ALL CHAPTERS · ALL VOLUMES

Principia Orthogona · Books 1–9 · Series Map · June 2026

G = U ∘ F ∘ K ∘ C
C — Compression
K — Threshold
F — Fold
U — Unfolding
G — Conclusion
∞ — Meta-operator
T — Tone / Periodicity
Entry Points & Navigation
Hub pages, portals, and navigational structures
SERIES HUB
Principia Orthogona — Series Hub
All 9 volumes · Lean 4 audit trail · 17 orders of magnitude · start here
HUB · Book 3
Book 3 Hub — The Mini-Beast
Main entry point · Biology, physics, language · pedagogical entry for the series
HUB · Book 7
Book 7 — Scientist Gallery
Ada, Curie, Dirac, Escher, Faraday, Hawking, Lattes, Ramanujan, Thoreau · Live
HUB · Book 8
Book 8 — The Monster
Monster group · Moonshine · Galaxy mergers · Embryogenesis · Bitcoin · Live
HUB · Book 9
Book 9 — Omega Point
The Convergence Series · 39 chapters · Trinity · Gallery of Mathematical Mystics · Live
PRELUDE
The Book Begins
Operator legend, how to read, interactive spiral chapter map
A1→A2
JOURNEY
Student Journey Map
3-pass spiral navigator · CEFR timeline · localStorage progress
HUB
Living Book Hub
All chapters collected · G = U ∘ F ∘ K ∘ C in full
NAV
Labyrinth
Extended navigation · alternate reading paths
COURSE
16-Week Course
Structured program A1 → D1 · week-by-week schedule
Core Sequence — Book 3 Chapters
The main arc: G = U ∘ F ∘ K ∘ C applied through 18 chapters
Ch 0
Introduction to The Mini-Beast
The operator chain introduced · how to read this book
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
B1
Ch 1c · C
The dm³ Framework
Operator overview · contact manifold structure introduced
B1
Ch 2 · C
Generative Matrix
Compression, SVD, critical periods, myelination · growing up as rank increase
A2→B1
Ch 2b · C→K
Biological Instantiations
Compression in morphogen gradients · biological reading
B1
Ch 2c · C→K
Reading and Compression
Text as compressed signal · reading as decompression operator
B1
Ch 3 · T
Circadian Regulation
Contact 3-manifold, Reeb flow, helical attractors · Generative Contact Mechanics
B1
Ch 3b · K
Plasma Reconnection
Threshold in plasma physics · magnetic reconnection as K event
B1
Ch 3c · K
Sources and Evidence
How to cite, evaluate, and compress evidence · K in academic writing
B1
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 · volatility regime shift
B1→B2
Ch 4c · K
Milestone 1 Assessment
First checkpoint · C and K operators consolidated · writing portfolio review
B1
Ch 5 · F
Immune Memory
Clonal selection · affinity maturation · memory cells as the fold operator
B1→B2
Ch 5b · K→F
Oscillations and Coherence
When K and F interact · coherence as argument structure
B2
Ch 6 · U
Resonance
Cymatics, archaeoacoustics, Schumann resonance · universal scale structure
B2
Ch 6b · F
The Argument Structure
Academic argument as F operator · fold points in logic
B2
Ch 6c · F
Pedagogy as Mathematical Necessity
Teaching as operator application · the fold in education
B2
Ch 7 · G
Topological Orthogenesis
Non-abelian anyons, braid groups, 6-direction coherence · the weave of spacetime
B2
Ch 8 · ∞
Nested Infinities
Cantor, Mandelbrot, surreals, Gödel, renormalization · the theme of all science
B2+
Ch 9 · F→U
φ — The Subcritical Approach
Golden ratio, Fibonacci growth, criticality at the threshold
C1
Ch 10 · U
Lyapunov Stability
Stability exponents, attractors, convergence guarantees
D1
Ch 11 · K
Spectral Radius
The reach of unfolding · eigenvalues and the generator
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 · the meta-operator at work · T → 0
D2
Ch 14 · G
AXLE — The Sorry-Free Paper
Formal verification meets academic writing · Curry-Howard correspondence
D2
Ch 15 · C
H — Entropy and the Compression Circle
Shannon entropy revisits C · how much compression remains possible
D2
Ch 16 · U
Scale Invariance
Self-similarity across all scales · renormalization group · B ∝ M³⁄⁴
D2
Ch 17 · G
Epilogue — The Living Book
The full composition resolved · Gⁿ(x₀) → x* · the reader as operator
D2
Writing Arc — Private Chapters
These chapters require repository collaborator access (paid membership). They form the parallel writing arc of Book 3.
