# Full Text: The Template Textbook > Extracted from `Friedman_2026_Template_c6c97f24.pdf` --- ## Page 1 The Template Textbook A Modular, Fillable Scaffold for Book-Length Technical Works Daniel Ari Friedman Active Inference Institute daniel@activeinference.institute ORCID: 0000-0001-6232-9096 Edition 0.1 – 2026 DOI: 10.5281/zenodo.20533125 ## Page 2 Publishing Information The Template Textbook A Modular, Fillable Scaffold for Book-Length Technical Works Daniel Ari Friedman Active Inference Institute daniel@activeinference.institute ORCID: 0000-0001-6232-9096 Edition 0.1 – 2026 Text license: CC BY 4.0 Source-code license: Apache-2.0 DOI: 10.5281/zenodo.20533125 Source repository: https://github.com/docxology/template_textbook “Form follows function—that has been misunderstood. Form and function should be one, joined in a spiritual union.” — Frank Lloyd Wright Acknowledgements This template textbook is a structural scaffold. Replace this acknowledgement with your own once the chapters are filled. Suggested citation: Daniel Ari Friedman (2026). The Template Textbook: A Modular, Fil- lable Scaffold for Book-Length Technical Works (Edition 0.1). Active Inference Institute. https://github.com/docxology/template_textbook. https://doi.org/10.5281/zenodo.20533125. This open textbook is generated from version-controlled Markdown, tested Python modules, programmatic figures, and rendered Mermaid diagrams. Corrections and improvements may be submitted via the source repository linked above. Accessibility note: the compact PDF is optimized for dense print. Reader-profile builds, HTML output, and source Markdown can be generated from the same manuscript materials. ## Page 3 CONTENTS 2 Contents 1 Front Matter 10 1.1 Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2 About This Template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 How to Read This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Methodology: How This Book Is Generated . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Preface 12 2.1 Why This Book Exists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Who This Book Is For . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 How to Use the Labs and Question Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 A Note on Reproducibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Part 0: Orientation and Methods 13 4 Orientation to the Field 14 4.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.3 A Worked Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.4 Going Deeper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5 Core Methods and Tools 16 5.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.2 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.3 A Worked Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.4 Going Deeper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6 Quantitative Foundations 19 6.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 6.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 6.2 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.3 A Worked Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.4 Going Deeper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 ## Page 4 CONTENTS 3 7 Part I: Fundamentals 21 8 First Principles 22 8.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 8.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 8.2 From a system to a model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 8.3 A first quantitative law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 8.4 Worked example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 8.5 How the pieces connect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 8.7 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 8.8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 8.9 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 9 Building Blocks 26 9.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 9.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 9.2 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 9.3 A Worked Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 9.4 Going Deeper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 9.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 9.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 9.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 10 Structure and Form 28 10.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 10.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 10.2 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 10.3 A Worked Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 10.4 Going Deeper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 10.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 10.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 10.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 10.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 11 Part II: Core Systems 31 12 Systems Overview 32 12.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 12.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 12.2 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 12.3 A Worked Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 12.4 Going Deeper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 12.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 12.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 12.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 12.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 ## Page 5 CONTENTS 4 13 Dynamics and Change 34 13.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 13.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 13.2 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 13.3 A Worked Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 13.4 Going Deeper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 13.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 13.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 13.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 13.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 14 Regulation and Control 37 14.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 14.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 14.2 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 14.3 A Worked Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 14.4 Going Deeper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 14.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 14.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 14.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 14.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 15 Part III: Applications and Synthesis 39 16 Applied Models 40 16.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 16.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 16.2 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 16.3 A Worked Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 16.4 Going Deeper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 16.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 16.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 16.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 16.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 17 Case Studies 42 17.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 17.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 17.2 The data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 17.3 Fitting a trend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 17.4 Interpolation versus extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 17.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 17.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 17.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 17.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 18 Frontiers and Open Problems 46 18.1 Learning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 ## Page 6 CONTENTS 5 18.1.1 Study Blueprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 18.2 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 18.3 A Worked Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 18.4 Going Deeper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 18.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 18.6 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 18.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 18.8 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 19 Lab — Orientation to the Field 48 19.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 19.