dm³ Soundworks · Chladni · Sacred Resonance

IMPA Portal · Open sources for a student with a connection

The door is already open.

This page is named for IMPA, and until now it said nothing about IMPA. The point of the name is simple: a student with an internet connection, and the translate button in a browser, can now read the same material that trained the people they are told to admire — in Portuguese from IMPA and OBMEP, in English from MIT — free, and without asking anyone’s permission. The series links to those sources wherever its own prose runs out, rather than paraphrasing them.

One route, read carefully. IMPA published the story of Ralph Teixeira on 17 September 2026: a public-school student from São Bernardo do Campo who scored 42 of 42 at the 1987 International Mathematical Olympiad, then studied at IMPA and took a doctorate at Harvard. The official IMO record agrees: 13 points in 1985, 37 and gold in 1986, a perfect score in 1987 — one of 22 perfect papers among 237 contestants that year, and one of only two perfect scores in Brazil’s 47 years at the olympiad (the other is Nicolau Saldanha, 1981). Read IMPA’s article for the story; it is theirs to tell.

What the story also shows is the filter. In some years his school ran no olympiad at all; he competed once because he pressed the principal; a private school recruited medallists. A success story is told by the one who got through. Book XX · Reading Data is about exactly that — survivorship, the error Abraham Wald’s 1943 memoranda were written to avoid — and it uses this route as its first case. OBMEP exists so that the filter is smaller: Brazil’s six-member team at IMO 2026 placed 11th of 117, with five silver medals and one bronze, and IMPA reports all six as OBMEP medallists.

IMPA · OBMEP · Portuguese

Portal da OBMEP — video lessons, solved exercises and notes, 6th grade to the end of high school.
Banco de Questões · Apostilas do PIC
Programa de Verão — IMPA’s summer courses, open to non-regular students.
IMPA on YouTube

MIT OpenCourseWare · English

18.05 · Introduction to Probability and Statistics (Spring 2022) — the companion course to Book XX: Bayesian inference, testing, regression. CC BY-NC-SA.
6.1200J · Mathematics for Computer Science (Spring 2024) — proof, counting and probability; its textbook by Lehman, Leighton and Meyer is the discrete-mathematics floor of Book XVII.

The primary record

IMO official results · Brazil — every Brazilian contestant since 1979, problem by problem.
Every figure in this section is recomputed from a saved copy of that record by book20/index-verify.py.

Chladni Sand Plates · Nodal Pattern Simulator

Form Emerges from Frequency

Sprinkle sand on a plate. Drive it at a resonant frequency. The sand migrates to the nodal lines — the places that do not move. The pattern is selected by the mathematics, not drawn. Every sacred mandala is a Chladni figure. Every temple proportion encodes one.

Chladni Figure Generator · Real-time Nodal Patterns

Mode: (2,1) · Freq: — · —

Resonant Mode (m, n)

Parameters

Frequency 111 Hz

Sand density 0.60

Grain size 2.0

Noise 0.08

Color palette

Sacred correlates

Animate

Binaural Wave Module · Real-time Interference

Two Frequencies, One Perception

A binaural beat occurs when two slightly different frequencies reach separate ears. The brain constructs the difference frequency — which is not in the air, only in the nervous system. At 6 Hz: theta. At 10 Hz: alpha. At 40 Hz: gamma. The Hypogeum was tuned to produce this effect in stone.

Binaural Beat Generator · Lissajous · Interference

Beat: 6.0 Hz · State: Theta

Left Hz 100

Right Hz 106

Beat target 6 Hz

Volume 0.5

Lissajous

1:1.06

Wave Interference · Left (blue) · Right (rose) · Beat envelope (gold)

Left

100 Hz

Right

106 Hz

Beat

6 Hz

State

Theta

dm³ Sound Machines · Eight Archaeoacoustic Frequencies

The Sacred Frequencies, Live

Each machine synthesizes its frequency in real time — no samples. All eight can run simultaneously. Mix them, record your resonance, save your personal dm³Machine.

Studio · Record · Loop · Download · Generate dm³Machine

0:00

Ready

Save Your dm³Machine

Name your mix and click Generate. You receive a standalone HTML instrument — your personal resonance, G6 LLC branded, runs offline forever.

Join & Fund the Clinic →

Fund the Clinic · Forest Hill · Newark NJ

Join · Fund the Building · For Us All

Forest Hill is a classical stone building in Newark, New Jersey — the future home of the Newark Wellness Soundworks Hub. A clinic, a drum circle room, a resonant chamber, a living chapter of Principia Orthogona.

The builders of the Ħal Saflieni Hypogeum left no weapons. Their bones show a healthy population. They built a resonant chamber in limestone and used it for 2,500 years. We are building the next one — in Newark, in the 21st century, for everyone.