Ch 1 · C 🔒
The Seed
C(x) = αx · the seed reading · standalone
B1
Ch 2 · C→K 🔒
Allostatic Load
λ = Σwᵢsᵢ · allostasis as operator composition
B1
Ch 6 · F 🔒
Resonant Systems
Falsifiability as fold · resonance in argument structure
B2
Ch 7 · F→U 🔒
Crystalline Structure
Wigner crystal, moiré patterns · E = kT·ln(Ω)
B2→C1
Ch 8 · U 🔒
Axiomatic Foundations
Γ ⊢ φ · formal proof structure as U operator
C1
Bonus Chapters
Supplementary chapters: extended domains, Greek-letter deep dives, and operator variations
Bonus E
GTCT for Everyone
9 axioms · 12 operators · 4 theorems · full A1→D1 prompt library
BONUS
Bonus W
The Wigner Crystal
dm³ fold diagram · interactive crystal simulation
BONUS
Bonus π
The Recurrence Ladder
π, φ, μ, η, Δ, Σ, Ω · constants as operators on the number line
BONUS
Bonus π–Ω
Full Recurrence Ladder
Extended version · all seven Greek-letter operators
BONUS
Bonus Λ
Polylaminin
Λ operator · laminin protein structure as dm³ fold
BONUS
Bonus Ψ
Quantum Gravity · Mind · dm³
Ψ operator · quantum decoherence · entanglement threshold · OQG open programme
BONUS
Bonus ρ
Spectral Radius · Collatz · RH Surgery
ρ operator · Collatz c=3 threshold · seven proofs · V5 research programme
BONUS
Ch 8b · U
Meru
Sacred geometry as dm³ · Sri Yantra as contact manifold
BONUS
Bonus E (alt)
GTCT for Everyone — Early Version
Earlier edition of the GTCT bonus chapter
BONUS
Bônus E · PT
GTCT para Todos — Edição Brasileira
Versão em português · capítulo E completo
PT-BR
Interactive Simulations
Standalone simulation tools — referenced from chapters and usable independently
SIM
Spectral Radius
Syracuse return map · Collatz visualizer · operator reach
LIVE
SIM v2
Spectral Radius v2
Revised version · live at AXLE
LIVE
SIM
Wigner Crystal Fold Diagram
Interactive dm³ fold · moiré angle selector
LIVE
SIM
Lyapunov Simulator
Stability exponents · attractor basin visualizer
LIVE
Public Samples & Portals
Free access chapters and portal pages
Chapter T
Tubulin as Computronium
Complete free chapter · microtubule computation as dm³
FREE
Sample W
The Wigner Crystal — Sample
Free public sample · Wigner crystal as contact fold
FREE
PORTAL
IMPA Purchase Portal
PayPal · Gumroad · pricing · delivery · collaborator access
PORTAL
Student Portal
All prompts A1 → D2 · chapter access · progress tracking
SALES
Get the Trilogy
Principia Orthogona Vol. I · II · III · pricing and access
Edição Brasileira
Portuguese-language sessions and chapters
Livro 3
Livro 3 — Edição Brasil
Edição brasileira completa · G = U ∘ F ∘ K ∘ C em português
PT-BR
Sessão 1
Geometria de Contato
Variedade de contato M · forma de contato α · campo de Reeb
PT-BR
Sessão 2
Teorema da Bacia
Bacia atratora · ponto fixo · demonstração do teorema de Banach
PT-BR
Sessão 3
Esqueleto Lean 4
Verificação formal · estrutura de prova em Lean 4 · AXLE Target 5
PT-BR
Books 7 · 8 · 9 — Live Volumes
All three volumes live as of June 2026. Book 7 = Scientist Gallery · Book 8 = The Monster · Book 9 = Omega Point / The Convergence Series
Book 7
The Scientist Gallery
Ada · Curie · Dirac · Escher · Faraday · Hawking · Lattes · Ramanujan · Thoreau
LIVE
B7
César Lattes — Pion Discovery
Brazilian physics · pion discovery 1947 · dm³ instantiation
LIVE
Book 8
The Monster Group
196,883-dimensional representation · Moonshine conjecture · dm³ operator identity
LIVE
B8
Monstrous Moonshine
j-function · McKay's observation · G-chain as Dynkin diagram
LIVE
B8
Galaxy Mergers
Merger dynamics as G-chain event · gravitational contact geometry
LIVE
B8
Embryogenesis
Morphogenesis as dm³ fold · Whitney A₁ in cellular differentiation
LIVE
B8
Bitcoin as dm³
Proof-of-work as K operator · halving as n-bonacci threshold