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 19.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 19.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 19.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 19.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 20 Lab — Core Methods and Tools 50 20.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 20.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 20.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 20.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 20.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 20.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 21 Lab — Quantitative Foundations 51 21.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 21.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 21.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 21.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 21.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 21.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 22 Lab — First Principles 52 22.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 22.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 22.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 22.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 22.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 22.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 23 Lab — Building Blocks 53 23.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 23.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 23.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 23.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 23.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 23.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 ## Page 7 CONTENTS 6 24 Lab — Structure and Form 54 24.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 24.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 24.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 24.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 24.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 24.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 25 Lab — Systems Overview 55 25.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 25.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 25.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 25.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 25.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 25.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 26 Lab — Dynamics and Change 56 26.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 26.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 26.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 26.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 26.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 26.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 27 Lab — Regulation and Control 57 27.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 27.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 27.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 27.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 27.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 27.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 28 Lab — Applied Models 58 28.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 28.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 28.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 28.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 28.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 28.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 29 Lab — Case Studies 59 29.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 29.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 29.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 29.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 29.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 29.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 30 Lab — Frontiers and Open Problems 61 ## Page 8 CONTENTS 7 30.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 30.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 30.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 30.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 30.5 Computational Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 30.6 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 31 Question Bank — Orientation to the Field 62 31.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 31.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 31.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 32 Question Bank — Core Methods and Tools 63 32.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 32.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 32.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 33 Question Bank — Quantitative Foundations 64 33.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 33.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 33.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 34 Question Bank — First Principles 65 34.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 34.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 34.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 35 Question Bank — Building Blocks 66 35.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 35.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 35.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 36 Question Bank — Structure and Form 67 36.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 36.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 36.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 37 Question Bank — Systems Overview 68 37.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 37.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 37.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 38 Question Bank — Dynamics and Change 69 38.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 38.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 38.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 39 Question Bank — Regulation and Control 70 39.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 ## Page 9 CONTENTS 8 39.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 39.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 40 Question Bank — Applied Models 71 40.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 40.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 40.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 41 Question Bank — Case Studies 72 41.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 41.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 41.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 42 Question Bank — Frontiers and Open Problems 73 42.1 Recall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 42.2 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 42.3 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 43 Appendix A — Authoring Guide: Filling the Stubs 74 43.1 The Big Idea: One Source of Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 43.2 Step 1 — Decide the Structure in config.yaml . . . . . . . . . . . . . . . . . . . . . . . . . . 74 43.3 Step 2 — Materialise the Stubs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 43.4 Step 3 — Fill the Content Contract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 43.5 Step 4 — Add a Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 43.6 Step 5 — Add a Glossary Term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 43.7 Step 6 — Add a Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 43.8 Step 7 — Audit and Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 43.9 Growing the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 44 Appendix B — Notation and Symbols 77 44.1 Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 44.2 Symbol Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 45 Appendix C — Mathematical Review 78 45.1 Functions and Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 45.2 Growth and Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 45.3 Saturating Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 45.4 Linear Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 45.5 Basic Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 46 Appendix — Formalisms 79 46.1 1. