ALL CHAPTERS

HUB

G6 Geometry Hub / Cajueiro Soundworks

Main entry · Book 3, AXLE, Orthogenesis · Portuguese soundworks index

HUB

G6 Geometry Hub (full edition)

Course, Book 3, AXLE, Orthogenesis Lean 4, Journey Map — all in one

PRELUDE

Prelude — The Book Begins

Operator legend · how to read · interactive spiral chapter map

A1→A2

PILOT

The Mini-Beast · Pilot Page

Book 3 pilot landing page · series overview · entry point

JOURNEY

Student Journey Map

41 chapters · 3-pass spiral navigator · CEFR timeline · localStorage progress

LIVE

ARCHIVE

Journey Map v1 (backup)

Earlier build of the spiral journey navigator

MAP

Series Layer Map

Principia Orthogona G¹–G⁵ · full series architecture visualised

HUB

Living Book Hub

All chapters collected · dm³ track + EfR track · two parallel programs

VISUAL

dm³ Generative Attractor

Seven domains · animated canvas · G = U ∘ F ∘ K ∘ C in motion

LIVE

CLASS

Book 3 Classroom Index

Teacher and student classroom navigation · structured access

NAV

The Labyrinth

Extended navigation · alternate reading paths through Book 3

COURSE

16-Week Course

A1 → D1 · week-by-week schedule · 21 LLM prompts · 4 milestone papers

SOURCE

English for Researchers C1→D2 (source)

16-week program source HTML · full build

Ch 0

Introduction: One Equation, Many Rooms

The lemniscate and the analemma · the seed is the same

A2

Ch 0 · Student Ed.

How to Read This Book — Student Edition

A1 student-facing entry · operator chain introduced gently

A1→A2

Ch 1 · G

The Cajueiro Principle

The visible output conceals the hidden generator · first biological instantiations

A2

Ch 1b · C

The Cajueiro Principle — Seed & Fixed Point

The seed reading · C operator as origin · EfR companion

B1

Ch 1c · C

The dm³ Framework: A Review

Operators C K F U · κ* · contact normal form · 4-system parameter table

B1

Ch 1d · C

Ch 1 — One Equation, Many Rooms

Journey companion · operator chain entry-level · journey map linked

A2→B1

Ch 2 · C

Generative Matrix

Compression · SVD · critical periods · myelination · growing up as rank increase

A2→B1

Ch 2b · C→K

Biological Instantiations: The Four Orbits

HPA · Neural · Circadian · Immune · μ_max ω β κ* all four

B1

Ch 3 · T

Circadian Regulation

Contact 3-manifold · Reeb flow · helical attractors · 24h orbit

B1

Ch 3b · K

Plasma-Sheet Reconnection

Magnetotail as dm³ · μ_max=−0.42 · κ*≈10⁻³ km⁻¹ · Cluster/MMS/Parker

B1→B2

Ch 4 · K

Neural Oscillations

Theta-gamma coupling · K* coherence threshold · sleep consolidation

B1→B2

Ch 4b · K

Market Volatility Manifolds

Flash crash as K event · μ_max=−0.67 · β=2.4 · NYSE TAQ 10⁹ ticks

B1→B2

Ch 5 · F

Immune Memory

Clonal selection · affinity maturation · memory cells as fold operator

B1→B2

Ch 5b · F

Neural Embedding & the Coherence Bridge

Theorem 5.4 — six systems, one category dm³ · exact morphisms · coming

Coming

Ch 6 · U

Resonance

Cymatics · archaeoacoustics · Schumann · universal scale structure

B2

Ch 6b · U

The Resonant Chamber

Contact geometry in physical space · resonant chamber as threshold

B2

Ch 6c · F

Pedagogy as Mathematical Necessity

CEFR → TOGT · 14-week program · three seed sentences

B2

Ch 7 · G

Topological Orthogenesis

Non-abelian anyons · braid groups · 6-direction coherence · weave of spacetime

B2

Ch 7b · F→U

The Crystalline Return

Wigner crystal · G6 crystal · 33.516 Hz Schumann coupling · dm³ architecture

B2→C1

Ch 8 · ∞

Nested Infinities

Cantor · Mandelbrot · surreals · Gödel · renormalization

B2+

Ch 8b · U

The Axiomatic Turn

Γ ⊢ φ · formal proof structure as U operator · Lean 4 first steps

C1

Ch 8c · U

The Mountain and the Serpent (Meru)

Sacred geometry as dm³ · Sri Yantra as contact manifold · Meru axis

BONUS

Ch 9 · F→U

φ — The Subcritical Approach

Golden ratio · Fibonacci · φ=1.618 below c*=3 · criticality threshold

C1

Ch 10 · U

Lyapunov Stability

Stability exponents · attractors · convergence · μ_max = −2

D1

Ch 11 · K

Spectral Radius

Eigenvalues and the generator · ρ(ℒ) ≈ 0.751 · transfer operator

D1→D2

Ch 12 · G

Fixed Point — The Conclusion as Attractor

Banach theorem closes the loop · G(x*) = x*

D1→D2

Ch 13 · ∞

The Nirvana Machine — Revision as Annealing

Meta-operator at work · T → 0 · simulated annealing as U operator

D2

Ch 14 · G

AXLE — The Sorry-Free Paper

Formal verification meets academic writing · Curry-Howard

D2

Ch 15 · C

H — Entropy and the Compression Circle

Shannon entropy revisits C · how much compression remains

D2

Ch 16 · U

Scale Invariance

Self-similarity · renormalization group · B ∝ M³⁄⁴

D2

Ch 17 · G

Epilogue — The Living Book

The full composition resolved · Gⁿ(x₀) → x* · reader becomes operator

D2

EfR Ch 1 · C

We Perceive the Unfolding First — Cajueiro

C operator as reading strategy · A2→B1

A2→B1

EfR Ch 2 · C

Compressing the Abstract

Scientific reading at the threshold · finding κ* in a paper

B1

EfR Ch 3 · K

Source Mapping

Citations · DOIs · literature chain · K in academic writing

B1→B2

EfR M1 · F

Paper 1 — Your First Zenodo Publication

Milestone 1 · the fold — before and after you publish

B2→C1

EfR Ch 5 · K→F

Neural Oscillations (EfR edition)

