Atratores

Attractors — mathematics, sound, and visible form · May 2026
Pablo Nogueira Grossi · G6 LLC · Newark NJ · Principia Orthogona · GitHub · AXLE
100+ Lean 4 theorems · 0 sorry · 5/5 accepted XII Bienal SBM
Sound Machines 8 instruments
drone · binaural
OM Machine
Continuous drone on the primordial tone. 136 Hz earth year, fractal shimmer.
● Live
breath · resonance
So-Ham Machine
Breath-cycle resonance — "I am That". Ascending and descending tonal guides.
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pranayama · entrainment
Pranayama Machine
Guided breathing with tonal entrainment. 4-7-8, box, Nāḍī Śodhana.
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wellness · dm³
Wellness Soundworks
dm³ Soundworks therapeutic suite. All seven machines in one page.
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G6 · dm³ · k:m=6:1
G6 Drone Machine
Six-fold resonance at the G6 Crystal threshold. (T*,μmax,τ) = (2π,−2,2). ε₀=1/3.
● Live
yantra · geometry
Śrī Yantra Śakti Machine
Nine-triangle geometric resonance. Entonação justa / pitagórica / igual.
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Bhairava · attractor
Swarnakarshana Bhairava
Tantric attractor — harmonic convergence. Hrāṃ Hrīṃ Hrūṃ tríade bīja.
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tartaruga · chladni · ocean New
🐢 Tartaruga · Turtle Shell Machine
Sea turtle carapace as dm³ contact manifold attractor. Chladni simulator + 8-layer ocean sound + scute map. Projeto TAMAR. C→K→F→U on curved biological surface.
✦ New · May 2026
Exhibitions & Installations 4 works
XII Bienal SBM · EXP13 · every day
Cymatics with Machines
Cimática com Máquinas — bilingual interactive exhibition. Chladni figures, seven sound machines, dm³ contact geometry. UFRN, Natal 2026.
✓ Accepted EXP13
simulation · dm³ · contact
Helical Attractor
3D browser simulation of the helical attractor on the contact manifold M = ℝ²₊ × ℝ. Drag to rotate, scroll to zoom.
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archaeoacoustics · resonance
Ħal Saflieni Resonance
Eigenfunction analysis of the Hypogeum prehistoric space. 110 Hz Oracle Chamber. Malta, 3600 BCE.
● Live
installation · Newark
Site-specific sound installation. Newark, NJ.
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Conferences 2026 — 7/7 Accepted Bienal SBM · XIII LAW3M · UFRN Natal
CodeTitleEvent · Schedule
EXP13 Cimática com Máquinas · Figuras de Chladni XII Bienal SBM · Every day Aug 3–7 · CETECH Foyer · All day
MC48 Atratores Helicoidais em Variedades de Contato · dm³ System XII Bienal SBM · Tue Aug 4 · E1LAB · 16:30–18:30 · 2h, single session
OF53 A Escada de Recorrência: Do k-nacci ao limiar τ=2 XII Bienal SBM · Fri Aug 7 · H3 · 14:00–16:00
CO144 O Princípio do Cajueiro e o Livro Inglês para Pesquisadores via TOGT XII Bienal SBM · Wed Aug 5 · F6 · 17:30–18:30
P290 Atratores Helicoidais em Variedades de Contato de Dimensão 3 · EDO de Brinquedo XII Bienal SBM · Thu Aug 6 · CCET Foyer · 16:00–17:00
LAW3M Contact-Geometric Theory of Generative Transitions · Seven Proofs of the Tribonacci Constant XIII LAW3M · Oct 19–23 · Natal-RN · ✓ Accepted · Pablo Nogueira Grossi
LAW3M Plasma Companion Star · MHD Reconnection · dm³ Saddle Geometry XIII LAW3M · Oct 19–23 · Natal-RN · ✓ Accepted · Pablo Nogueira Grossi
Travel funding for the October LAW3M programme — see Support & Sponsors · Contact grossiatwork@gmail.com
Support & Sponsors G6 LLC · Newark, NJ
The ask
US$ 3,000

Travel and materials for XIII LAW3M · Natal-RN · 19–23 October 2026, where two papers have been accepted. Covers airfare, lodging, and printing for the exhibition materials.

How it works

Sponsorship is a commercial arrangement with G6 LLC (Newark, New Jersey). Businesses can generally treat sponsorship as an advertising and marketing expense — confirm with your own accountant.

G6 LLC is a New Jersey LLC, not a charity. Contributions are not charitable donations.
Recognition

Supporter logos appear on this portal, on the exhibition signage at EXP13 · Cimática com Máquinas, and on printed materials. The exhibition runs every day of the XII Bienal at the CETECH foyer and is free and open to the public.

Supporters
Sponsor slots open — logo placement available for this and the October programme.
Depois da exposição · After the exhibition

🐢 Leve as crianças ao Projeto TAMAR. A tartaruga do Capítulo τ é real. O casco é uma variedade de contato — as placas se organizam como uma partição de Voronoi — mas antes disso é um animal que precisa de proteção, e o TAMAR tem centros de visitação no Rio Grande do Norte.

Take the children to Projeto TAMAR. The Chapter τ turtle is a real animal before it is a contact manifold. If this exhibition sends one school group to a TAMAR visitor centre, it has done its job. Placement here is free and unpaid — see A Tartaruga Cósmica · Turtle Shell Machine.

