Gravity Across Scales: Nano, Meso, and Macro Instantiations of the dm³ Operator Chain

Gravity Across Scales: Nano, Meso, and Macro Instantiations of the dm³ Operator Chain WEBPAGE - Gravity Across Scales: Nano, Meso, and Macro Instantiations of the dm³ Operator Chain Title Gravity Across Scales: Nano, Meso, and Macro Instantiations of the dm³ Operator Chain Authors Pablo Nogueira Grossi — G6 LLC, Newark, New Jersey, USA — ORCID: 0009-0000-6496-2186 Description / Abstract We show that the dm³ operator chain G = U∘F∘K∘C, defined on the contact 3-manifold (ℝ³, α = dz − r²dθ), has mathematically precise instantiations at three physical scales. We supply complete proofs of the four central mathematical results: (T1) the unit helix Γ = {r=1, θ̇=1, ż=1} is a globally attracting limit cycle with exponential convergence rate μ = −2; (T2) the inner-basin boundary r★ is the Whitney A₁ fold of the asymptotic radial map, certified numerically to r★ = 0.77594059; (T3) the unique saddle of the reduced system has coordinate r_s = 2cos(3π/7), root of x³−x²−2x+1=0, and tr(J)|saddle = 2cos(2π/7) ≈ 1.247; (T4) the contact manifold (ℝ³, α) is a local Sasakian model with Reeb field ∂_z. We further identify the proved T-duality fixed point T★ = 2π with the self-dual radius R = 1, and the ADE fold hierarchy A₁→A₂→A₃ with the gauge groups SU(2)→SU(3)→SU(4) via the McKay correspondence. All physical claims beyond contact geometry are clearly labelled conjectured. Keywords contact geometry · helical attractor · Whitney singularity · Lyapunov stability · Sasakian geometry · T-duality · ADE classification · nano meso macro · g-series · dm³ framework Resource type: Preprint License: Creative Commons Attribution 4.0 International (CC BY 4.0) Publication date: 2026-06-18 Journal / Conference: Principia Orthogona Series — ISBN 979-8-9954416-6-3 Related identifiers: Is part of → doi:10.5281/zenodo.19117399 (series concept DOI, always-latest) References → doi:10.5281/zenodo.20682934 (TOGT / NucPhysB paper) References → doi:10.5281/zenodo.20710023 (Alterna paper) References → doi:10.5281/zenodo.19117400 (Vol I archive) Version: 1 Language: English Funding: G6 LLC (self-funded) Both events are in Natal, UFRN — same city, same campus, weeks apart. Here's the full picture: XII Bienal de Matemática (SBM) Dates: 3–7 August 2026 Location: UFRN campus, Natal, Rio Grande do Norte Organiser: Sociedade Brasileira de Matemática (SBM) First time in Natal — historically significant edition Programme: plenary lectures on the 7 Millennium Problems (Clay Institute), mini-courses, workshops, posters, oral communications Key past deadlines (registration still open until 2 Aug): poster/mini-course proposals closed 31 March; results announced 1 June; final programme out by 7 June; material submission by 5 July Registration: open until 2 August 2026 — sbm.org.br/xii-bienal XIII LAW3M (Latin American Workshop on Magnetism, Magnetic Materials, and Their Applications) Dates: 19–23 October 2026 Location: UFRN, Natal, Rio Grande do Norte Organiser: Federal University of Rio Grande do Norte (UFRN) / Latin American Association of Magnetism (ALMA) Abstract deadline: July 12 (as referenced in your abstract files) Website: law3m2026.org · gnms.fisica.ufrn.br/xiiilaw3m The two events are 10 weeks apart, both at UFRN Natal. The Bienal is pure mathematics (good fit for the contact geometry / Principia Orthogona work), while LAW3M is where - two or three (this one) LAW3M abstracts are already submitted for October. Sources: XIII LAW3M XIII LAW3M Overview – GNMS/UFRN XII Bienal – Sobre o Evento SBM Cronograma de Eventos