Principia Orthogona — The Spiral

G1

Vol I — GOMC · The Operator Framework

First turn · Foundation · Contact geometry established

Published

C The dm³ Framework — Operators, Manifolds, Contact Normal Form

K The Critical Curvature Threshold κ*

F The Generative Transition & Contact Normal Form

U The Separation Theorem · Law of Monsters

Zenodo DOI ↗ SSRN Preprint ↗

G2

Vol II — TOGT · Contact Realization

Second turn · Applications across domains · g₃₃ = 33

Published

CPlasma-Sheet Reconnection

KNeural Embedding & Coherence Bridge

FMarket Volatility Manifolds

UBiological Oscillatory Systems (HPA, Circadian, Immune)

Zenodo DOI ↗

G3

Vol III — The Mini-Beast · Pilot

Third turn · ESL + STEM pilot · 14-Week program · This site

Live

Part I — Biological Instantiations · C · Weeks 1–4 · A2–B1

COverturepre

CPrelude — How to Read This Bookpre

CCh 1 · The Cajueiro PrincipleW1–2

CCh 2 · Generative MatrixW2–3

TCh 3 · Circadian RegulationW3–4

KCh 4 · Neural OscillationsW4–5

KCh 5 · Immune AdaptationW6

Part II — Physical & Financial · K·T · Weeks 5–10 · B1–C1

UCh 6 · Resonance · CymaticsW6–7

FCh 7 · The Crystalline ReturnW7–8

TCh 4b · Market Volatility Manifolds→ PDF Ch 4 · not yet HTML

TCh 3c · The Circadian TraderD2

GCh 8 · The Axiomatic TurnW9–10

GCh H · Collatz as dm³ Corollarybonus

GCh. Ocio · The Fixed Pointbonus

Part III — Research Writing · F→U · Weeks 11–14 · C1–D2

FCh 9 · φ · The Subcritical ApproachW11

UCh 10 · Lyapunov · StabilityW13

UCh 11 · Spectral RadiusW14

GCh 12 · Fixed Point — ConclusionW15

GCh 13 · Revision as ContractionW16

GCh 14 · AXLE · Formal VerificationW16

UCh 15 · Entropy & ScaleW17

UCh 16 · Scale InvarianceW17

GCh 17 · Epilogue — The Living BookW17

Extended · Ch E — GTCT for Everyone · Bridge to G4

ECh E · The Generative Time CircuitD2+

G3 Home ↗ Student Portal IMPA Portal

G4

Vol IV — GTCT · Dimensional Theory

Fourth turn · 7 chapters · 6 appendices · 12-phase cycle · g₃₃ = 33

Live

0Preface — Lemniscata & Analemma

1Ch 1 · The Seven Axioms

2Ch 2 · The Dimensional Field

3Ch 3 · Dimensional Operators

4

4Ch 4 · The Correspondence Theorem

5Ch 5 · The Orthogonality Theorem [v2]

6Ch 6 · The Recursion Theorem [v2]

7Ch 7 · Emergence as Fixed Point [v2]

TCh 8 · The Nature of Time

AAppendices A–F

G4 Full Hub ↗ G4 Table of Contents

G5

Vol V — The Seed · Complete Completeness · A Semente

Fifth turn · G⁵ · The fixed point the series was always approaching · 528 pp

Final

preStudent Edition — How to Read This Book

1AXLE: Mathematics as Language

∞The G-Series Map: Five Turns of the Spiral

…Full Vol V content — see GTCT_Vol5_v8_FinalSubmission.pdf

Zenodo DOI ↗ ISBN 979-8-9954416-5-6 · G6 LLC · 2026

G1 → G2 → G3 → G4 → G5