LCL-833: 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 CreatorsLessard, Guillaume (El’Nox Rah)iD01t Productions, Quebec, Canada ORCID0009-0000-3465-3753 DescriptionThis publication master consolidates the LCL-833 record into a single clean manuscript. It proves the genus-5 surface-code topology identities, CPTP closure of the logical channel, the exact Jones closed form at the fifth root of unity ( q = e2π i/5 ), uniqueness of the maximally mixed stationary state under the stated full-algebra hypothesis, and the exact ( Z{12} × Z{12} ) operator and braiding identities. It also proves, under explicit assumptions, the coherence identity ( α = 1 - 2εeff ) and the MICR stopping law, with certified entrance at ( T_C = 18 ) for the adopted anchor ( αₒₚ = 0.8783 ). Interpretive mantra language, observer-language correspondences, and the retained law ( ω_C = (g - 1)αₒₚ ) remain explicitly separated from theorem-grade claims. We present LCL-833 as a mathematical framework for topological quantum error correction on the genus-5 surface-code record ([[832,10,4]]). Logical protection is organized around a Jones-theoretic calibration at ( q = e2π i/5 ), together with a retained Jones-Khovanov framework label from the uploaded source record. In the publication-master proof stack, the closed-form scalar quantity used directly in the theorem-grade derivations is the Jones evaluation, while any broader Khovanov-augmented interpretation is kept at the declared framework level rather than promoted as an independently proved scalar theorem. All propagated numerical quantities are anchored to the retained LCL-832 operating-point constant ( αₒₚ = 0.8783 ), giving ( Ggap = 1 - αₒₚ ≈ 0.1217 ) and ( εeff = (1-αₒₚ)/2 ). The logical channel is written in the standard form( Λ_L = D ∘ N⊗ n ∘ E ),and is proved CPTP whenever the encoding map (E), physical noise channel (N), and decoder (D) are CPTP. Under the stated contraction hypothesis, the MICR threshold is reached at( T_C = {52 ln 2}{|ln Ggap|} = 18 ). The manuscript uses a stratified epistemic policy to separate exact theorems, exact conditional results, exact-by-construction identities, empirical anchors, model axioms, and interpretive overlays. This prevents semantic drift between topological invariants, operational parameters, and philosophical language. The result is a publication-safe closure document intended as a formal archival statement of the LCL-833 framework and its verified mathematical core. Keywordstopological quantum error correction; surface codes; logical channels; Liouvillian dynamics; Jones polynomial; Khovanov homology; genus-5 surface codes; GKSL; stabilizer codes; CPTP channels; MICR; stratified axiomatics Resource typePreprint LicenseCC BY-NC-ND 4.0 PublisherZenodo LanguageEnglish CommunityLCL-832: Quantum-Computational Framework for Self-Referential Systems (id01t) Related identifierIs preceded by: 10.5281/zenodo.18743234 (LCL-832)