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

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-19
DOI
https://doi.org/10.5281/zenodo.22849726
Primary Topic
Zeolite Catalysis and Synthesis
Type
preprint
Controls
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preprint

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

Pablo Nogueira Grossi
Zenodo (CERN European Organization for Nuclear Research)
Zeolite Catalysis and Synthesis
preprint

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

Pablo Nogueira Grossi
preprint en

Abstract

webpage: Operator Firing Order as a Mechanism for Ethanol-to-Hydrocarbon Selectivity: A Contact-Geometric Analysis of ZSM-5 and MCM-22 Zeolites Description: Zeolite pore topology governs product selectivity in ethanol conversion to hydrocarbons, yet the mechanism by which topology determines which intermediates form and survive has remained unresolved: HZSM-5 and HMCM-22 have nominally identical acid chemistry and both possess 10-ring apertures, but produce markedly different product distributions, coke locations, and deactivation profiles. This paper proposes that the differentiating variable is the sequential firing order of four geometric operations experienced by a reacting intermediate: Compression (adsorption, C), Constraint (aperture gating, K), Folding (branching/oligomerization/aromatization, F), and Unfolding (selective desorption, U). ZSM-5's 10-ring channels enforce the order C▷K▷F▷U (constraint before folding); MCM-22's 12-ring supercages and external pockets enforce C▷F▷K▷U (folding before constraint). Version 3 located exactly where the order-dependence comes from: the aperture gate commutes exactly with a pointwise nonlinearity, so it is the fold's inter-site coupling (amplitude transport) that fails to commute, both with the on-site nonlinearity and, in consequence, with the gate. Version 4 corrects the scope of the resulting selectivity theorem and completes part of a second one: Theorem 4 ("operator order determines selectivity") is restated at the scope its own proof actually supports — order-dependence given the two specific aperture values used, not independent of aperture in general, as v3 had claimed. Theorem 5 (the contact-geometric scaling law relating ZSM-5 and MCM-22 dynamics) had asserted, without deriving, that a rescaling preserves the governing contact 1-form — and that rescaling formula was itself arithmetically backwards, moving a barrier feature in the wrong direction given its own stated scale factor. V4 replaces it with an explicit coordinate dilation, verifies directly that it preserves the contact form, derives the correctly-directed wavefunction relation from the WKB correspondence, and kernel-verifies the contactomorphism claim in Lean 4. The hypothesis is supported by five independent published lines of evidence (molecular dynamics, operando DRIFTS, and structural-modification studies, reread through the operator-order lens — v4 adds an explicit caveat that these document consistency with the framing, not independent confirmation of it, since none of the five measured "operator order" directly), a reproducible coarse-grained nonlinear-Schrödinger (DNLS) simulation in which the two orders produce a ~35× selectivity ratio (v4 adds a caveat that this ratio is a property of the chosen simulation inputs, not yet checked against any measured selectivity ratio), and seven formal theorems connecting the hypothesis to the simulation model. Every claim carries an explicit status tag — [VERIFIED] (Lean 4 kernel), [DERIVED] (a complete proof given in the text, not yet formalized in Lean — new in v4), [MODEL], [SIMULATION], or [OPEN] — and nothing outside the first tag is presented as proved. Three falsifiable predictions are derived, each with an explicit experimental protocol and pass/fail criterion, directly testable by contact-time DRIFTS. The formal layer is machine-checked: the accompanying Lean 4 development (github.com/TOTOGT/io) compiles against the Lean kernel, with per-theorem axiom audits (#print axioms) showing exactly [propext, Classical.choice, Quot.sound] — no sorryAx — for all 20 verified theorems: the three commutation theorems of Theorem 1 (ZeoliteCommutation.lean), the contactomorphism theorem of Theorem 5(i) (ContactMorphism.lean, new in v4, independently verified against a local olean v4.32 toolchain), nine supporting results (CatGT_Main.lean), and seven chain-level order-dependence theorems in exactly existential form (Theorem53NonCommutativity.lean). The remaining formal obligations are explicitly tracked as open: continuum-limit gate/fold non-commutation (Theorem 1(iii)); Theorem 5's induced wavefunction correspondence and L² norm preservation (parts ii–iii — complete pen-and-paper proofs, tagged [DERIVED], not yet in Lean); and the selectivity–order bijection (Theorem 7). No claim in this work is asserted as machine-verified without a corresponding, inspectable proof or CI log. Changes in v4. Three corrections to v3, none of which touch Theorem 1 or its kernel-checked results, which are unchanged. First, Theorem 5's proof sketch asserted preservation of the contact 1-form under a rescaling without deriving it — and that formula was itself inconsistent with its own stated scale factor (k₁₂ = 4/3): it placed a barrier feature at the wrong coordinate, moving it in the opposite direction from what the theorem claimed. V4 replaces it with a coordinate dilation, verified directly (and now kernel-checked) to preserve the contact form, together with the correctly-directed wavefunction relation. Second, Theorem 4 claimed operator order determines selectivity independent of aperture; its own proof only supports that claim at the two specific apertures used in Theorems 2–3, and v4 restates it accordingly. Third, v4 adds two evidentiary caveats (described above) distinguishing what the paper's literature review and simulation actually establish from what they're consistent with, and adds a fourth Open Question: comparing the simulated 35× ratio against measured selectivity data (e.g. Sousa et al. 2014) has not yet been done. Files: manuscript (.tex/.pdf), DNLS simulation code (dm3_dnls_zeolite_simulation.py), figures, kernel-checked Lean 4 proofs (ZeoliteCommutation.lean, ContactMorphism.lean — new in v4), derivations with per-claim verification status (OPERATOR_ORDER_DERIVATIONS_AND_STATUS.md), and a standalone v3→v4 changelog (CHANGES_v3_to_v4.md — new in v4).

Zenodo (CERN European Organization for Nuclear Research)
GfK (United States) (US)
Zeolite Catalysis and Synthesis
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