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 46.2 2. A theorem with proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 46.3 3. A lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 46.4 4. Algorithms (pseudocode) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 46.5 5. A step-by-step derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 46.6 6. A system of numbered equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 46.7 7. Dimensioned quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 46.8 8. Notation summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 ## Page 10 CONTENTS 9 47 Appendix — Format Gallery 82 47.1 1. Text and inline formatting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 47.2 2. Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 47.3 3. Block quotes and callouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 47.4 4. Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 47.5 5. Mathematics and units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 47.6 6. Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 47.7 7. Diagrams (Mermaid) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 47.8 8. Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 47.9 9. Cross-references and citations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 47.1010. Media and data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 47.1111. Pedagogical blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 47.1212. Miscellany . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 48 Master Glossary 93 48.0.1 Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.2 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.3 Emergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.5 Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.6 Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.7 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.8 Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.9 Observable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.10Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.11Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.12State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.13System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 48.0.14Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 48.0.15Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 49 Appendix E — Index of Key Terms 95 49.1 Placeholder Entries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 ## Page 11 1 FRONT MATTER 10 1 Front Matter 1.1 Dedication TKTK — dedicate this book to whom you choose. One or two lines is conventional. Delete this comment and the placeholder once written. 1.2 About This Template This is not a finished book. It is a scaffold — a complete, internally consistent skeleton for a book-length technical work, with every structural element in place and every author-specific passage left as a marked stub for you to fill. The whole book is data-driven from a single source of truth, config.yaml. That file declares the parts, the chapters inside each part, the front matter, the appendices, and the labs and question banks. The table of contents, chapter numbering, figure numbering, and the manuscript-integrity tests all read from it. You grow the book by editing config.yaml and then materialising any missing files — you never hand-number a chapter, figure, equation, or table. What is already provided for you: • Twelve chapters across four parts, each a valid chapter shell with a labelled heading, a figure, a metadata badge, a Study Blueprint, Learning Objectives, a worked formalism (equation + parameter table), an inline Mermaid diagram, and Summary / Key Terms / Further Reading / Practice sections. • A matching lab and question bank for every chapter, under labs/ and questions/. • A tested computational backbone in src/ — the worked equations are real, tested Python func- tions (textbook.models), and figures are generated deterministically. Chapter prose calls these func- tions rather than retyping the mathematics. • A test gate (tests/test_manuscript_integrity.py plus scripts/audit_textbook_quality.py) that checks the structural contract holds as you write. Everywhere author-specific content belongs, you will find a stub marker: , TODO:, or TKTK. The quality audit counts these, so your progress toward a finished book is measurable. See Appendix A — Authoring Guide and AGENTS.md for the full filling workflow. 1.3 How to Read This Book The book is organised into four parts that build on one another. A first-time reader should move through them in order; an instructor can assign parts independently. • Part 0 — Orientation and Methods. Where the field sits, the core methods and tools, and the quantitative foundations the rest of the book assumes. Start here even if you are experienced; it fixes notation and conventions. • Part I — Fundamentals. First principles, the building blocks, and how structure and form arise. The conceptual bedrock. • Part II — Core Systems. A systems overview, dynamics and change, and regulation and control. The working theory. ## Page 12 1 FRONT MATTER 11 • Part III — Applications and Synthesis. Applied models, case studies, and frontiers with open problems. Where the ideas meet practice and the edge of what is known. Each chapter ends with a Practice section pointing to its lab (a guided, hands-on exercise) and its question bank (self-check questions). Work the lab after reading; use the question bank to confirm you can recall and apply the material. New terms are linked to the Master Glossary the first time they appear. 1.4 Methodology: How This Book Is Generated This manuscript is rendered, not typeset by hand. The pipeline reads config.yaml, runs the analysis scripts that produce figures and diagrams, assembles the Markdown sections in declared order, and renders a PDF through Pandoc with pandoc-crossref resolving every cross-reference and citation. To build the book from the repository root: uv run python scripts/02_run_analysis.py --project templates/template_textbook uv run python scripts/03_render_pdf.py --project templates/template_textbook or run the full pipeline with ./run.sh. See README.md for the manuscript directory layout and SYNTAX.md for the exact authoring syntax. ## Page 13 2 PREFACE 12 2 Preface 2.1 Why This Book Exists TKTK — state, in two or three paragraphs, the problem this book solves and why it is worth a reader’s time. What gap in the existing literature does it fill? What will a reader be able to do after finishing it that they could not do before? This template is domain-neutral by design. Wherever the sample chapters speak of “systems”, “dynamics”, or “regulation”, substitute the concepts of your own field. The structure — orientation, fundamentals, core systems, applications — generalises across most technical subjects; the content is yours to supply. 2.2 Who This Book Is For TKTK — describe the intended reader. Assumed background? A prerequisite course or a specific level of mathematical maturity? Whether the book suits self-study, a one-semester course, or a reference shelf. The book assumes the quantitative foundations laid out in Part 0 and nothing more. A reader comfortable with that material can follow every chapter. 2.3 How to Use the Labs and Question Banks Each chapter is paired with two companion documents: • A lab (under labs/) — a guided, hands-on exercise that puts the chapter’s worked formalism to work. Labs are meant to be done, not just read: run the tested functions in textbook.models, vary the parameters, and observe how the predictions change. Work the lab immediately after reading the chapter, while the ideas are fresh. • A question bank (under questions/) — self-check questions that confirm you can recall and apply the chapter’s load-bearing claims. Use it as a diagnostic: a question you cannot answer points you back to a specific section. Instructors can assign the lab as homework and draw exam or quiz items from the question bank. Because both are generated from the same config.yaml as the chapters, they stay in lockstep with the manuscript as it grows. 2.4 A Note on Reproducibility Every equation in this book is implemented as a tested function and every figure is generated deterministically from code. Nothing in the prose is computed by hand. If you build the book yourself you will get byte- identical figures and numbers — see README.md for the build commands. — The Author, TKTK (place), TKTK (date) ## Page 14 3 PART 0: ORIENTATION AND METHODS 13 3 Part 0: Orientation and Methods This part covers orientation and methods. It contains the following chapters: • Orientation to the Field — sec. 4 • Core Methods and Tools — sec. 5 • Quantitative Foundations — sec. 6 How to use this part. ## Page 15 4 ORIENTATION TO THE FIELD 14 4 Orientation to the Field Figure 1. Overview schematic for “Orientation to the Field”. Replace this generated placeholder with a real figure produced by src/visualization/plots.py. Level 1/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: none 4.1 Learning Objectives By the end of this chapter you should be able to: 1. TODO: state the first measurable learning objective. 