This is the page where the honest answer is mostly "not much." dm³ is not particle physics and this work makes no claim on the Standard Model. But three ICHEP tracks have real overlap, and one of them is a much better fit than anything on the mathematics programmes.
Said plainly, first
Nothing in the dm³ framework predicts a cross-section, constrains a coupling, or bears on any measurement at the LHC. Where the word "plasma" appears in this work it means astrophysical MHD — reconnection geometry in current sheets — not collider physics. Anyone who tells you a contact-geometry toy ODE has something to say about beyond-the-Standard-Model searches is selling something. The overlaps below are methodological, and they are narrow.
The strongest fit · Education & Outreach
LOC liaison: Sandra PADULA (UNESP, Brazil)
This is where the work actually belongs. EXP13 — Cimática com Máquinas is a free, every-day public exhibition running at the CETECH foyer at UFRN through 7 August: Chladni figures driven by a microphone, seven sound machines, nodal sets on the square plate, the disc, the sphere and the 3-sphere — each with the theorem stated and proved on the page.
It is built for the same problem this track exists to solve: showing a general audience that a differential equation has a visible shape, without lying to them about the mathematics.
Dissipative stability · relativistic hydrodynamics
LOC liaison: Marcelo MUNHOZ (USP, Brazil)
Relativistic viscous hydrodynamics has a long-running problem that is fundamentally about
dissipative dynamical systems: causality and stability of the evolution equations, and which
initial data actually flow to the attractor. dm³ is a toy dissipative system on a contact manifold
whose basin of attraction turns out to be asymmetric — the symmetric Lyapunov estimate
misclassifies orbits, and the sharp inner edge sits at r★ = 0.77594059 rather than at
the estimate's 2/3.
Verified numerics · Lean 4
LOC liaison: Carsten HENSEL (CBPF, Brazil)
AXLE is a Lean 4 / Mathlib4 development carrying over 100 machine-checked theorems with zero
sorry in its verified core, and nine open problems named explicitly as sorry
rather than hidden. The interesting part for this track is not the mathematics — it is the
discipline. The gap between "we integrated it and got this number" and "we proved it" is marked in
the source, in a way a reader can check.
The local bridge
Of every name on the ICHEP organising structure, this one is on the same campus where EXP13 is installed. Not a research overlap — a logistical one.
Where it thins out
Two further tracks touch the work loosely and are listed here only so the boundary is visible.
Astroparticle Physics and Cosmology (LOC: Vitor DE SOUZA, USP) is the nearest home for
the MHD reconnection material — critical curvature at the X-point,
κ*(x₀) = min{‖IIx₀‖, √Ksec(x₀)} — though that work is
astrophysical and unpublished in this field.
New Developments in QFT, String Theory and Quantum Information
(Horatiu NASTASE and Tereza MENDES; LOC: Rogerio ROSENFELD, IFT-UNESP) is where an operator-algebra
formalism would be evaluated by people equipped to dismantle it — which is the useful outcome.
Practical note
ICHEP parallel sessions ran 30 July – 1 August at the Praiamar Natal Hotel & Convention Center; plenaries are 3–5 August at the Natal Convention Center and are streamed live. The XII Bienal runs 3–7 August at UFRN, and the Brazil–China–Portugal conference 6–7 August, also at UFRN. Three international meetings, one city, one week. The exhibition is free and needs no badge.