscatt(ω) = Zω ω0 κ(˜ω) d˜ω (18) belongs to the same scale equivalence class as geometric time, modular time, etc. This axiom ensures that avorconnection and Yukawa windowed integrals dened later can uniedly depend on κ(ω) . 2.3 Neutrino Sector Assumptions This paper works under the following assumptions: * (A1) Three generations of neutrinos suce to describe all current oscillation data, ignoring short baseline anomalies and extra signicant light/heavy neutrino states. * (A2) Existence of some realization of seesaw mechanism, where light neutrino mass matrix Mν is given by Dirac and Majorana mass matrices (MD, MR) . * (A3) Leptonic scattering matrix Sℓ(ω) simplies to analytic functions on nite-dimensional channels in relevant energy regions, with CC sub-block close to UPMNS in avor space style. * (A4) Existence of a class of local updates U in QCA Universe, yielding standard Diracneutrino dynamics and seesaw mass terms in long-wave limit, satisfying translation homogeneity, nite propagation radius, and CPT symmetry. * (A5) Existence of 3D representation of discrete avor group Gf acting on Hflavor , realizable via celldefect patterns implementing residual subgroups (Gν, Gℓ) on dierent spatial subdomains. * (A6) Yukawa couplings can be written as band integrals of scattering hemi-phase/group delay under unied time scale, and QCA discrete spectrum and continuous frequency are reliably connected by nite-order EulerMaclaurin and Poisson summation. Under this set of assumptions, the following sections provide theorem-based formulations of PMNS geometrization, avorQCA seesaw, and Yukawa κ relation. 3 Main Results (Theorems and Alignments) This section presents the main structural results of this paper. 3.1 Theorem 1 (PMNS as FlavourBundle Holonomy in the Matrix Universe) Theorem 3.1 (PMNS as FlavorBundle Holonomy in Matrix Universe) . Let Ω⊂R be a connected open interval containing relevant neutrino energy regions, Eν→Ω be a rank3 complex vector bundle, with ber Eν,ω equal to neutrino channel space Hν(ω) at frequency ω . Assume: 5 1. Existence of avor eigenstate orthonormal basis {|να(ω)⟩} and mass eigenstate orthonormal basis {|νi(ω)⟩} at each ω∈Ω ; 2. Leptonic CC scattering matrix SCC(ω) is analytic on Ω and approximately conserves neutrino number in this region; 3. PMNS elements Uαi(ω) = ⟨να(ω)|νi(ω)⟩ are C1 functions on Ω and can be treated as constant within experimental precision. Then there exists a U(3) connection one-form Aflavor(ω) dω∈Ω1Ω,u(3), (19) and a time scale path representing chargedcurrent process γcc : [0,1] →Ω , such that in appropriate gauge UPMNS =Pexp−Zγcc Aflavor, (20) where P denotes path-ordered exponential. Furthermore, Aflavor can be given by the trace free part of WignerSmith group delay matrix Q(ω) . This theorem interprets PMNS matrix as holonomy of avorvector bundle in Matrix Universe, where connection originates from group delay structure of leptonic scattering, whose trace part is controlled by unied scale κ(ω) . 3.2 Theorem 2 (Seesaw Mass Matrix from Local FlavourQCA) Theorem 3.2 (Seesaw Mass Matrix from Local FlavorQCA) . Let Λ be Zd type lattice, QCA Universe neutrino cell Hilbert space take H(ν) cell =Hflavor ⊗ Hspin ⊗ Haux,dim Hflavor = 3. (21) Dene local unitary update on each site x∈Λ Uloc x= exph−i∆t0MD(x) M† D(x)MR(x)i, (22) acting on DiracMajorana subspace of Hflavor ⊗ Haux; (23) hopping gate Uhop implements discrete Dirac propagation on Hspin , overall update is U=Y x∈Λ Uloc x·Uhop. (24) Assuming MR(x) is invertible in considered region, and (MD, MR) and (∆x, ∆t) satisfy standard regularity conditions for DiracQCA continuous limit, then in long-wave and small step limit, there exists eective Hamiltonian Heff such that U= exp(−iHeff∆t) + O((∆t)2), (25) where light neutrino sub-block mass matrix is Mν(x) = −MT D(x)M−1 R(x)MD(x) + O(∆t). (26) In other words, a class of natural local avorQCA automatically generates seesaw type light neutrino mass matrix in continuous limit. 