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 = e^2 i/5), uniqueness of the maximally mixed stationary state under the stated full-algebra hypothesis, and the exact (Z12 Z12) operator and braiding identities. It also proves, under explicit assumptions, the coherence identity (= 1 - 2₄₅₅) and the MICR stopping law, with certified entrance at (TC = 18) for the adopted anchor (₎₏ = 0. 8783). Interpretive mantra language, observer-language correspondences, and the retained law (C = (g - 1) ₎₏) 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 = e^2 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 (₎₏ = 0. 8783), giving (G₆₀₏ = 1 - ₎₏ 0. 1217) and (₄₅₅ = (1-₎₏) /2). The logical channel is written in the standard form (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 (TC = 52 2| G₆₀₏| = 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)