SZL Thesis v8 (Canonical) — Three Machine-Checked Theorems for a Governed-AI Kernel: Coherence-Monotone Strict Decay, a Constructive Kleene Least-Fixed-Point Characterization, and Its Unconditional ω-Continuous Strengthening

Canonical consolidated thesis (supersedes drafts v6 and v7; the single DOI document). Presents THREE machine-checked Lean 4 theorems forming the verified core of the SZL Holdings governed-AI kernel, framed within a cross-disciplinary methodology: (1) Wave24 - under pure-dephasing Lindblad/GKSL dynamics the l1 coherence monotone C (t) =C0*exp (-gamma*t) is strictly antitone, decays to zero, and the Lambda-v5 closure floor is crossed at a unique time t*= (1/gamma) ln (qC0/Lambdaₘin) ; (2) Wave25 - a constructive Kleene iterate-supremum characterization of the Lambda-aggregator least fixed point given an explicit omega-continuity commute hypothesis; (3) Wave26 - the unconditional strengthening that derives that commute property from omega-Scott-continuity (full Kleene fixpoint theorem). All verified with Lean 4 v4. 18. 0 + Mathlib v4. 18. 0, no sorry, Lean-core axioms only, merged to main. HONEST NOVELTY: the contribution is the machine-checked formalization plus governance application; no new physics or pure mathematics is claimed (underlying results classical: Lindblad 1976, Baumgratz-Cramer-Plenio 2014, Kleene 1938, Tarski 1955). The cross-disciplinary lineage (Sherman Morgan constrained optimization, Stewart collision/EOS, BFT quorum, agentic routing) is adapted methodological structure, attributed to original authors, never reclaimed. Honest doctrine: locked-proven = exactly 8 F1, F4, F7, F11, F12, F18, F19, F22 @ c7c0ba17; the three new theorems are EXPERIMENTAL/CI-green tier and NEVER join the locked 8; Lambda unconditional uniqueness stays Conjecture 1 (machine-checked FALSE; these are convergence results, not uniqueness) ; Khipu BFT = Conjecture 2; SLSA L1+L2 attested, L3 roadmap; trust never 100%. Jack Kruse = narrative only.