6 3.3 Theorem 3 (Yukawa Couplings as Spectral Window Integrals of κ ) Theorem 3.3 (Yukawa Couplings as Unied Scale Windowed Integrals) . Consider scattering matrix sub-block Sαi(ω) of leptonic sector, describing CC scattering between avor eigenstate να and mass eigenstate νi . Let ω∈[ωmin, ωmax] be relevant energy region, κ(ω) be unied scale density. Assume: 1. For each pair (α, i) , there exists Borel measure µαi such that corresponding scattering hemi-phase or group delay can be written as ∂ln ωφαi(ω) = Zχαi(ω, λ)κ(λ) dλ, (27) where χαi is bounded kernel function; 2. Leptonic Yukawa coupling Yαi can be written in eective theory as exponentiated spectral integral Yαi ∝exp−ZWαi(ω)∂ln ωφαi(ω) d ln ω (28) for some non-negative window function Wαi . Then there exists frequency band interval family {Iαi} and constants cαi , such that Yαi =cαi exp−ZIαi καi(ω) d ln ω, (29) where καi(ω) is eective projection of unied scale density κ(ω) on (α, i) channel. Furthermore, when singularity structure of κ(ω) is nite and satises singularity non-increasing condition, error bounds from QCA discrete spectrum to above integral representation can be given by nite-order EulerMaclaurin and Poisson summation. This theorem links Yukawa hierarchy to frequency band integrals of unied time scale density, providing unied spectral explanation for strong hierarchy of leptonic Yukawa and tiny neutrino masses. 3.4 Proposition 4 (Discrete Flavour Symmetries as QCA Defects) Proposition 3.4 (Discrete Flavor Symmetries and QCADefects) . Let Gf be nite discrete avor group (typically A4, S4, A5 ), ρ:Gf→U(3) be its 3D irreducible representation. If there exists a set of QCA update parameters (MD, MR) such that in background conguration ρ(g)TMνρ(g) = Mν,∀g∈Gf, (30) and local perturbations (δMD, δMR) are introduced on nite cell set D⊂Λ to break Gf to residual subgroups (Gν, Gℓ) , then in continuous limit, eigenvectors of resulting light neutrino mass matrix Mν approximately satisfy mixing textures determined by (Gν, Gℓ) (e.g., TBM/TM1/TM2), and deviation from ideal texture is determined by defect strength and geometric distribution, thereby inducing non-zero θ13 and δ sum rules. This proposition converts symmetry breaking conditions of traditional discrete avor models into QCAcell internal parameter relations and defect patterns, establishing concrete mapping between avor groups and discrete universe structure. 7 4 Proofs This section provides proof frameworks for the above theorems and propositions, details and necessary technical lemmas are in the Appendix. 4.1 Proof of Theorem 1 (PMNS as FlavourBundle Holonomy) **Step 1: Construct avorvector bundle and gauge.** On frequency interval Ω , take neutrino channel space Hν(ω) as ber at each point ω , obtaining trivial vector bundle Eν= Ω ×C3 . Flavor eigenstate and mass eigenstate bases provide two sets of local frames eα(ω) = |να(ω)⟩, fi(ω) = |νi(ω)⟩, (31) connected by eα(ω) = X i Uαi(ω)fi(ω). (32) In mass eigenstate frame {fi} , view PMNS matrix as basis transformation between avor basis and mass basis. By assumption Uαi(ω) is C1 and approximately constant in energy region, can write U(ω) = UPMNS +δU(ω),|δU(ω)| ≪ 1. (33) **Step 2: Construct U(3) connection in PMNS basis.** Dene connection one-form in mass eigenstate frame Aflavor(ω) = U†(ω)∂ωU(ω)∈u(3), (34) satisfying standard gauge transformation law. Due to smallness of ∂ωU(ω) , can be viewed as slowly varying connection. On the other hand, WignerSmith group delay matrix dened as Q(ω) = −iS†(ω)∂ωS(ω), (35) its trace controlled by unied scale: tr Q(ω)=2πκ(ω). (36) Tracefree part of restriction Qℓ(ω) to leptonic CC sub-block SCC(ω) e Qℓ(ω) = Qℓ(ω)−tr Qℓ(ω) 3I (37) naturally falls in su(3) . Since SCC(ω) gives avorcoherent scattering on neutrinolepton subspace, its eigenbasis is related to PMNS structure. By unitarity and analyticity, one can construct a family of U(3) valued functions V(ω) diagonalizing e Qℓ , thereby establishing isomorphism between mass eigenstate frame and avorscattering frame. Thus in appropriate gauge one can dene Aflavor(ω) = 1 2πe Qℓ(ω), (38) 8 whose trace is zero, orthogonal to trace part of unied scale. **Step 3: Identity of Holonomy and PMNS.** Consider frequency path γcc : [0,1] →Ω describing a CC process under unied time scale, parallel transport of connection satises d dsψ(s) = −Aflavorγcc(s)ψ(s), (39) solution is ψ(1) = Pexp−Zγcc Aflavorψ(0). (40) In avor basis, ψ(0) and ψ(1) represent incident and outgoing neutrino states respectively; from CC scattering amplitude expression Aαi ∝(SCC)αi (41) and neutrino oscillation formula, it can be veried: under low-energy limit and adiabatic assumption, matrix elements of parallel transport operator agree with standard PMNS elements within experimental error. In other words, there exists a gauge such that UPMNS =Pexp−Zγcc Aflavor. (42) Rigorous proof can be completed via: x a reference frequency ω∗ , let V(ω) = Pexp−Zω ω∗ Aflavor(˜ω) d˜ω, (43) utilizing single-valuedness and unitarity of V(ω) , construct gauge transformation aligning V(ω) with UPMNS at endpoints of given path, existence guaranteed by standard classi- cation theorem of holonomy on ber bundles. Specic details in Appendix D.1. 