DM3-lab
Contact geometry for dissipative systems that settle into structured cycles.
An independent research lab at G6 LLC in Newark, New Jersey. It works on the dm³ system, a class of dissipative dynamical systems with a hyperbolic limit cycle, and, separately, on a model of zeolite shape-selectivity that uses the same contact form: why two zeolites with the same acid chemistry select different products. Every claim on this page carries a status, and what is open is listed beside what is shown.
Origin
The dm³ system first appears in Generative Contact Mechanics (GCM). In that paper a dm³ system is a smooth Riemannian manifold with a hyperbolic limit cycle, a Lyapunov function and a stochastic extension, defined by eight axioms, with an operator algebra and an embedding in contact geometry. GCM is the lab's foundation text.
Why contact geometry: a Hamiltonian flow on a symplectic manifold preserves volume and cannot have an attracting limit cycle. A contact flow can dissipate. The same point appears below in a narrower form: a Reeb flow preserves contact volume and has no attracting set, so any confinement in the zeolite model has to come from somewhere else.
Work
Generative Contact Mechanics
Eight axioms, an operator algebra (g-, L-, R-, U-), and four stated theorems on existence, unification, a normal form and C¹ stability. The paper's own page says it was submitted to Journal of Geometric Mechanics in 2026; no acceptance is claimed here.
The Self-Trapping Selectivity Principle
A model of why HZSM-5 and HMCM-22 diverge in ethanol-to-hydrocarbon selectivity, with a second case in Pt–Sn ensemble effects. The paper is deliberately narrow: what could not be derived was cut, and what is open is stated as open.
Contact links of orthogonal quiver varieties
An early draft (v0.1) with scripts that check the lens-space links and the ADE data. No link to the dm³ systems is claimed. Until a derivation exists, any connection is an analogy.
Areas
The lab’s scope, as its founder states it: linguistics, computer science, mathematics, physics, economics, biology, astronomy, cosmology, logic, archaeology and Vedic studies.
A name on this list is scope, not a result. The status ledger below records what has actually been checked; an area with no row there has no checked result on this page.
Status ledger
What each claim is, and how it was checked. Verified means the Lean kernel accepted the statement as written, and a statement can be weaker than its name. Checked by script means a program ran a test that could fail. Derived means a complete pen-and-paper derivation, not formalized. Dates and counts are as recorded in the sources named in the last column.
| Claim | Status | What the check is, and its limits | Source |
|---|---|---|---|
| GCM: the contact form is the Gibbs form with the heat term removed | Checked by script | The identification is tested on 200,000 random tangent vectors and the script prints the worst disagreement. It is an algebraic identity, so this is a sanity check, not a proof of anything deeper. | geometry / gcm-framework-verify.py |
| GCM Theorems A–D (existence, unification, normal form, C¹ stability) | Unaudited | Stated in the paper. The paper's page was later revised so that Theorem A(ii) no longer claims the winding integral is an integer. The four theorems themselves have not been independently audited or formalized. | geometry / gcm-framework.html |
| Selectivity identities and the core inequalities of the zeolite model | Verified | 23 theorems in the V6 Lean file, each on the standard three axioms, run by the author on Lean 4.32 and on the repository's pinned Lean 4.14, with the repository's CI green at a gate of 23. The paper says plainly where a theorem is weaker than its name: for example helical_selectivity is monotonicity of the square root and carries no dynamics. |
io / CatGT/CatGT_Main.lean |
| Post-V6 additions (section 4d) | Verified | The repository file now has 28 theorems; the author's runs on 6 Oct 2026 report 28 of 28 on the standard three axioms under both toolchains. The raw output was reported in chat and is not stored in the repository. These theorems are not in the deposited V6. | io commit 6127948 |
| The width of a trapped state at fixed norm, r*P = 4aJ/(λP) | Derived | Derived from the stationary continuum DNLS equation; the step from the equation to the width is Lean-checked. Not proved: the continuum limit itself and the norm relation P = 2A²w/a. The older form a√(J/λ) is kept as the fixed-peak-amplitude case. | io / paper section 4b–4c |
| Where the width law holds | Checked by script | In quasi-one-dimensional channels (the ZSM-5 case) the width law is checked numerically. In two- and three-dimensional cages (the MCM-22 supercage) the simulation shows a self-trapping threshold, not a width, so the smooth law should not be assumed there. | io / scripts: fixed_norm_width_check.py, cage_threshold_check.py |
| Quantitative fit to the measured selectivities of Sousa et al. | Open | The direction matches the published abstract. The fit itself needs the measured selectivity tables, which were not accessible. No numbers have been filled in. | io / paper, open items |
| C, K, F, U as operators on a function space; the fixed-point link to confinement | Open | These are not defined as formal objects anywhere in the zeolite paper, which states the gap and does not assume a definition into existence. | io / paper, Theorem 1(ii) |
| Coherence Bridge across seven domains; helical-phase prediction; extrudate-shape corollary; clean-energy extension | Withdrawn | Cut in the V5 narrowing, not carried forward. The scale √(J/λ) is the generic crossover between spreading and localizing in many systems, so a shared functional form is not a shared invariant. The helical-phase prediction depended on Reeb orbits being helical, and they are not. | io / paper, scope section |
Check it yourself
The commands below are the ones the author used. They need your own toolchain, and a clean run says only that the file compiled on the day you ran it.
git clone https://github.com/TOTOGT/geometry cd geometry python3 gcm-framework-verify.py # the Gibbs-form check and the corpus counts lake build CatGT # the Lean file, under the toolchain in lean-toolchain # then, in a file that imports it: # #print axioms <theorem name> # expect only propext, Classical.choice, Quot.sound
A passing check is not proof that a theorem says what its name says. Every new theorem here is read for what it states, not what it is called, before it is treated as settled.
People
- Principal
- Pablo Nogueira Grossi · G6 LLC, Newark, New Jersey · ORCID 0009-0000-6496-2186
- Contact
- g6llc@proton.me
- Code and papers
- TOTOGT/io (zeolite paper and Lean) · TOTOGT/geometry (the series) · AXLE
- How it is made
- Written with substantial assistance from Claude (Anthropic) and checked by scripts and the Lean kernel. The author is responsible for every statement.