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 · NYFA fiscal sponsor
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.
● Live pranayama · entrainment
Pranayama Machine
Guided breathing with tonal entrainment. 4-7-8, box, Nāḍī Śodhana.
● Live wellness · dm³
Wellness Soundworks
dm³ Soundworks therapeutic suite. All seven machines in one page.
● Live 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.
● Live Bhairava · attractor
Swarnakarshana Bhairava
Tantric attractor — harmonic convergence. Hrāṃ Hrīṃ Hrūṃ tríade bīja.
● Live 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.
● Live archaeoacoustics · resonance
Ħal Saflieni Resonance
Eigenfunction analysis of the Hypogeum prehistoric space. 110 Hz Oracle Chamber. Malta, 3600 BCE.
● Live installation · Newark
229 Ballantine
Site-specific sound installation. Newark, NJ.
● Live
XII Bienal SBM — 5/5 Accepted UFRN · Natal · August 3–7, 2026
CodeTitleSchedule
EXP13 Cimática com Máquinas · Figuras de Chladni Every day Aug 3–7 · CETECH Foyer · All day
MC48 Atratores Helicoidais em Variedades de Contato · dm³ System Tue Aug 4 & Thu Aug 6 · E1LAB · 16:30–18:30
OF53 A Escada de Recorrência: Do k-nacci ao limiar τ=2 Fri Aug 7 · H3 · 14:00–16:00
CO144 O Princípio do Cajueiro e o Livro Inglês para Pesquisadores via TOGT Wed Aug 5 · F6 · 17:30–18:30
P290 Atratores Helicoidais em Variedades de Contato de Dimensão 3 · EDO de Brinquedo Thu Aug 6 · CCET Foyer · 16:00–17:00
Travel funding: NYFA fiscal sponsorship confirmed (501(c)(3)) · Fundraiser launching · Contact pablogrossi@hotmail.com
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.
● Live Sessão 1 · PT/EN
Geometria de Contato
Contact Geometry — bilingual. dm³ operator introduced from first principles.
● Live Sessão 2 · PT/EN
Teorema da Bacia
Theorem Basin — bilingual. ε₀=1/3, r*≈0.773, asymmetric basin correction.
● Live Sessão 3 · Lean 4
Esqueleto Lean · Lean Skeleton
Lean 4 bilingual session. From dm³ equations to formal proofs.
● Live
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*≈0.773 ≠ 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
● Live 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.
● Live 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
G6 Opus Map · Principia Orthogona · All Repositories
G6 Opus · Principia Orthogona · Map of Maps
Pablo Nogueira Grossi · G6 LLC · Newark NJ · ORCID 0009-0000-6496-2186
C → K → F → U → ∞
geometry / Book 3 HTML
AXLE / Lean 4
DM3-lab / numerics
grossi-ops / foundations
3M / Monster Law
GTCT / framework
Collatz / Atratores
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Principia Orthogona · Complete Opus
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the crystal is the book