Teleportation Syntrodynamics; Algebra Quantum Computing

We present Teleportation Syntrodynamics; Algebra Quantum Computing (TSAQC) — a unified mathematical framework that synthesizes teleportation syntrodynamics, quantum algebraic computation, and Lorentzian information geometry within a string-theoretic context. Its guiding modeling assumption is that quantum information propagation is represented not as transmission through spacetime but as null-geodesic evolution on an 11-dimensional manifold M11 ≅ R^(1,3) × X7, where X7 admits a G2-structure (or the product form CY3 × S1) compatible with M-theory compactification — a geometric metaphor for the simulator's state space, not a claim about physical spacetime. The core contribution is the Syntropy Algebra C11, a real associative algebra with 13 fundamental generators, comprising dual imaginary units i, j satisfying j = i⁻¹ and cyclic frequency generators {ω_k} (k = 1…11) forming Z11. This algebra embeds into twistor space PT ≅ CP³ via the Penrose transform, where quantum states become holomorphic sections and teleportation manifests as boundary-state synchronization enforced by the Master Stability Predicate L_teleport ≡ ⟨C4⟩ = 0. We prove the Topological Lock Theorem: security derives not from computational hardness but from the arithmetic rigidity of the Riemannian Zeta Spectral Guard (Rζ > 0.95) combined with the E8 automorphism symmetry of C11 via the McKay correspondence. The framework yields Infinite Finality for distributed ledger systems — where consensus is replaced by unique constraint satisfaction — and enables distance-independent quantum communication via the Null Twistor Vacuum. The Hopf Gold Synthesis extends this framework to 13-dimensional Hopf algebras, providing topological protection through non-invertible (weak Hopf) quantum group symmetries in the sense of the recent fusion-category classification of non-invertible phases. Divergences arising in the frequency algebra are handled by zeta-function regularization, treated purely as a numerical stabilization scheme for the simulator. Computationally, we implement a GPU-accelerated Syntropy Σ/QIPR/SQIPR simulator with novel metrics: the Syntropic Quantum Inverse Participation Ratio (SQIPR) and Syntropic Stability Index (SSI). The Boundary Field Interface v14.0 operationalizes the framework through Hepta-Modal Synthesis, monitoring real-time equilibrium via the Syntropic Norma (N_syn ≈ 0.5). All claims in this contribution are claims about Quantum Information Technology — state preparation, gate synthesis, and stability in quantum simulation.