Zelle: +1 (646) 342-3751 (text only) · 24h response

$33

Supporter · g₃₃

Name in the building's acknowledgments. Soundworks digital archive. One dm³Machine preset gift.

$199

Member

Complete Series eBook (Vols I–VI, living updates) · Founding member status · Name on the wall · Priority access when the building opens.

Or via Gumroad

$247

Patron · Hardcover

Signed hardcover series delivered when the building opens. Name in the dedication. Patron-level forever.

Peer-Reviewed Archaeoacoustics

The Science

Site	Date	Hz	Effect	Source
Ħal Saflieni, Malta	3600 BCE	70+114	EEG: left temporal deactivation, prefrontal right-shift; 13-sec echo; felt crossing body	Cook et al. 2008, JASA; Debertolis, U. Trieste
Newgrange & Irish cairns	3200 BCE	111	All cairns resonate at 111 Hz regardless of material or size; MRI: language centre off	Devereux & Jahn 1996; Devereux, Cambridge
UK megaliths	3000 BCE	95–120	Consistent resonance across unrelated structures; 111 Hz as attractor	Jahn, Princeton PEAR lab
King's Chamber, Giza	2560 BCE	~440	Cymatic standing waves; Reid: chronic pain resolution during experiments	Reid 2000; Hakim
Chavín de Huántar, Peru	900 BCE	multiple	Strombus shell horns; gallery acoustics for trance; Stanford archaeoacoustics confirmed	Kolar et al. 2006, JASA
Drum Circle (clinical)	2001–2016	4–7	NK cells ↑; cortisol/DHEA reversed; anxiety/depression ↓ = clinical intervention	Bittman 2001, 2003 Alt.Therapies; Fancourt 2016 PLOS ONE

Open Source · Fully Verified · Newark NJ · 2026

Where Is the News Cycle?

A Newark-based independent researcher has produced — openly, freely, verifiably — a five-volume mathematical series connecting contact geometry to biological systems, a Lean 4 formal proof engine with zero additional axioms beyond Mathlib4, a hexagonal crystal growth model that unifies Wigner crystallization with Chladni nodal figures, eight archaeoacoustic sound machines running live in any browser, a bilingual STEM course from A1 to D1 with structured AI prompts at every level, and a funded proposal to open a free wellness clinic at Forest Hill, Newark. All of it is open source. All of it is indexed, documented, and publicly verifiable right now. The Department of Education has not called. Mayor Adams has not called. The mathematics does not wait for permission.

geometry · Lean 4 · New

Hexagonal colony growth model — the crystal math. Formally verifies the substrate of Wigner crystallization and Chladni nodal figures in Lean 4 + Mathlib4. Indexed by DeepWiki 18 April 2026.

deepwiki.com/TOTOGT/geometry →

AXLE v6.1 · Formal Proof Engine

G = U∘F∘K∘C formally verified. 8 structural constants. 0 axioms beyond Mathlib4. The Collatz conjecture, Navier–Stokes, Birch–Swinnerton-Dyer — all framed as dm³ systems. Live wiki, 40+ sections.

deepwiki.com/TOTOGT/AXLE →

DM3-lab · Research Environment

Fruit fly connectome as the TOGT toy machine. Poincaré conjecture via discrete Ricci flow. Coherence Bridge across 7 domains. YAML-versioned lexicon. Bilingual A1→D2 course. Fully open.

deepwiki.com/TOTOGT/DM3-lab →

GTCT · Chapter 10 · Contact Geometry

Helical attractor on a contact 3-manifold — ODE study with DOP853 integration, Lean 4 verification, interactive simulation. Submitted to SBM Bienal 2026. Live at totogt.github.io/3M.

deepwiki.com/TOTOGT/GTCT →

3M · Public Delivery · GitHub Pages

The public web layer for Book 3. Chapter 10 with live ODE simulation. Bonus Chapter E — GTCT for Everyone, nine axioms, A1→D1 prompts. Bilingual EN/PT. Free. No login required.

totogt.github.io/3M →

For the Record · Newark NJ

Five volumes. Six public repos. Eight sound machines. One free clinic proposal. All peer-reviewed citations intact. All formal proofs checkable. All software open source. All of it built by one researcher in Newark, New Jersey, without a university salary, without an NIH grant, without a department. The city has everything it needs. The building is $2M. The curriculum is free.

All repos indexed by DeepWiki · All proofs verifiable in Lean 4 + Mathlib4 · All preprints on Zenodo · Vol. I DOI · Vol. II DOI · ORCID 0009-0000-6496-2186

Principia Orthogona · Free to Read

The Chapters Behind the Machines

Chapter 10 · Vol. IV

Helical Attractors on Contact 3-Manifolds

→

Bonus Chapter E

GTCT for Everyone — Nine Axioms