LIVE
B8
Mycelium Network
Fungal network as multi-orbit system · cooperative minimum theorem
LIVE
B8 · Closing
The Threshold
Where the math ends and the inquiry begins · closing chapter of Book 8
LIVE
Book 9
Genesis — G Operator
Expansion semigroup {g_t} · G as Genesis · Omega Point Vol IX
LIVE
B9
Logos — L = [F,K]
Coherence operator · contact bracket · the Word as mathematical structure
LIVE
B9
Resonance — R Operator
Koinonia · frequency-selection projection · collective resonance
LIVE
B9
Union — U Operator
Unitive Way · τ₁₂ ≤ min(τ₁,τ₂) · tau = 2 as collective threshold
LIVE
B9
Trinity Triptych
Father · Son · Spirit as G-chain components · three-operator triptych
LIVE
B9 · Mystics
Rumi — Whirling as Contact Geometry
Sama as a = dz − r²dθ · the dervish as helical attractor
LIVE
B9 · Mystics
Teilhard de Chardin
Noosphere · Omega Point original · convergence theology meets dm³
LIVE
B9 · Mystics
Ramanujan — The Notebook
Mock theta functions · the goddess and the formula · intuition as operator
LIVE
B9
Belief — The Inner Pharmacy
Placebo as dm³ operator · belief threshold · nocebo and the fold
LIVE
B9
Transmission
Anunnaki · Arrival · Disclosure · dm³ as received knowledge
LIVE
Operator Chain — Greek Letter Chapters
n-bonacci recurrence ladder chapters — π through Ω. All five written as of June 2026; ρ built June 2026.
Bonus μ
μ — Lyapunov Exponent
μ_max = −2 · transverse decay rate · stability radius[Ch 10] ε₀ = 1/3
WRITTEN
Bonus η
η — Tribonacci Constant
η ≈ 1.839 · spectral radius of Collatz transfer matrix · η weighting η⁻ᵏ
WRITTEN
Bonus Δ
Δ — Tetranacci: First Supercritical Step
Δ ≈ 1.928 · depth 4 > c* = 3 · three decaying modes
WRITTEN
Bonus Σ
Σ — Pentanacci: Strong Supercritical
Σ ≈ 1.966 · four decaying modes · five-fold biology
WRITTEN
Bonus Ω
Ω — Hexabonacci → τ = 2
Ω ≈ 1.984 → 2 · fixed point of the recurrence ladder · Complete Completeness
WRITTEN
Chapter T — Tubulin (Three Variants)
Three editions of the Tubulin chapter — Greek-coded canonical, alternate, and Portuguese (tubulina)
Bonus T (canonical)
Tubulin as Computronium
Greek-coded canonical edition · microtubule computation as dm³ · τ = 2 threshold
WRITTEN
Ch T (alt)
Tubulin — Alternate Edition
Earlier edition of the tubulin chapter · same content, alternate nav
ALT
Ch T · PT
Tubulina — Edição Brasileira
Versão em português · tubulina como computrônio
PT-BR
Additional Core Chapters
Written chapters not yet in the main map — including stubs scaffolded this session
Ch 0 · Student Ed.
Student Edition — Book 3
How to read this book · operator guide · CEFR structure
A1→A2
Ch 1d · C
One Shape, Three Origins
The figure-eight / A₁ singularity in algebra, astronomy, and Lean proof
B1
Ch 6d · U
Resonant Systems
Resonance and falsifiability as fold · argument structure
B2
Ch 7b · F→U
Crystalline Structure
Wigner crystal, moiré patterns · E = kT·ln(Ω)
B2→C1
Ch 8c · U
Axiomatic Foundations
Γ ⊢ φ · formal proof structure as U operator · Lean 4
C1
Ch 5c · K
Neural Coherence
Scaffold (May 2026) — neural coherence as K threshold event
STUB
Ch 7c · G
The Bridge
Scaffold (May 2026) — transition bridge chapter between volumes
STUB
Ch 1 · C seed
The Seed
Scaffold (May 2026) — C(x) = αx · the seed reading
STUB
Ch 2 · C→K allostatic
Allostatic Load
Scaffold (May 2026) — λ = Σwᵢsᵢ · allostasis as operator composition
STUB
Ch 7 · G circuit
The Complete Circuit
Scaffold (May 2026) — G⁶⁴ closure · complete circuit in English
STUB
Ch 7 · G circuito
Circuito Completo
Esboço (maio 2026) — circuito completo G⁶⁴ em português
PT-BR
GTCT Track & D2 Line
Book 4 / GTCT material — advanced chapters including D2 academic track and student edition
GTCT · Student Ed.
