SATI CODEX: Driven-Dissipative Open Quantum Field Theory of Neural Collective Coherence

Abstract

SATI CODEX | Driven-Dissipative Open Quantum Field Theory of Neural Collective Coherence – Complete Mathematical Closure Edition (May 2026) Authors: Guillaume Lessard (El’Nox Rah), ORCID: 0009-0000-3465-3753 Affiliation: iD01t Research Lab | iD01t Productions, Longueuil, Quebec, Canada DOI: 10.5281/zenodo.18743234 Abstract / Description The SATI CODEX presents a definitive, corrected first-principles framework for neural collective coherence based on driven-dissipative open quantum field theory. Starting from a minimal (3+1)-dimensional effective Lagrangian (Eq. 1) with spontaneous symmetry breaking, the framework rigorously derives the driven Jaynes-Cummings Hamiltonian and the Lindblad master equation. Exact Heisenberg-Langevin solutions yield the master observable response function (Eq. 11): $$R_{obs}(0;C)=\frac{4\eta^{2}}{\gamma\kappa}\frac{C}{(1+C)^{2}}$$ This function exhibits a unique global maximum at the critical cooperativity $C^{*}=1$. Key contributions include: Rigorous Mathematical Proofs: Complete proofs for five core theorems: Coupling Threshold ($g > 0$), Strong-Coupling Detuning, Purcell Rates and Entropy Suppression, Thermal Robustness, and Information-Coupling. Bridge Theorem (BT-1): The identification of neural-QED through the reduction of a collective Dicke Hamiltonian to an effective single-mode Jaynes-Cummings model. This yields an enhanced collective cooperativity $C_{N} = N C_{1}$ and defines the critical ensemble size $N_{c} = 1/C_{1}$. Quantum Signatures: Exact derivation of sub-Poissonian photon statistics with a Mandel Q parameter of $Q(1) = -1/4$ at criticality. This is accompanied by derivations of Wigner variance ($\sigma^2 = 3/4$) and logarithmic negativity ($E_N \approx 0.35$ ebits) as genuine entanglement signatures. Thermal Robustness at 310 K: A nonequilibrium mechanism utilizing Fröhlich condensation and a super-Ohmic reservoir ($J(\omega) \propto \omega^3$) is shown to protect coherent dynamics at biological temperatures. The collective Fröhlich drive ($\eta_{col} \approx 6.02$ MHz) overwhelmingly exceeds the required noise-suppression threshold ($\eta_{min} \approx 0.004$ Hz). Topological Protection: Introduction of the LCL832 quantum error-correcting code, a [832, 10, d] generalized bicycle CSS code providing $k=10$ logical qubits with a Richardson-extrapolated fidelity of 0.8950. Falsifiable Predictions: Six quantitative predictions (P1–P6) are established, including a mean-field critical exponent $\nu = 1/2$ for critical slowing down. Keywords: quantum neuroscience, neural coherence, Jaynes-Cummings model, Fröhlich condensation, cooperativity, driven-dissipative systems, collective quantum effects, critical phenomena, consciousness theory, quantum biology. License: CC BY 4.0 Version: Full Closure Edition – May 2026 Categories: Physics (Quantum Optics, Quantum Field Theory), Neuroscience (Theoretical), Biophysics, Non-equilibrium Statistical Mechanics. Note: This edition includes full step-by-step algebraic proofs, corrects previous typos in the second derivative expansion, and provides the two universal biological closure formulas (Eq. 16 and 17).