Seven plenaries on this programme touch the dm³ work directly. This page says where, and what I would actually ask. It is a list of questions, not of claims.
The system, in one paragraph
dm³ is a toy ODE on the contact manifold M = ℝ²₊ × ℝ:
ṙ = r(1−r²) + 2(r−1)e⁻ᶻ, θ̇ = 1, ż = r² − 2(r−1)²e⁻ᶻ.
It has an attracting limit cycle at r = 1. A Grönwall estimate gives a
symmetric ball of guaranteed convergence, |r−1| < 1/3. High-precision
DOP853 integration says the real inner boundary is at r★ = 0.77594058, not 2/3.
The basin is asymmetric, and the symmetric estimate does not merely lose sharpness — it
misclassifies orbits. That gap is the whole pedagogical content of the minicurso.
Contact geometry and Reeb dynamics
Hill's problem to modern geometry is global surfaces of section and Reeb dynamics on contact manifolds. dm³ is a dissipative cousin: the same ambient object, without the Hamiltonian.
Planar vector fields · the shortest route to a proof
Because θ̇ = 1 decouples, dm³ reduces to a planar system in (r, z).
That puts it inside the class this talk is about.
(r,z) field bound the
inner basin analytically? A polyhedron argument would replace a numerical certificate with a proof —
the single most valuable thing anyone could hand this project.Singularities
Volume I classifies the dm³ bifurcations against Whitney A₁–A₃, and the A₁ node is the bridge file between DM3-lab and AXLE across seven physical instances.
Continued fractions and the n-bonacci constants
The DNLS chain work turns on the tribonacci constant η ≈ 1.8393 and its
tetrabonacci successor, with a criticality threshold observed at that value.
Geometric flows and the curvature threshold
The K operator in the dm³ chain is a curvature operator with a verified threshold
κ* ≤ √(7/9) ≈ 0.882. The framework treats curvature as the thing that removes
options rather than the thing that drives motion.
Cyclotomy and the sixfold constants
The G6 Crystal is a hexagonal form with aspect ratio 66 = 33·τ, and the verified constants
include g₆₄ = 2⁶ = 64 and T* = 2π. Sixfold symmetry throughout.
g₃₃ = 33 a cyclotomic object, or numerology that has
survived because nobody with the right training has looked at it? An honest answer either way is
worth more than the constant.Teaching · why CO144 exists
CO144 argues that English for mathematical researchers can be taught through the mathematics itself, with science entering from day 21 of instruction rather than after fluency.
One honest gap
AXLE carries over 100 Lean 4 theorems with zero sorry in the
verified core. The basin boundary is not among them. The Lean statement currently
proves only that some ρ★ exists in the interval (2/3, 1) — which 0.77594058 satisfies, and so does
0.773, and so does 0.8. The value itself rests on DOP853 integration, not on a proof. It is a
certificate, not a theorem, and it is named as such in the file. Closing that gap is the open
problem this exhibition is advertising.