2. TODO: state the second learning objective. 3. TODO: state the third learning objective. 4.1.1 Study Blueprint • Big idea: • Core concepts: regulation, boundary, state. • Quantitative lens: the worked formalism in eq. 1. • Data skill: • Common misconception to repair: • Primary lab: sec. 19. • Question bank: sec. 31. • Bridge to computation: textbook.models. Opening Vignette: TKTK — a motivating story ## Page 16 4 ORIENTATION TO THE FIELD 15 4.2 Orientation This section introduces the central ideas of Orientation to the Field. Foundational treatments include [Kim, 2020, Brown, 2017]. Key terms such as regulation, boundary, state are defined in the glossary. 4.3 A Worked Formalism The recurring quantitative model for this chapter is shown in eq. 1: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (1) It is implemented and tested in textbook.models.logistic_growth; never retype the maths in prose or scripts — call the tested function. The parameters appear in tbl. 1. Table 1. Parameters of the worked model for this chapter. Symbol Meaning Units 𝑟 intrinsic rate 1/time 𝐾 carrying capacity quantity 𝑁0 initial value quantity A concept map of how the pieces fit together: Note 4.4 Going Deeper See the overview in fig. 1 and revisit the objectives above as you read. Further evidence: [Kim, 2020, Brown, 2017]. 4.5 Summary 4.6 Key Terms feedback, gradient, threshold, network. 4.7 Further Reading • TODO: one-line annotation [Wilson, 2021]. 4.8 Practice • Lab: sec. 19 • Question bank: sec. 31 ## Page 17 5 CORE METHODS AND TOOLS 16 Figure 2. Mermaid diagram 5 Core Methods and Tools Level 1/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: none 5.1 Learning Objectives By the end of this chapter you should be able to: 1. TODO: state the first measurable learning objective. 2. TODO: state the second learning objective. 3. TODO: state the third learning objective. 5.1.1 Study Blueprint • Big idea: • Core concepts: model, parameter, variable. • Quantitative lens: the worked formalism in eq. 2. • Data skill: • Common misconception to repair: • Primary lab: sec. 20. • Question bank: sec. 32. • Bridge to computation: textbook.models. ## Page 18 5 CORE METHODS AND TOOLS 17 Figure 3. Overview schematic for “Core Methods and Tools”. Replace this generated placeholder with a real figure produced by src/visualization/plots.py. Opening Vignette: TKTK — a motivating story 5.2 Orientation This section introduces the central ideas of Core Methods and Tools. Foundational treatments include [Kim, 2020, Brown, 2017]. Key terms such as model, parameter, variable are defined in the glossary. 5.3 A Worked Formalism The recurring quantitative model for this chapter is shown in eq. 2: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (2) It is implemented and tested in textbook.models.logistic_growth; never retype the maths in prose or scripts — call the tested function. The parameters appear in tbl. 2. Table 2. Parameters of the worked model for this chapter. Symbol Meaning Units 𝑟 intrinsic rate 1/time 𝐾 carrying capacity quantity 𝑁0 initial value quantity ## Page 19 5 CORE METHODS AND TOOLS 18 A concept map of how the pieces fit together: Figure 4. Mermaid diagram Note 5.4 Going Deeper See the overview in fig. 3 and revisit the objectives above as you read. Further evidence: [Kim, 2020, Brown, 2017]. 5.5 Summary 5.6 Key Terms emergence, regulation, boundary, state. 5.7 Further Reading • TODO: one-line annotation [Wilson, 2021]. 5.8 Practice • Lab: sec. 20 • Question bank: sec. 32 ## Page 20 6 QUANTITATIVE FOUNDATIONS 19 6 Quantitative Foundations Figure 5. Overview schematic for “Quantitative Foundations”. Replace this generated placeholder with a real figure produced by src/visualization/plots.py. Level 1/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: none 6.1 Learning Objectives By the end of this chapter you should be able to: 1. TODO: state the first measurable learning objective. 2. TODO: state the second learning objective. 3. TODO: state the third learning objective. 6.1.1 Study Blueprint • Big idea: • Core concepts: feedback, gradient, threshold. • Quantitative lens: the worked formalism in eq. 3. • Data skill: • Common misconception to repair: • Primary lab: sec. 21. • Question bank: sec. 33. • Bridge to computation: textbook.models. Opening Vignette: TKTK — a motivating story ## Page 21 6 QUANTITATIVE FOUNDATIONS 20 6.2 Orientation This section introduces the central ideas of Quantitative Foundations. Foundational treatments include [Smith, 2020, Doe, 2019]. Key terms such as feedback, gradient, threshold are defined in the glossary. 6.3 A Worked Formalism The recurring quantitative model for this chapter is shown in eq. 3: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (3) It is implemented and tested in textbook.models.logistic_growth; never retype the maths in prose or scripts — call the tested function. The parameters appear in tbl. 3. Table 3. Parameters of the worked model for this chapter. Symbol Meaning Units 𝑟 intrinsic rate 1/time 𝐾 carrying capacity quantity 𝑁0 initial value quantity A concept map of how the pieces fit together: Note 6.4 Going Deeper See the overview in fig. 5 and revisit the objectives above as you read. Further evidence: [Smith, 2020, Doe, 2019]. 6.5 Summary 6.6 Key Terms observable, system, model, parameter. 6.7 Further Reading • TODO: one-line annotation [Lee, 2021]. 6.8 Practice • Lab: sec. 21 • Question bank: sec. 33 ## Page 22 7 PART I: FUNDAMENTALS 21 Figure 6. Mermaid diagram 7 Part I: Fundamentals This part covers fundamentals. It contains the following chapters: • First Principles — sec. 8 • Building Blocks — sec. 9 • Structure and Form — sec. 10 How to use this part. ## Page 23 8 FIRST PRINCIPLES 22 8 First Principles Figure 7. A logistic growth curve for three growth rates, approaching the carrying capacity 𝐾= 100. Produced deterministically by visualization.plots.plot_logistic_growth. Level 1/3 ⋅25 min read ⋅40 min lecture ⋅Prerequisites: none This chapter is a worked reference. It is filled to completion to show what a finished chapter looks like. The other chapters in this template ship as structurally-complete stubs (marked with stub comments and TODO notes); fill them the same way. 8.1 Learning Objectives By the end of this chapter you should be able to: 1. Explain what it means to model a system as a small set of state variables and a rule for how they change. 2. Distinguish a parameter from a variable, and identify each in a worked model. 3. Derive and interpret the logistic growth law and predict its long-run behaviour toward an equilibrium. 4. Compute model values with the tested function textbook.models.logistic_growth rather than re-deriving arithmetic by hand. 8.1.1 Study Blueprint • Big idea: A great deal of change in the world is captured by a handful of variables and a single rule relating their rates — the first principle of quantitative modelling. • Core concepts: system, state, parameter, equilibrium. • Quantitative lens: the logistic law in eq. 5. • Data skill: read an S-curve and estimate its carrying capacity by eye, then confirm numerically. ## Page 24 8 FIRST PRINCIPLES 23 • Common misconception to repair: “exponential” and “logistic” are not the same — unbounded growth is an early-time approximation, not the rule. • Primary lab: sec. 22. • Question bank: sec. 34. • Bridge to computation: textbook.models.logistic_growth. Opening Vignette: Counting before you explain. A population biologist watches a colony double, then double again, then — unexpectedly — slow. A start-up tracks users that grow the same way before the market saturates. A chemist measures a reaction that races, then crawls as substrate runs low. Three unrelated fields, one shape. The job of a first model is not to capture everything; it is to capture that shape with as few moving parts as possible. 