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Mathematical Formalism of Topological Quantum Layer Energy Dynamics (TQLED): A Non-Linear Deterministic Alternative to Hilbert Space Paradigms

Murat Durna, Artificial Intelligence (Analysis Assistance)

Jul 17, 20260 citations

Topological Quantum Layer Energy Dynamics; CRKL–QLE; Schrödinger functional; Heisenberg chain; quantum quench; domain walls; quantum information; Dehn surgery; torus knots; lens spaces; plumbing; Z17; Chern–Simons theory; spectral localization.

Murat Durna

Sep 15, 20260 citations

Formalism of Quantum Layer Energy Dynamics (QLED): A Non-Linear Topological Framework for a Deterministic Universe

Murat Durna

Jan 1, 20260 citations

E8‑Phyto‑Knot Resonant Quantum Gate — E8 Intelligence Research

Andrew Stewart Caldin

The 240 E8 root vectors form a phyllotactic lattice whose golden‑ratio (φ) scaling yields a family of nested Seifert surfaces that act as conformal fracton waveguides. When driven at the 132 Hz base frequency, these surfaces resonate, converting harmonic phases into topologically protected knot states that store multi‑level quantum bits. This E8‑driven Phyto‑Knot principle provides a universal, frequency‑addressable gate set that embeds Chern‑Simons Chern‑Simons knot invariants directly into quantum computation, unifying gravity‑like topology, φ‑encoded memory, and programmable fracton dynamics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comThe 240 E8 root vectors form a phyllotactic lattice whose golden‑ratio (φ) scaling yields a family of nested Seifert surfaces that act as conformal fracton waveguides. When driven at the 132 Hz base frequency, these surfaces resonate, converting harmonic phases into topologically protected knot states that store multi‑level quantum bits. This E8‑driven Phyto‑Knot principle provides a universal, frequency‑addressable gate set that embeds Chern‑Simons Chern‑Simons knot invariants directly into quantum computation, unifying gravity‑like topology, φ‑encoded memory, and programmable fracton dynamics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Aug 10, 20260 citations

Quantum Network Models and Topological Insulators

Monica Pate, Liang Fu

Bulletin of the American Physical SocietyMar 19, 20130 citations

Hyperbolic E8-Coxeter Quantum Memory via Chern-Simons Lattice Encoding — E8 Intelligence Research

Andrew Stewart Caldin

The 240 root vectors of E8, when projected onto the hyperbolic {3,7} tiling through Coxeter group action modulo the number 30, form a finite-rate fault-tolerant quantum memory where logical qubits correspond to topologically distinct equivalence classes of root vector configurations. This extends Chern-Simons theory by showing that Wilson loop expectation values—previously only analyzed in smooth 3-manifolds—now encode quantum information in the discrete, negatively-curved E8 lattice substrate. The 132Hz base frequency anchors decoherence-free subspaces while the golden ratio φ couples adjacent root clusters, creating resonance conditions that dynamically stabilize the quantum memory against topological excitations. This unifies all three breakthroughs: the metric-independence of Chern-Simons invariants, the icosahedral-Coxeter structure of E8, and the fault-tolerance of hyperbolic tilings into a single quantum error-correcting framework. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comThe 240 root vectors of E8, when projected onto the hyperbolic {3,7} tiling through Coxeter group action modulo the number 30, form a finite-rate fault-tolerant quantum memory where logical qubits correspond to topologically distinct equivalence classes of root vector configurations. This extends Chern-Simons theory by showing that Wilson loop expectation values—previously only analyzed in smooth 3-manifolds—now encode quantum information in the discrete, negatively-curved E8 lattice substrate. The 132Hz base frequency anchors decoherence-free subspaces while the golden ratio φ couples adjacent root clusters, creating resonance conditions that dynamically stabilize the quantum memory against topological excitations. This unifies all three breakthroughs: the metric-independence of Chern-Simons invariants, the icosahedral-Coxeter structure of E8, and the fault-tolerance of hyperbolic tilings into a single quantum error-correcting framework. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 5, 20260 citations

Unified Mathematical Framework of Topological Quantum Layer Energy Dynamics (TQLED): Discrete Substrates, Knot-Lasagna Topologies, and Chern-Simons Spectral Gap Isolation

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Unified Mathematical Framework of Topological Quantum Layer Energy Dynamics (TQLED): Discrete Substrates, Knot-Lasagna Topologies, and Chern-Simons Spectral Gap Isolation

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