GTCT Volume V — Student Edition
Bilingual EN/PT · 8 levels · Lean 4 snippets · Berimbau machine · SBM Bienal material
A1→D1
D2 · Academic
D2 — Academic Track
Full academic writing track · D2-level · operator chain in research context
D2
D2 · Parashurama
Parashurama — D2 Track
D2 supplementary chapter · advanced operator application
D2
Capítulo E · PT
GTCT para Todos — Capítulo E
Versão em português do capítulo E · edição brasileira
PT-BR
Session 1 · EN
Contact Geometry — English Session
English stub paired with sessao1-geometria-contato.html
STUB
Session 2 · EN
Theorem Basin — English Session
English stub paired with sessao2-teorema-bacia.html
STUB
Session 3 · EN
Lean Skeleton — English Session
English stub paired with sessao3-esqueleto-lean.html
STUB
AXLE Simulations & Interactive Portal
Simulation pages imported from the AXLE repo — live interactive physics and geometry tools
SIM · AXLE
AXLE Main Simulation
Primary dm³ simulation · imported from AXLE repo (May 2026)
LIVE
SIM · Storm
Storm Manifold Simulation
Contact manifold storm dynamics · AXLE import
LIVE
PORTAL · AXLE
AXLE Portal
AXLE-line portal page · imported from repo (May 2026)
SIM · Helical
Helical Attractor
Helical attractor visualization · early simulation stub
STUB
Sound Machines & Wellness Applied (Book 3 Ancillary)
Eight Web Audio API machines + wellness content — cymatics, mantras, temple acoustics, and resonance therapy
MACHINE · T
Berimbau Cymatics
Brazilian berimbau timbre in dm³ cymatic analysis · SBM Bienal exhibition
LIVE
MACHINE · T
Ħal Saflieni Resonance
110 Hz hypogeum resonance · Neolithic acoustic geometry
LIVE
MACHINE · T
Hypogeum Temple Resonance
Temple acoustic simulation · contact geometry of sacred resonance
LIVE
MACHINE · OM
Om Machine
Aum / Om frequency layering · Reeb period resonance
LIVE
MACHINE · T
Pranayama Machine
Breath cycle as dm³ operator · 4-7-8 ratios · T* = 2π
LIVE
MACHINE · T
Soham Machine
So-Ham breath mantra · G-chain in respiratory cycle
LIVE
MACHINE · F
Śrī Yantra Śakti Machine
Sacred geometry sound · nine interlocking triangles as fold operator
LIVE
MACHINE · T
Swarnakarshana Bhairava Machine
Tantric resonance machine · contact geometry of mantra
LIVE
MACHINE · G6
G6 Drone Machine
Drone tone generator · G6 LLC signature sound
LIVE
WELLNESS
Wellness Soundworks
Therapeutic sound portfolio · all machines collected
LIVE
WELLNESS
Newark Wellness
Community wellness application · dm³ in public health context
Additional Navigation & Index Pages
Secondary navigation hubs, index pages, and series-level maps
INDEX
Classroom Index
Classroom-facing chapter navigator · lesson plan structure
INDEX
dm³ Lab Index
Lab-track navigator · simulation and proof-oriented path
INDEX
Fractal Index
Fractal geometry chapters grouped · self-similar reading path
INDEX
Geometry Hub Index
Contact geometry chapters navigator
MAP
Series Layer Map
Five-volume series map · all layers of the Principia Orthogona
DEDICATION
Guru Puja
Dedication and acknowledgement page · transmission lineage
SPECIAL
Yuga 6
Temporal cycle essay · dm³ in cosmological time
PILOT
Mini-Beast Pilot
Early pilot version of Book 3 · historical reference
REF
229 Ballantine
Reference / supplementary material
Archive & Staging (Candidates for _archive/)
Files that may be retired, superseded, or consolidated — kept for reference; not in the main reading path
ARCHIVE · v1
Journey — v1 Backup
Superseded by journey.html · kept for diff reference
GATE
Access Required
Paywall gate page · shown when chapter requires membership
SOURCE
16-Week Course — Source
Source edition of course-16weeks.html · confirm if this should be retired
PATCH
IMPA Portal — Patch
Patch for impa-portal.html · confirm if merged
9
Volumes Live
150+
HTML Files
60+
Core Chapters
39
Book 9 Chapters
25
Book 8 Chapters
8+
Simulations
A2→D2
CEFR Range
40+
Zenodo Papers
G6 LLC  ·  g6llc@proton.me  ·  +1 (646) 342-3751