8.2 From a system to a model A model is a deliberate simplification. We choose a small number of state variables — here, a single quantity 𝑁(𝑡) — and write a rule for how the state changes. The art is leaving things out: a first model that fits on one line teaches more than a faithful one that fills a page. The variables are what change; the parameters are what we hold fixed while we reason. In the growth model below, 𝑁is the variable, while the rate 𝑟and the carrying capacity 𝐾are parameters. Confusing the two is the most common beginner error: if you find yourself “solving for 𝐾over time,” you have mislabelled a parameter as a variable. 8.3 A first quantitative law Unbounded (exponential) growth assumes nothing ever pushes back. Real systems saturate. The simplest law that grows fast when small and levels off when large is the logistic equation, written as a rate of change in eq. 4 and in closed form in eq. 5: 𝑑𝑁 𝑑𝑡= 𝑟𝑁(1 −𝑁 𝐾) (4) 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (5) Read eq. 4 aloud: the rate of change is proportional to how much there is (𝑟𝑁) times how much room remains (1 −𝑁/𝐾). When 𝑁is small the second factor is near 1 and growth is nearly exponential; as 𝑁 approaches 𝐾the factor approaches 0 and growth stalls. The parameters are collected in tbl. 4. Table 4. Parameters of the logistic model. Variables change over time; parameters are held fixed while reasoning. Symbol Name Role Example value 𝑁(𝑡) quantity variable computed 𝑟 intrinsic rate parameter 0.8 s−1 ## Page 25 8 FIRST PRINCIPLES 24 Symbol Name Role Example value 𝐾 carrying capacity parameter 100 units 𝑁0 initial value parameter 5 units 8.4 Worked example Take 𝑟= 0.8, 𝐾= 100, and 𝑁0 = 5. Rather than evaluate the exponential by hand, call the tested backbone: import numpy as np from textbook import models t = np.array([0.0, 2.0, 5.0, 10.0]) N = models.logistic_growth(t, r=0.8, carrying_capacity=100.0, initial=5.0) # N -> [ 5.00, 20.68, 74.18, 99.37 ] The trajectory starts at 𝑁(0) = 5.00, reaches 𝑁(2) = 20.68, passes the steep middle near 𝑡= 5 with 𝑁(5) = 74.18, and by 𝑡= 10 has all but arrived at 𝑁(10) = 99.37 — within one part in a hundred of the carrying capacity. This is the S-curve plotted in fig. 7: an early near-exponential rise, an inflection, and a long approach to the asymptote. The long-run behaviour is exact, not approximate. Because 𝑟> 0, the term 𝑒−𝑟𝑡→0, so 𝑁(𝑡) →𝐾. The proof is one line and is recorded as Theorem 1 in sec. 46; the same fact is asserted numerically by the test suite, so the prose and the code cannot silently disagree. 8.5 How the pieces connect This loop — choose, write, solve, predict, compare — is the first principle the rest of the book elaborates. Foundational treatments of model-building include [Brown, 2017] and [Patel, 2018]. 8.6 Summary A model trades completeness for clarity: a few state variables and one rule. The logistic law adds a single idea — finite room — to exponential growth, and that idea changes the long-run behaviour from unbounded increase to a stable equilibrium at the carrying capacity 𝐾. Compute with the tested logistic_growth function so your worked numbers are reproducible and correct by construction. 8.7 Key Terms system, model, state, parameter, equilibrium. 8.8 Further Reading • Brown [2017] — a readable introduction to reasoning from first principles; start with its opening chapter on what a model is for. • Patel [2018] — a broader survey of model families; use it to see where the logistic law sits among alternatives. 8.9 Practice • Lab: sec. 22 — measure an S-curve and estimate its parameters. ## Page 26 8 FIRST PRINCIPLES 25 Figure 8. Mermaid diagram • Question bank: sec. 34 — recall through synthesis. ## Page 27 9 BUILDING BLOCKS 26 9 Building Blocks Figure 9. Overview schematic for “Building Blocks”. Replace this generated placeholder with a real figure produced by src/visualization/plots.py. Level 1/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: none 9.1 Learning Objectives By the end of this chapter you should be able to: 1. TODO: state the first measurable learning objective. 2. TODO: state the second learning objective. 3. TODO: state the third learning objective. 9.1.1 Study Blueprint • Big idea: • Core concepts: equilibrium, feedback, gradient. • Quantitative lens: the worked formalism in eq. 6. • Data skill: • Common misconception to repair: • Primary lab: sec. 23. • Question bank: sec. 35. • Bridge to computation: textbook.models. Opening Vignette: TKTK — a motivating story ## Page 28 9 BUILDING BLOCKS 27 9.2 Orientation This section introduces the central ideas of Building Blocks. Foundational treatments include [Taylor, 2019, Smith, 2020]. Key terms such as equilibrium, feedback, gradient are defined in the glossary. 9.3 A Worked Formalism The recurring quantitative model for this chapter is shown in eq. 6: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (6) It is implemented and tested in textbook.models.logistic_growth; never retype the maths in prose or scripts — call the tested function. The parameters appear in tbl. 5. Table 5. Parameters of the worked model for this chapter. Symbol Meaning Units 𝑟 intrinsic rate 1/time 𝐾 carrying capacity quantity 𝑁0 initial value quantity A concept map of how the pieces fit together: Note 9.4 Going Deeper See the overview in fig. 9 and revisit the objectives above as you read. Further evidence: [Taylor, 2019, Smith, 2020]. 9.5 Summary 9.6 Key Terms state, observable, system, model. 9.7 Further Reading • TODO: one-line annotation [Doe, 2019]. 9.8 Practice • Lab: sec. 23 • Question bank: sec. 35 ## Page 29 10 STRUCTURE AND FORM 28 Figure 10. Mermaid diagram 10 Structure and Form Level 1/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: none 10.1 Learning Objectives By the end of this chapter you should be able to: 1. TODO: state the first measurable learning objective. 2. TODO: state the second learning objective. 3. TODO: state the third learning objective. 10.1.1 Study Blueprint • Big idea: • Core concepts: threshold, network, dynamics. • Quantitative lens: the worked formalism in eq. 7. • Data skill: • Common misconception to repair: • Primary lab: sec. 24. • Question bank: sec. 36. • Bridge to computation: textbook.models. ## Page 30 10 STRUCTURE AND FORM 29 Figure 11. Overview schematic for “Structure and Form”. Replace this generated placeholder with a real figure produced by src/visualization/plots.py. Opening Vignette: TKTK — a motivating story 10.2 Orientation This section introduces the central ideas of Structure and Form. Foundational treatments include [Lee, 2021, Garcia, 2022]. Key terms such as threshold, network, dynamics are defined in the glossary. 10.3 A Worked Formalism The recurring quantitative model for this chapter is shown in eq. 7: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (7) It is implemented and tested in textbook.models.logistic_growth; never retype the maths in prose or scripts — call the tested function. The parameters appear in tbl. 6. Table 6. Parameters of the worked model for this chapter. Symbol Meaning Units 𝑟 intrinsic rate 1/time 𝐾 carrying capacity quantity 𝑁0 initial value quantity ## Page 31 10 STRUCTURE AND FORM 30 A concept map of how the pieces fit together: Figure 12. Mermaid diagram Note 10.4 Going Deeper See the overview in fig. 11 and revisit the objectives above as you read. Further evidence: [Lee, 2021, Garcia, 2022]. 10.5 Summary 10.6 Key Terms model, parameter, variable, equilibrium. 10.7 Further Reading • TODO: one-line annotation [Patel, 2018]. 10.8 Practice • Lab: sec. 24 • Question bank: sec. 36 ## Page 32 11 PART II: CORE SYSTEMS 31 11 Part II: Core Systems This part covers core systems. It contains the following chapters: • Systems Overview — sec. 12 • Dynamics and Change — sec. 13 • Regulation and Control — sec. 14 How to use this part. ## Page 33 12 SYSTEMS OVERVIEW 32 12 Systems Overview Figure 13. Overview schematic for “Systems Overview”. Replace this generated placeholder with a real figure produced by src/visualization/plots.py. Level 1/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: none 12.1 Learning Objectives By the end of this chapter you should be able to: 1. TODO: state the first measurable learning objective. 2. TODO: state the second learning objective. 3. TODO: state the third learning objective. 12.1.1 Study Blueprint • Big idea: • Core concepts: equilibrium, feedback, gradient. • Quantitative lens: the worked formalism in eq. 8. • Data skill: • Common misconception to repair: • Primary lab: sec. 25. • Question bank: sec. 37. • Bridge to computation: textbook.models. Opening Vignette: TKTK — a motivating story ## Page 34 12 SYSTEMS OVERVIEW 33 12.2 Orientation This section introduces the central ideas of Systems Overview. Foundational treatments include [Patel, 2018, Nguyen, 2023]. Key terms such as equilibrium, feedback, gradient are defined in the glossary. 