Science as language rhythm · reading and writing at B2→C1

B2

EfR Ch 6 · F

The Argument Architecture

Academic argument as F operator · fold points in logic · C1→C2

C1→C2

EfR Ch 7 · U

The Bridge

From argument to publication · crossing into D1 · referenced from Ch 6

Coming

Bonus E

GTCT for Everyone

9 axioms · 12 operators · 4 theorems · full A1→D1 prompt library

BONUS

Bonus E (alt)

GTCT for Everyone — Alternate Build

Earlier/alternate edition of the GTCT bonus chapter

BONUS

Bonus W

The Wigner Crystal in Living Systems

G6 Crystal · Schumann 33.516 Hz · G⁶:33 conjecture · six faces

BONUS

Bonus π

The Recurrence Ladder

π φ μ η Δ Σ Ω → τ=2 · constants as operators on the number line

BONUS

Bonus π–Ω

Full Recurrence Ladder (extended)

All seven Greek-letter operators in one combined page

BONUS

Bonus Λ

Polylaminin — Protein Shape Transformations

Λ operator · laminin protein structure as dm³ fold · biological geometry

BONUS

Bonus T

Tubulin as Computronium

Ulam's question · microtubule computation as dm³ · biological fold

BONUS

Bonus T (alt)

Tubulin as Computronium (alt build)

Alternate build of the Tubulin chapter

BONUS

Bonus T (PT)

Tubulina como Computrônio

Portuguese-facing build of the Tubulin chapter

PT-BR

Sample T

Tubulin — Public Sample

Free public sample chapter · microtubule computation as dm³

FREE

Sample W

Wigner Crystal — Public Sample

Free public sample · Wigner crystal as contact fold

FREE

Bonus η · DNLS

Tribonacci / DNLS

η=1.839 · Discrete Nonlinear Schrödinger · long-time dynamics · critical λ

BONUS

Ch 7 · Crystalline

The Crystalline Return

Wigner crystal · G6 architecture · Schumann · moiré patterns

B2→C1

Ch 8 · Meru

The Mountain and the Serpent

Sacred geometry as dm³ · Sri Yantra as contact manifold · Meru axis

BONUS

D2 · Epistemology

Evolutionary Epistemology and the Limits of Formalism

D2 philosophy · the honest sorry · avatar sequence as operator chain

D2

D2 · Philosophy

The Paraśurāma Hinge

Internal transformation · K as formal hinge · Kalkī is here now · Lean sorry

D2

D2 · Yoga-ESL

Yuga 6 — Yoga-ESL · The Origin

Source of the teaching · Yoga as operator chain · Śrī Brodānanda

D2

D2 · Ritual

Pratyakṣa Pāda Pūjā

Śrī Brodānanda · G6 LLC · the teacher's offering · guru puja

D2

SIM · λ

Lyapunov Exponent — Syracuse Return Map

Live λ · adjustable N, seed n₀, noise σ · AXLE Target 5

LIVE

SIM · ρ v1

Spectral Radius — Transfer Operator

Syracuse return map · Collatz visualizer · ρ(ℒ) ≈ 0.751 · v1

LIVE

SIM · ρ v2

Spectral Radius v2

Revised transfer operator · Ruelle–Perron–Frobenius · live at AXLE

LIVE

SIM · dm³

Wigner Crystal Fold Diagram

Interactive dm³ fold · moiré angle selector · G6 crystal visualiser

LIVE

SIM · Collatz

Collatz as dm³ System

c=3 as triad fingerprint · 3×11=33 · crystal geometry corollary

LIVE

SIM · Storm

Storm Manifold

Contact structure visualised in real time · atmospheric dm³

LIVE

SIM · Attractor

dm³ Generative Attractor

Seven domains · animated canvas · G = U ∘ F ∘ K ∘ C

LIVE

SIM · Portal

Simulation Portal

Entry point for all simulations · Collatz · Lyapunov · storm manifold

PORTAL

Student Portal (Sportal)

A1 → D2 · 21-prompt sequence · chapter access · progress tracking

PORTAL

dm³ Soundworks / IMPA Portal

Chladni · sacred resonance · purchase portal · PayPal · Gumroad

GATE

Chapter Access Gate

Paywall gate · dm³ Research Lab · paid chapter access page

SALES

Get the Trilogy

Principia Orthogona Vol. I · II · III · pricing and access

CLINIC

229 Ballantine Pkwy — Clinic Fund

Membership tiers · free clinic · Newark NJ · supporter / patron

Livro 3

The Mini-Beast — Edição Brasil

Edição brasileira completa · G = U ∘ F ∘ K ∘ C em português

PT-BR

Capítulo E · PT

O Circuito Temporal Generativo

GTCT para todos · versão em português · capítulo E completo

PT-BR

Sessão S1

Geometria de Contato & o Sistema dm³

Variedade M · forma α · campo de Reeb · Mini-Curso Vol. IV

PT-BR

Sessão S2

Teorema da Bacia Assimétrica

Bacia atratora · ponto fixo · Teorema de Banach demonstrado

PT-BR

Sessão S3

Esqueleto Lean 4 & AXLE Issue #12

Verificação formal · estrutura Lean 4 · AXLE Target 5

PT-BR