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 distribu-tions despite similar Brønsted acidity an empirical contrast that pore-size argu-ments alone cannot explain. We show that this reversal arises from a dierence in operator ring order : in ZSM-5, the pore aperture constrains the reaction trajec-tory 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 beforeencountering the 10-ring exit lter (C → F → K → U). We formalise this withinthe TO/TOGT framework, which maps heterogeneous catalysis onto a contact 3-manifold Xcat = (R3, αcat) acted on by the operator pipeline G = U ◦ F ◦ K ◦ C.The central result the Helical Selectivity Principle (Theorem 3) establishesthat only reaction pathways with radial coordinate r ≤ r∗(λ) = pJ/λ can reach the stable catalytic xed point x∗, where J is inter-site coupling and λ is the on-sitebinding energy modelled by the Discrete Nonlinear Schrödinger (DNLS) equation[10]. This geometric inequality recovers the empirical pore cut-o of HZSM-5 and HMCM-22, the PtSn ensemble eect, and the trilobe/tetralobe extrudate optimi-sation as corollaries. Four falsiable predictions are stated; Falsiable Prediction 4 reversal of the DRIFTS surface-intermediate sequence in MCM-22 under alteredtemperature or feed conditions is the primary experimental test. Parts (i)(ii) ofthe central theorem are a proof sketch; the Global Contactomorphism Conjecture isstated precisely and not claimed. Lean 4 formalisation (CatGT_Main.lean): 6 closedtheorems, 3 honest admits, 0 hidden sorries. Attached: 1. zeolite_operator_selectivity_FINAL.pdf ← Main paper 2. dm3_zeolite_figures.pdf ← Figures 3. ALGEBRAIC_PROOFS_ALL_7_THEOREMS.md ← Supplementary proofs 4. dm3_dnls_zeolite_simulation.py ← Reproducible code 5. ZENODO_README.md ← Documentation 6. CatGT_PROOFS_COMPLETE.lean ← Formal verification 7. dm3_zeolite_figures.png ← Alt format (optional)