Enquiries: grossiatwork@gmail.com · Pablo Nogueira Grossi · G6 LLC · Newark, NJ
Chapters — Living Book Principia Orthogona · Book 3
Chapter τ · new New
🐢 The Cosmic Tortoise
A Tartaruga Cósmica. Sea turtle shell as dm³ contact manifold. Chladni figures on curved surfaces. Mount Meru on the turtle's back. Ouroboros closing. Projeto TAMAR. C→K→F→U in bone.
✦ New · May 2026
Chapter 8
The Mountain and the Serpent
Mount Meru, Ouroboros, ancient infinities. Pascal's Triangle as F operator. The intuition before the notation.
● Live
Capítulo E · PT
GTCT — Circuito Temporal Generativo
Teorema T1. Tempo como C→K→F→U→T. O retorno em espiral. Seis exercícios graduados.
● Live
Chapter E · EN
GTCT — Generative Time Circuit
Theorem T1. Time as C→K→F→U→T. The spiral return. Six graded exercises.
● Live
Chapter η
DNLS — N-bonacci Criticality
Discrete Nonlinear Schrödinger. Tribonacci/Tetrabonacci chain. η≈1.839 criticality threshold.
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Sessão 1 · PT/EN
Geometria de Contato
Contact Geometry — bilingual. dm³ operator introduced from first principles.
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Sessão 2 · PT/EN
Teorema da Bacia
Theorem Basin — bilingual. ε₀=1/3, r*≈0.77594059, asymmetric basin correction.
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Sessão 3 · Lean 4
Esqueleto Lean · Lean Skeleton
Lean 4 bilingual session. From dm³ equations to formal proofs.
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Lean 4 / AXLE Formal Verification 100+ theorems · 0 sorry
FileContentStatus
A1Singularity.leanUniversal A₁ node · 7 physical instances · DM3-lab ↔ AXLE bridge✓ proved
PolarVortex.leanSaturn north-polar vortex · moat · hexagon · three-layer dm³✓ proved
SaturnRing.leanCassini Division 2:1 resonance · dm³ limit cycle · G6 Crystal✓ proved
Chain_updated.leangronwall_outer · spiral_return_exists (T1) · poincare_collatz_contracting✓ 4 proved · 2 axioms
AutophagyDm3.leanAutophagy + Triple-Alpha · 26 theorems · Chapter A✓ 26 thm · 0 sorry
VolumeTwo.lean8 theorems proved · eigenvalue, τ=2, ε₀=1/3, singularity bijection✓ 8 proved · 4 open
turtle_carapace.lean NewVoronoi dm³ partition · scute fold events · curved-surface Chladni (Ch.τ)⚠ open · AXLE #τ
inner_basin_asymmetricr*≈0.77594059 ≠ r_att−ε₀=2/3 · asymmetric basin · AXLE #13⚠ axiom pending
poincare_collatz_generalGeneral orbit convergence · dm³ analogue of Collatz · $1M⚠ open · ★★★★★
github.com/TOTOGT/AXLE ↗  ·  github.com/TOTOGT/GTCT ↗
Books, Papers & Zenodo Series 21 deposits
Series root (all volumes)10.5281/zenodo.19117399concept DOI · always resolves to latest
Vol. I v3 — Operator algebra10.5281/zenodo.20298665C→K→F→U · Whitney A₁–A₃ · Lean 4
Vol. II v2a — Contact geometry10.5281/zenodo.20159456dm³ · τ=2 · ε₀=1/3 · 8 thm proved · dashboard.html
GTCT Ring 5 v310.5281/zenodo.20230641Theorem T1 · DOP853 · 0 sorry
Autophagy / Triple-Alpha Ch.A10.5281/zenodo.2016881226 theorems · 0 sorry · biology
DNLS / N-bonacci Ch.η10.5281/zenodo.20026942η≈1.839 · criticality
FruitFly Connectome10.5281/zenodo.19210136neural architecture · dm³
Book 3 · The Mini-BeastSSRN 6805940pending approval · Principia Orthogona Vol. III
Vol. I + II combinedSSRN 643962611 downloads · live
21 Papers · Zenodo
Principia Orthogona — Full Series
Complete series index with all 21 Zenodo records, DOIs, and descriptions.
● Live
Engineering Spec
Collatz Engineering
dm³ axioms · G6 Crystal · AXLE Target 5 · Python · Julia · Lean 4
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Livro 3 · PT-BR
The Mini-Beast · Brasil
Book 3 of Principia Orthogona. Portuguese edition. All six chapters.
● Live
Chapter τ · New
🐢 The Cosmic Tortoise
Sea turtle shell · dm³ · Chladni curved surface · Projeto TAMAR · Meru on the back
✦ New
DNLS — Discrete Nonlinear Schrödinger Tribonacci & Tetrabonacci chains
Chapter η · DNLS
N-bonacci Criticality
η≈1.839. Discrete Nonlinear Schrödinger. Tribonacci/Tetrabonacci criticality threshold.
● Live
Paper · PDF
DNLS Paper with Figures
Full paper: nbonacci_dnls_paper_with_figs.pdf · DOI 10.5281/zenodo.20026942
● PDF
GCTC / GTCT — Operator Chain Ring 5 · Lean 4
Chapter E · EN
GTCT for Everyone
Generative Time Circuit Theorem. C→K→F→U→T. Theorem T1. Six graded exercises.
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Capítulo E · PT
GTCT para Todos
Circuito Temporal Generativo. C→K→F→U→T. Teorema T1. Versão portuguesa.
● Live
Game Theory · EMMEs
Game Theory · THEORY Token
F operator — irreversible commitment — Solana EMMEs Token. Theory as a game.
● Live
3D · simulation
Helical Attractor Simulation
Live 3D browser simulation. ṙ = r(1−r²)+2(r−1)e⁻ᶻ · θ̇=1 · ż=r²−2(r−1)²e⁻ᶻ
● Live