Field Interaction Theory ‘Qd12 Infinite Eternal Matrix Energy Field’ the Qd₁₂ Matrix: A Mathematically Closed, Information-Preserving Architecture of Our Reality

Mathematical Closure of the Qd₁₂ Architecture
Field Interaction Theory Qd₁₂ (FIT-Qd₁₂) establishes that all physical phenomena arise from a 12-dimensional Infinite Eternal Matrix Energy Field equipped with a unique spectral triple (A12, H∞, D12), a negative-energy (NE) holographic boundary (the 2D Ledger), and a stabilizing Dimensional Void Zone (DVZ). In this fully developed formulation, each Qd₁₂ Field is an oblong, curvature-defined operator region embedded within an infinite, repeating Matrix Field Array. Every adjacency between Fields obeys a universal seven-layer structure Qd12∣NE∣Ledger∣DVZ∣Ledger∣NE∣Qd12, whose geometry is rigidly fixed by Ledger curvature, NE-medium pressure, and DVZ convexity. This architecture ensures the eternal stability of the multiverse, forbids information leakage between Fields, and prevents any form of diagonal or chain-reaction collapse.
Because each Qd₁₂ Field is intrinsically oblong, the DVZ possesses two and only two collapse-capable necks: (1) a narrow vertical Side-to-Side neck, whose sharply compressed DVZ curvature produces Mode A (asymmetric) universes with directional initial conditions; and (2) an extended horizontal Top–Bottom gooseneck, whose broader DVZ geometry produces Mode B (symmetric) universes. Dimensional collapse is triggered solely when the interference spectrum of two adjacent Qd₁₂ Fields exceeds a finite spectral threshold, DQd12+Dwaves >Λcollapse, where Dwaves encodes A/B/E wave interactions.
Collapse is a non-singular, operator-bounded PDE instability and never a geometric divergence. The neck geometry determines the resulting universe’s symmetry: Mode A collapse imprints a preferred cosmic axis—reproducing the CMB hemispheric asymmetry, Cold Spot displacement, filament alignment, directional expansion, and anisotropic Hubble-rate signatures—while Mode B collapse yields isotropic,symmetry-dominated early universes.
Post-collapse physics is governed by two geometric tensors derived entirely from Ledger and NE boundary dynamics.
The • NE Curvature Tensor CμνNE, which functions as dark matter through frozen curvature rather than particles; and
The • Ledger Pressure Tensor PμνLedger, which produces dark energy as directional boundary tension rather than vacuum energy.
Together, these tensors reproduce halo formation, filamentary cosmic-web structure, lensing behavior, Bullet-Cluster–type phenomena, and anisotropic late-time cosmic acceleration—including the observed Hubble-tension dipole.

Neutrinos uniquely couple to the Ledger through a Completely Positive,Trace-Preserving information-deposit channel, making them the sole “Ledger-active” Standard Model particles. Their Ledger-induced reset phase produces the appearance of sterile behavior without requiring new particles; the resulting CPTP deformation predicts direction-dependent oscillation anomalies for JUNO, DUNE, Hyper-K, IceCube/Gen2, and KM3NeT.
A sequence of structural theorems—No-Diagonal-Collapse, NE/DVZ Convexity, Collapse-Locality, No-Chain-Reaction, and the Ledger Information-Completeness Lemma—demonstrates that the Infinite Matrix Field Array is eternally stable. Universes created on the same Qd₁₂ Field may exhibit weak gravitational bleed-through, while universes separated across different Fields remain gravitationally isolated, exchanging only adjacency-induced tension visible as dark-energy anisotropy.
Finally, Appendix A supplies the complete spectral-action derivation of Standard Model gauge groups, fermion representations, PMNS/CKM structure, Yukawa constraints, and the Higgs sector, confirming finite, non-divergent emergence of all 4D physics from the 12D operator system. The paper culminates in the Grand Theorem (Ω.1).
If a universe is non-singular, information-preserving, spectrally finite, dark-sector geometric, collapse-generated, globally unitary, and embedded in a stable multiverse, then the only mathematically self-consistent architecture capable of satisfying these conditions is the 12-dimensional Qd₁₂ Matrix Field with Ledger, NE, and DVZ layers. No alternative framework is compatible with global closure.
Thus FIT-Qd₁₂ provides the first complete, finite, and information-preserving Theory of Everything, unifying quantum field theory, gravity, cosmology, the dark sector, and neutrino physics within a single operator-geometric architecture.

Keywords: Qd₁₂ Matrix Field, Spectral Triple, Information-Preserving Cosmology, Dimensional Collapse, 2D Holographic Ledger (2DHL), Dimensional Void Zone (DVZ), Ledger Curvature Operator, Negative-Energy Curvature (NE Curvature Tensor), Ledger Pressure Tensor; Dark Matter as Curvature, Dark Energy as Boundary Tension, Multiverse Stability Theorem, No-Diagonal-Collapse Theorem, Spectral Norm Collapse Threshold, Parallel-Universe Gravitational Bleed-In, Neutrino Information Cycle, Ledger-Induced Sterile Neutrinos, Rope–Thread–Fiber (RTF) Structure, Dual-Time Compactification (T₂), Cosmogenesis (Droplet–Balloon–Honey Spread), Asymmetric Cosmology, Spectral Action, Noncommutative Geometry, Theory of Everything.