12.3 A Worked Formalism The recurring quantitative model for this chapter is shown in eq. 8: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (8) It is implemented and tested in textbook.models.logistic_growth; never retype the maths in prose or scripts — call the tested function. The parameters appear in tbl. 7. Table 7. Parameters of the worked model for this chapter. Symbol Meaning Units 𝑟 intrinsic rate 1/time 𝐾 carrying capacity quantity 𝑁0 initial value quantity A concept map of how the pieces fit together: Note 12.4 Going Deeper See the overview in fig. 13 and revisit the objectives above as you read. Further evidence: [Patel, 2018, Nguyen, 2023]. 12.5 Summary 12.6 Key Terms state, observable, system, model. 12.7 Further Reading • TODO: one-line annotation [Kim, 2020]. 12.8 Practice • Lab: sec. 25 • Question bank: sec. 37 ## Page 35 13 DYNAMICS AND CHANGE 34 Figure 14. Mermaid diagram 13 Dynamics and Change Level 1/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: none 13.1 Learning Objectives By the end of this chapter you should be able to: 1. TODO: state the first measurable learning objective. 2. TODO: state the second learning objective. 3. TODO: state the third learning objective. 13.1.1 Study Blueprint • Big idea: • Core concepts: parameter, variable, equilibrium. • Quantitative lens: the worked formalism in eq. 9. • Data skill: • Common misconception to repair: • Primary lab: sec. 26. • Question bank: sec. 38. • Bridge to computation: textbook.models. ## Page 36 13 DYNAMICS AND CHANGE 35 Figure 15. Overview schematic for “Dynamics and Change”. Replace this generated placeholder with a real figure produced by src/visualization/plots.py. Opening Vignette: TKTK — a motivating story 13.2 Orientation This section introduces the central ideas of Dynamics and Change. Foundational treatments include [Brown, 2017, Wilson, 2021]. Key terms such as parameter, variable, equilibrium are defined in the glossary. 13.3 A Worked Formalism The recurring quantitative model for this chapter is shown in eq. 9: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (9) It is implemented and tested in textbook.models.logistic_growth; never retype the maths in prose or scripts — call the tested function. The parameters appear in tbl. 8. Table 8. Parameters of the worked model for this chapter. Symbol Meaning Units 𝑟 intrinsic rate 1/time 𝐾 carrying capacity quantity 𝑁0 initial value quantity ## Page 37 13 DYNAMICS AND CHANGE 36 A concept map of how the pieces fit together: Figure 16. Mermaid diagram Note 13.4 Going Deeper See the overview in fig. 15 and revisit the objectives above as you read. Further evidence: [Brown, 2017, Wilson, 2021]. 13.5 Summary 13.6 Key Terms regulation, boundary, state, observable. 13.7 Further Reading • TODO: one-line annotation [Taylor, 2019]. 13.8 Practice • Lab: sec. 26 • Question bank: sec. 38 ## Page 38 14 REGULATION AND CONTROL 37 14 Regulation and Control Figure 17. Overview schematic for “Regulation and Control”. Replace this generated placeholder with a real figure produced by src/visualization/plots.py. Level 1/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: none 14.1 Learning Objectives By the end of this chapter you should be able to: 1. TODO: state the first measurable learning objective. 2. TODO: state the second learning objective. 3. TODO: state the third learning objective. 14.1.1 Study Blueprint • Big idea: • Core concepts: network, dynamics, emergence. • Quantitative lens: the worked formalism in eq. 10. • Data skill: • Common misconception to repair: • Primary lab: sec. 27. • Question bank: sec. 39. • Bridge to computation: textbook.models. Opening Vignette: TKTK — a motivating story ## Page 39 14 REGULATION AND CONTROL 38 14.2 Orientation This section introduces the central ideas of Regulation and Control. Foundational treatments include [Wilson, 2021, Taylor, 2019]. Key terms such as network, dynamics, emergence are defined in the glossary. 14.3 A Worked Formalism The recurring quantitative model for this chapter is shown in eq. 10: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (10) It is implemented and tested in textbook.models.logistic_growth; never retype the maths in prose or scripts — call the tested function. The parameters appear in tbl. 9. Table 9. Parameters of the worked model for this chapter. Symbol Meaning Units 𝑟 intrinsic rate 1/time 𝐾 carrying capacity quantity 𝑁0 initial value quantity A concept map of how the pieces fit together: Note 14.4 Going Deeper See the overview in fig. 17 and revisit the objectives above as you read. Further evidence: [Wilson, 2021, Taylor, 2019]. 14.5 Summary 14.6 Key Terms parameter, variable, equilibrium, feedback. 14.7 Further Reading • TODO: one-line annotation [Smith, 2020]. 14.8 Practice • Lab: sec. 27 • Question bank: sec. 39 ## Page 40 15 PART III: APPLICATIONS AND SYNTHESIS 39 Figure 18. Mermaid diagram 15 Part III: Applications and Synthesis This part covers applications and synthesis. It contains the following chapters: • Applied Models — sec. 16 • Case Studies — sec. 17 • Frontiers and Open Problems — sec. 18 How to use this part. ## Page 41 16 APPLIED MODELS 40 16 Applied Models Figure 19. Overview schematic for “Applied Models”. Replace this generated placeholder with a real figure produced by src/visualization/plots.py. Level 1/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: none 16.1 Learning Objectives By the end of this chapter you should be able to: 1. TODO: state the first measurable learning objective. 2. TODO: state the second learning objective. 3. TODO: state the third learning objective. 16.1.1 Study Blueprint • Big idea: • Core concepts: equilibrium, feedback, gradient. • Quantitative lens: the worked formalism in eq. 11. • Data skill: • Common misconception to repair: • Primary lab: sec. 28. • Question bank: sec. 40. • Bridge to computation: textbook.models. Opening Vignette: TKTK — a motivating story ## Page 42 16 APPLIED MODELS 41 16.2 Orientation This section introduces the central ideas of Applied Models. Foundational treatments include [Patel, 2018, Nguyen, 2023]. Key terms such as equilibrium, feedback, gradient are defined in the glossary. 16.3 A Worked Formalism The recurring quantitative model for this chapter is shown in eq. 11: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (11) It is implemented and tested in textbook.models.logistic_growth; never retype the maths in prose or scripts — call the tested function. The parameters appear in tbl. 10. Table 10. Parameters of the worked model for this chapter. Symbol Meaning Units 𝑟 intrinsic rate 1/time 𝐾 carrying capacity quantity 𝑁0 initial value quantity A concept map of how the pieces fit together: Note 16.4 Going Deeper See the overview in fig. 19 and revisit the objectives above as you read. Further evidence: [Patel, 2018, Nguyen, 2023]. 16.5 Summary 16.6 Key Terms state, observable, system, model. 16.7 Further Reading • TODO: one-line annotation [Kim, 2020]. 16.8 Practice • Lab: sec. 28 • Question bank: sec. 40 ## Page 43 17 CASE STUDIES 42 Figure 20. Mermaid diagram 17 Case Studies Level 2/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: First Principles This chapter is a worked reference in a different style from sec. 8: where that chapter derives a model, this one applies one to a small dataset. The remaining chapters ship as stubs. 17.1 Learning Objectives By the end of this chapter you should be able to: 1. Frame a real question as a comparison between a system under control and treatment conditions. 2. Summarise grouped observable data with means and a measure of spread, and read an error-bar figure. 3. Fit a simple dose–response trend with textbook.models.linear_fit and state what its slope and 𝑅2 mean. 4. Distinguish a defensible interpolation from an unjustified extrapolation. 