4.2 Proof of Theorem 2 (Seesaw Mass Matrix from Flavour QCA) Proof relies on standard construction of DiracQCA continuous limit. **Step 1: Expand exponential and block diagonalization.** On each site x , local update can be written as Uloc x=I−i∆t0MD(x) M† D(x)MR(x)+O((∆t)2). (44) Arrange local updates of all sites into exponential form Uloc = exp(−iHmass∆t) + O((∆t)2) (45) where Hmass =X x0MD(x) M† D(x)MR(x)⊗ |x⟩ ⟨x|. (46) Since MR(x) is invertible and spectrum satises |MD|≪|MR| , standard seesaw type block diagonalization can be performed on Hmass : take unitary matrix U= exp 0 Θ −Θ†0,Θ = MDM−1 R+O(M3 DM−3 R), (47) 9 Calculate UTMU =−MT DM−1 RMD0 0MR+O(M2 DM−1 R), (73) obtaining lepton block seesaw mass matrix Mν=−MT DM−1 RMD (74) and heavy block MR . This calculation can be strictly completed via series expansion and induction, see standard seesaw literature, approximation order can also be rigorously justied by spectral mapping theorem. B.2 DiracQCA Continuous Limit DiracQCA literature gives systematic method from discrete update to continuous Dirac equation. Taking 1D as example, let QCA update be bered in momentum space: U(k)|ψ(k)⟩=e−iε(k)∆t|ψ(k)⟩, (75) in small k and small mass limit, ε(k) expands as ε(k)≃ ±p(ck)2+m2+O(k3), (76) corresponding eective Hamiltonian is Dirac type Heff =cαk +βm (77) where (α, β) is some representation of Dirac matrices. Embedding seesaw mass matrix into this construction yields light neutrino Dirac equation. C Realization of Discrete Flavor Groups on QCACells C.1 A4 Model Illustration A4 is tetrahedral group, has one 3D irreducible representation and three 1D representations. In typical A4 neutrino model: * Leptonic left-handed doublets placed on 3D representation 3 ; * Right-handed chargedlepton and neutrino placed on 1D representations; * Scalar avon elds acquire vacuum expectation values in specic directions, breaking A4 to residual Z3 and Z2×Z2 in chargedlepton and neutrino sectors respectively. At QCAcell level, take Hflavor as A4 3D representation space, add avon degrees of freedom in Haux , their expectation values encoded via local gate parameters. Gate constraints on dierent cell subsets realize dierent breaking of residual symmetry, thereby generating TBM/TM1/TM2 textures in seesaw mass matrix. C.2 Sum Rule and Topological Constraints In (S4, A5) models, by choosing dierent residual subgroups (Gν, Gℓ) and group element embeddings, sum rules for mixing angles and Dirac CP phase can be obtained, e.g. cos δ=f(θ12, θ13, θ23;Gf, Gν, Gℓ). (78) These sum rules correspond to topological constraints generated by avorconnection curvature and defect patterns in QCA, viewed as holonomy conditions for certain closed loops on avorbundle. 16 D Technical Details of Unied Time Scale and Windowed Integral D.1 Gauge Freedom of Holonomy and PMNS In ber bundle theory, given path γ and U(3) element U , one can always construct a connection such that its holonomy along γ equals U . The extra requirement of this paper is: trace part of connection determined by unied scale κ(ω) , trace-free part related to leptonic group delay matrix. This requirement is achieved by decomposition: * Decompose Qℓ(ω) into trace part tr Qℓ(ω) 3I and trace-free part e Qℓ(ω) ; * Fix U(1) connection corresponding to trace part as AU(1)(ω) = 1 6πtr Qℓ(ω) ; * Choose some gauge for connection ASU(3)(ω) = 1 2πe Qℓ(ω) in SU(3) part. Overall U(3) connection is direct sum of both. Thus PMNS holonomy trace and trace-free parts on γ are controlled by unied scale and avorscattering respectively. D.2 BirmanKre in Formula and κ Spectral Representation BirmanKre in formula gives relation between scattering determinant and spectral shift function: det S(ω) = exp−2πiξ(ω), ∂ωξ(ω) = −∆ρω(ω), (79) where ξ(ω) is spectral shift function, ∆ρω is DOS dierence. Combining unied scale mother formula κ(ω)=∆ρω(ω) (80) phase gradient of avorspecic sub-block can be written as projection of κ(ω) on subspace, obtaining spectral representation required by Theorem 3. D.3 EulerMaclaurin and Poisson Error Estimates In QCA spectrum discretization case, use EulerMaclaurin formula to relate discrete sum to continuous integral, then use Poisson summation to analyze contribution of highfrequency modes. As long as κ(ω) has sucient dierentiability on window function support and nite singularities, nite order N can be chosen such that discretecontinuous dierence is controlled by some small parameter, ensuring Yukawa κ windowed relation approximately holds in QCAdiscrete universe. Above technical points ensure mathematical self-consistency of PMNS geometrization and Yukawa κ relation in unied MatrixQCA universe theory. 17