Operator Firing Order as the Missing Mechanism in Ethanol-to-Hydrocarbon Selectivity: Contact-Geometric Analysis of ZSM-5 and MCM-22 Zeolites

WEBSITE: CATGT

Zeolite shape selectivity is conventionally attributed to pore size, yet Sousa et al. [8, 9] demonstrated that HZSM-5 and HMCM-22 exhibit reversed product distributions despite similar Brønsted acidity — an empirical contrast that pore-size arguments alone cannot explain. We show that this reversal arises from a difference in operator ring order: in ZSM-5, the pore aperture constrains the reaction trajectory before molecular branching occurs (C → K → F → U), whereas in MCM-22, molecules enter the large supercage (inner free diameter 7.1 Å [20]) and branch before encountering the 10-ring exit filter (C → F → K → U).

We formalise this within the TO/TOGT framework, which maps heterogeneous catalysis onto a contact 3-manifold X_cat = (R³, α_cat) acted on by the operator pipeline G = U ∘ F ∘ K ∘ C. The central result — the Helical Selectivity Principle (Theorem 3) — establishes that only reaction pathways with radial coordinate r ≤ r*(λ) = √(J/λ) can reach the stable catalytic fixed point x*, where J is inter-site coupling and λ is the on-site binding energy modelled by the Discrete Nonlinear Schrödinger (DNLS) equation [10]. This geometric inequality recovers the empirical pore cut-off of HZSM-5 and HMCM-22, the PtSn ensemble effect, and the trilobe/tetralobe extrudate optimisation as corollaries.

Four falsifiable predictions are stated. Falsifiable Prediction 4 — reversal of the DRIFTS surface-intermediate sequence in MCM-22 under altered temperature or feed conditions — is the primary experimental test.

Epistemic status: Parts (i)–(ii) of the central theorem are a proof sketch. The Global Contactomorphism Conjecture is stated precisely and not claimed as proved. Lean 4 formalisation (CatGT_Main.lean): 6 closed theorems, 3 honest admits, 0 hidden sorries.