17.1.1 Study Blueprint • Big idea: A case study turns a general model into a decision about a specific dataset — and into an honest statement of its limits. • Core concepts: observable, gradient, threshold. • Quantitative lens: a linear dose–response fit, eq. 12. ## Page 44 17 CASE STUDIES 43 Figure 21. Group means with standard-error bars across six synthetic conditions, generated by visualization. gallery.errorbar_plot. In a real case study you would replace this gallery placeholder with your own measured group means. • Data skill: group, average, and fit; then sanity-check the fit against the raw numbers in tbl. 11. • Common misconception to repair: a high 𝑅2 on three points is not strong evidence — it is an invitation to collect more. • Primary lab: sec. 29. • Question bank: sec. 41. • Bridge to computation: textbook.models.linear_fit, descriptive_statistics. Opening Vignette: From a spreadsheet to a decision. A team runs a small pilot: a control condition and two treatment levels, two replicates each. The numbers land in a spreadsheet. The question is not “are they different?” — they obviously are — but “by how much, how confidently, and what should we predict next?” A case study is the discipline of answering those three questions without overreaching. 17.2 The data The pilot produced six measurements across three conditions, recorded in assets/data/sample_dataset. csv and reproduced in tbl. 11. Table 11. The pilot dataset: two replicates per condition. Condition Replicate Measurement Standard error control 1 2.10 0.20 control 2 2.30 0.18 ## Page 45 17 CASE STUDIES 44 Condition Replicate Measurement Standard error treatment (low) 1 3.60 0.25 treatment (low) 2 3.40 0.22 treatment (high) 1 4.80 0.35 treatment (high) 2 5.10 0.30 Grouping and averaging — the first move in almost every case study — gives means of 2.20 (control), 3.50 (low), and 4.95 (high). Across all six points the mean is 3.55 with a standard deviation of 1.13 (textbook. models.descriptive_statistics). The error-bar view is fig. 21. 17.3 Fitting a trend Encode the dose as 0, 1, 2 for control, low, and high, and fit a line with textbook.models.linear_fit: import numpy as np from textbook import models dose = np.array([0.0, 1.0, 2.0]) response = np.array([2.20, 3.50, 4.95]) # condition means fit = models.linear_fit(dose, response) # fit.slope ￿1.375, fit.intercept ￿2.175, fit.r_squared ￿0.999 The fitted relationship in eq. 12 is ̂𝑦(𝑑) = 1.375 𝑑+ 2.175 (12) with 𝑅2 = 0.999. The slope says each dose step adds about 1.4 units of response; the intercept, 2.175, is close to the measured control mean of 2.20, a reassuring internal check. 17.4 Interpolation versus extrapolation Using eq. 12 to estimate the response at an intermediate dose is reasonable: the model interpolates within the range it was fit on. Using it to predict a much higher dose — say 𝑑= 3, giving ̂𝑦= 6.3 — is an extrapolation the data cannot support. Real dose–response curves usually saturate (recall the threshold behaviour of the saturating response in sec. 8); a straight line will overpredict once the system approaches its ceiling. Figure 22. Mermaid diagram Warning. A linear fit through three averaged points reports 𝑅2 = 0.999, but that number describes how well the line passes through three dots — not how well it predicts the next exper- iment. Treat it as a reason to collect more data, not as a conclusion. Foundational guidance on this trap appears in [Kim, 2020] and [Wilson, 2021]. ## Page 46 17 CASE STUDIES 45 17.5 Summary A case study moves from raw observables to a summary, a fitted trend, and — crucially — an honest boundary around what the trend can claim. Here, averaging and a linear_fit recovered a clean dose– response slope of about 1.4 units per step with an intercept that matched the control, but the same fit must not be pushed beyond the measured range. The reusable move is: summarise, fit, then state the limits. 17.6 Key Terms observable, gradient, threshold, model. 17.7 Further Reading • Kim [2020] — practical guidance on summarising and visualising small datasets before fitting anything. • Wilson [2021] — on the difference between a good fit and a good prediction. 17.8 Practice • Lab: sec. 29 — re-run the grouping and fit, then add a fourth condition and watch the fit change. • Question bank: sec. 41 — recall through synthesis. ## Page 47 18 FRONTIERS AND OPEN PROBLEMS 46 18 Frontiers and Open Problems Figure 23. Overview schematic for “Frontiers and Open Problems”. Replace this generated placeholder with a real figure produced by src/visualization/plots.py. Level 1/3 ⋅30 min read ⋅45 min lecture ⋅Prerequisites: none 18.1 Learning Objectives By the end of this chapter you should be able to: 1. TODO: state the first measurable learning objective. 2. TODO: state the second learning objective. 3. TODO: state the third learning objective. 18.1.1 Study Blueprint • Big idea: • Core concepts: state, observable, system. • Quantitative lens: the worked formalism in eq. 13. • Data skill: • Common misconception to repair: • Primary lab: sec. 30. • Question bank: sec. 42. • Bridge to computation: textbook.models. Opening Vignette: TKTK — a motivating story ## Page 48 18 FRONTIERS AND OPEN PROBLEMS 47 18.2 Orientation This section introduces the central ideas of Frontiers and Open Problems. Foundational treatments include [Wilson, 2021, Taylor, 2019]. Key terms such as state, observable, system are defined in the glossary. 18.3 A Worked Formalism The recurring quantitative model for this chapter is shown in eq. 13: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (13) It is implemented and tested in textbook.models.logistic_growth; never retype the maths in prose or scripts — call the tested function. The parameters appear in tbl. 12. Table 12. Parameters of the worked model for this chapter. Symbol Meaning Units 𝑟 intrinsic rate 1/time 𝐾 carrying capacity quantity 𝑁0 initial value quantity A concept map of how the pieces fit together: Note 18.4 Going Deeper See the overview in fig. 23 and revisit the objectives above as you read. Further evidence: [Wilson, 2021, Taylor, 2019]. 18.5 Summary 18.6 Key Terms threshold, network, dynamics, emergence. 18.7 Further Reading • TODO: one-line annotation [Smith, 2020]. 18.8 Practice • Lab: sec. 30 • Question bank: sec. 42 ## Page 49 19 LAB — ORIENTATION TO THE FIELD 48 Figure 24. Mermaid diagram 19 Lab — Orientation to the Field Lab ⋅60 min ⋅Materials: notebook, calculator (or textbook.models) 19.1 Objectives 19.2 Background Linked chapter: sec. 4. 19.3 Procedure 1. TODO: first step. 2. TODO: second step. 19.4 Analysis Summarise results with textbook.models.descriptive_statistics. 19.5 Computational Workflow from textbook.models import logistic_growth # TODO: parameterise and plot the model for this lab's scenario. ## Page 50 19 LAB — ORIENTATION TO THE FIELD 49 19.6 Reflection ## Page 51 20 LAB — CORE METHODS AND TOOLS 50 20 Lab — Core Methods and Tools Lab ⋅60 min ⋅Materials: notebook, calculator (or textbook.models) 20.1 Objectives 20.2 Background Linked chapter: sec. 5. 20.3 Procedure 1. TODO: first step. 2. TODO: second step. 20.4 Analysis Summarise results with textbook.models.descriptive_statistics. 20.5 Computational Workflow from textbook.models import logistic_growth # TODO: parameterise and plot the model for this lab's scenario. 20.6 Reflection ## Page 52 21 LAB — QUANTITATIVE FOUNDATIONS 51 21 Lab — Quantitative Foundations Lab ⋅60 min ⋅Materials: notebook, calculator (or textbook.models) 21.1 Objectives 21.2 Background Linked chapter: sec. 6. 21.3 Procedure 1. TODO: first step. 2. TODO: second step. 21.4 Analysis Summarise results with textbook.models.descriptive_statistics. 21.5 Computational Workflow from textbook.models import logistic_growth # TODO: parameterise and plot the model for this lab's scenario. 21.6 Reflection ## Page 53 22 LAB — FIRST PRINCIPLES 52 22 Lab — First Principles Lab ⋅60 min ⋅Materials: a computer with the project installed (uv sync), or graph paper and a calculator 22.1 Objectives After this lab you will be able to (1) generate a logistic trajectory for chosen parameters, (2) read its carrying capacity and half-rise time from a plot, and (3) recover the growth rate from data with a simple fit. 22.2 Background This lab makes the chapter concrete: see sec. 8 for the logistic law and the meaning of 𝑟, 𝐾, and 𝑁0. You will produce the same S-curve shown in fig. 7 and then work backwards from numbers to parameters. 22.3 Procedure 1. Install the project: uv sync. Confirm the tests pass: uv run --extra dev python -m pytest test s/test_models.py -q. 2. Generate a trajectory for 𝑟= 0.8, 𝐾= 100, 𝑁0 = 5 at 𝑡= 0, 1, 2, … , 12 using the computational workflow below. 3. Plot 𝑁against 𝑡. Mark the value the curve approaches and the time at which 𝑁first exceeds 𝐾/2 = 50. 4. Repeat for 𝑟= 0.4 and 𝑟= 1.2, keeping 𝐾and 𝑁0 fixed. Overlay the three curves. 