LCL-833: A Jones,Khovanov Augmented Liouvillian Framework for Logical Protection in Genus-5 Surface Codes

LCL-833: A Jones, Khovanov Augmented Liouvillian Framework for Logical Protection in Genus-5 Surface Codes Authors/Creators: Lessard, Guillaume (El'Nox Rah), iD01t Productions, Quebec, Canada ORCID: 0009-0000-3465-3753 Description: We present LCL-833, a mathematical framework for topological quantum error correction on the genus-5 surface code [832, 10, 4]. Logical protection is achieved by weighting homology cycles with the Jones polynomial evaluated at the fifth root of unity q = e^ (2πi/5), augmented by a perturbative correction derived from the total rank of the reduced Khovanov homology. The resulting effective protection parameter δeff (K) = vJ (K) + 0. 05 RKh (K) is calibrated to control the operational coherence weight αop and the spectral gap Ggap of an explicit Gorini, Kossakowski, Sudarshan, Lindblad (GKSL) Liouvillian generator for the logical channel ΛL = D ∘ N (n) ∘ E. All quantities are anchored to the trefoil knot 3₁ using the LCL-832 calibration (αop = 0. 8783, Ggap ≈ 0. 1217). A stratified mapping based on Johnson's Stratified Axiomatics (2025) enforces acyclic dependency between topological invariants and operational parameters, preventing semantic drift. The construction yields a CPTP channel with a unique fixed point. Numerical validation on 31 knots confirms consistency with an overall improvement in logical protection as knot complexity increases. The framework analyzes a topological, Liouvillian relation ω/α = g, 1, a heuristic universal genus-g scaling law, and compares the protection hierarchy with standard planar and toric surface codes. An empirical anchor from LCL-832 provides a minimum-time prediction Tmin = ⌈53 ln 2 / |ln Ggap|⌉, machine-verified for all 31 knots. Keywords: topological quantum error correction, surface codes, logical channels, Liouvillian dynamics, Jones polynomial, Khovanov homology, stratified axiomatics, genus-5, GKSL, stabilizer codes. Resource type: Preprint License: CC BY-NC-ND 4. 0 Publisher: Zenodo Language: English Community: LCL-832: Quantum-Computational Framework for Self-Referential Systems (id01t) Related identifier: Preceded by DOI 10. 5281/zenodo. 18743234 (LCL-832)