22.4 Analysis Summarise each trajectory with textbook.models.descriptive_statistics(N) and tabulate the maxi- mum value and the time-to-half-capacity for each 𝑟. Describe, in one sentence, how increasing 𝑟changes the curve without changing where it ends. 22.5 Computational Workflow import numpy as np from textbook import models t = np.arange(0, 13, 1.0) for r in (0.4, 0.8, 1.2): N = models.logistic_growth(t, r=r, carrying_capacity=100.0, initial=5.0) t_half = t[np.argmax(N > 50)] print(f"r={r}: N(12)={N[-1]:.1f}, first t with N>50 is t={t_half:.0f}") print(" stats:", models.descriptive_statistics(N)) 22.6 Reflection 1. Two of your three curves end at almost the same value. Which parameter sets that value, and why is it independent of 𝑟? 2. A colleague claims the population “will keep growing forever.” Using eq. 5, explain in one sentence why it will not. 3. If your measured data rose past 𝐾and then fell back, what would that tell you about the adequacy of the logistic model for that system? ## Page 54 23 LAB — BUILDING BLOCKS 53 23 Lab — Building Blocks Lab ⋅60 min ⋅Materials: notebook, calculator (or textbook.models) 23.1 Objectives 23.2 Background Linked chapter: sec. 9. 23.3 Procedure 1. TODO: first step. 2. TODO: second step. 23.4 Analysis Summarise results with textbook.models.descriptive_statistics. 23.5 Computational Workflow from textbook.models import logistic_growth # TODO: parameterise and plot the model for this lab's scenario. 23.6 Reflection ## Page 55 24 LAB — STRUCTURE AND FORM 54 24 Lab — Structure and Form Lab ⋅60 min ⋅Materials: notebook, calculator (or textbook.models) 24.1 Objectives 24.2 Background Linked chapter: sec. 10. 24.3 Procedure 1. TODO: first step. 2. TODO: second step. 24.4 Analysis Summarise results with textbook.models.descriptive_statistics. 24.5 Computational Workflow from textbook.models import logistic_growth # TODO: parameterise and plot the model for this lab's scenario. 24.6 Reflection ## Page 56 25 LAB — SYSTEMS OVERVIEW 55 25 Lab — Systems Overview Lab ⋅60 min ⋅Materials: notebook, calculator (or textbook.models) 25.1 Objectives 25.2 Background Linked chapter: sec. 12. 25.3 Procedure 1. TODO: first step. 2. TODO: second step. 25.4 Analysis Summarise results with textbook.models.descriptive_statistics. 25.5 Computational Workflow from textbook.models import logistic_growth # TODO: parameterise and plot the model for this lab's scenario. 25.6 Reflection ## Page 57 26 LAB — DYNAMICS AND CHANGE 56 26 Lab — Dynamics and Change Lab ⋅60 min ⋅Materials: notebook, calculator (or textbook.models) 26.1 Objectives 26.2 Background Linked chapter: sec. 13. 26.3 Procedure 1. TODO: first step. 2. TODO: second step. 26.4 Analysis Summarise results with textbook.models.descriptive_statistics. 26.5 Computational Workflow from textbook.models import logistic_growth # TODO: parameterise and plot the model for this lab's scenario. 26.6 Reflection ## Page 58 27 LAB — REGULATION AND CONTROL 57 27 Lab — Regulation and Control Lab ⋅60 min ⋅Materials: notebook, calculator (or textbook.models) 27.1 Objectives 27.2 Background Linked chapter: sec. 14. 27.3 Procedure 1. TODO: first step. 2. TODO: second step. 27.4 Analysis Summarise results with textbook.models.descriptive_statistics. 27.5 Computational Workflow from textbook.models import logistic_growth # TODO: parameterise and plot the model for this lab's scenario. 27.6 Reflection ## Page 59 28 LAB — APPLIED MODELS 58 28 Lab — Applied Models Lab ⋅60 min ⋅Materials: notebook, calculator (or textbook.models) 28.1 Objectives 28.2 Background Linked chapter: sec. 16. 28.3 Procedure 1. TODO: first step. 2. TODO: second step. 28.4 Analysis Summarise results with textbook.models.descriptive_statistics. 28.5 Computational Workflow from textbook.models import logistic_growth # TODO: parameterise and plot the model for this lab's scenario. 28.6 Reflection ## Page 60 29 LAB — CASE STUDIES 59 29 Lab — Case Studies Lab ⋅75 min ⋅Materials: the project installed (uv sync), assets/data/sample_dataset.csv 29.1 Objectives After this lab you will be able to (1) load grouped data, (2) compute per-group means and an overall summary, (3) fit a dose–response trend, and (4) state where the fit may and may not be trusted. 29.2 Background This lab operationalises sec. 17. You will reproduce the chapter’s numbers (group means 2.20, 3.50, 4.95; fitted slope ≈1.375) and then probe the fit’s limits by adding a condition. 29.3 Procedure 1. Read assets/data/sample_dataset.csv into three groups (control, low, high). 2. Compute each group’s mean and the overall summary with textbook.models.descriptive_statist ics. 3. Encode dose as 0, 1, 2 and fit a line with textbook.models.linear_fit. Confirm slope ≈1.375, intercept ≈2.175, 𝑅2 ≈0.999. 4. Add a hypothetical fourth condition (dose 3) with a saturating response — say a mean of 5.3 rather than the linear prediction of 6.3 — refit, and compare the new slope and 𝑅2. 29.4 Analysis Tabulate the slope, intercept, and 𝑅2 for the three-point and four-point fits. In two sentences, explain why the four-point fit’s slope falls and what that implies about extrapolating the original line. 29.5 Computational Workflow import csv import numpy as np from textbook import models rows = list(csv.DictReader(open("manuscript/assets/data/sample_dataset.csv"))) groups: dict[str, list[float]] = {} for r in rows: groups.setdefault(r["condition"], []).append(float(r["measurement"])) means = {k: float(np.mean(v)) for k, v in groups.items()} dose = np.array([0.0, 1.0, 2.0]) response = np.array([means["control"], means["treatment_low"], means["treatment_high"]]) print(models.linear_fit(dose, response)) 29.6 Reflection 1. The intercept of the fit was close to the control mean. Why is that a useful internal consistency check? 2. Your four-point fit changed the slope. Which is the more honest summary of the system, and what would you measure next to decide? ## Page 61 29 LAB — CASE STUDIES 60 3. When is a straight-line dose–response model adequate, and when does the saturating model from sec. 8 become necessary? ## Page 62 30 LAB — FRONTIERS AND OPEN PROBLEMS 61 30 Lab — Frontiers and Open Problems Lab ⋅60 min ⋅Materials: notebook, calculator (or textbook.models) 30.1 Objectives 30.2 Background Linked chapter: sec. 18. 30.3 Procedure 1. TODO: first step. 2. TODO: second step. 30.4 Analysis Summarise results with textbook.models.descriptive_statistics. 30.5 Computational Workflow from textbook.models import logistic_growth # TODO: parameterise and plot the model for this lab's scenario. 30.6 Reflection ## Page 63 31 QUESTION BANK — ORIENTATION TO THE FIELD 62 31 Question Bank — Orientation to the Field Linked chapter: sec. 4. 31.1 Recall 1. TODO. (Answer: ) 2. TODO. (Answer: ) 31.2 Application 3. TODO. (Answer: ) 4. TODO. (Answer: ) 31.3 Synthesis 5. TODO. (Answer: ) ## Page 64 32 QUESTION BANK — CORE METHODS AND TOOLS 63 32 Question Bank — Core Methods and Tools Linked chapter: sec. 5. 32.1 Recall 1. TODO. (Answer: ) 2. TODO. (Answer: ) 32.2 Application 3. TODO. (Answer: ) 4. TODO. (Answer: ) 32.3 Synthesis 5. TODO. (Answer: ) ## Page 65 33 QUESTION BANK — QUANTITATIVE FOUNDATIONS 64 33 Question Bank — Quantitative Foundations Linked chapter: sec. 6. 33.1 Recall 1. TODO. (Answer: ) 2. TODO. (Answer: ) 33.2 Application 3. TODO. (Answer: ) 4. TODO. (Answer: ) 33.3 Synthesis 5. TODO. (Answer: ) ## Page 66 34 QUESTION BANK — FIRST PRINCIPLES 65 34 Question Bank — First Principles Linked chapter: sec. 8. Answers follow each question in italics; in a print build, move them to an answer key if you prefer. 34.1 Recall 1. In the logistic model 𝑁(𝑡), which symbols are parameters and which is the variable? (Answer: 𝑟, 𝐾, and 𝑁0 are parameters held fixed; 𝑁(𝑡) is the variable that changes with time 𝑡.) 2. What value does a logistic trajectory approach as 𝑡→∞when 𝑟> 0? (Answer: the carrying capacity 𝐾.) 34.2 Application 3. With 𝑟= 0.8, 𝐾= 100, 𝑁0 = 5, the chapter reports 𝑁(5) = 74.18 and 𝑁(10) = 99.37. Roughly what fraction of the carrying capacity remains unfilled at 𝑡= 10? (Answer: about 0.63% — 𝑁(10) is within one part in a hundred of 𝐾.) 4. Doubling 𝑟from 0.4 to 0.8 changes the curve in what way, and what does it leave unchanged? (Answer: the curve rises and reaches the neighbourhood of 𝐾sooner — a steeper S — but the final level 𝐾is unchanged because 𝐾is a separate parameter.) 34.3 Synthesis 5. A dataset grows nearly exponentially at first, then levels off, but the plateau sits well below the resources you believe are available. Propose one modification to the logistic model that could explain a lower-than-expected plateau, and name the parameter it would change. (Answer: any mechanism that effectively lowers the carrying capacity — competition, a toxin, or a resource cap — would reduce 𝐾; the plateau tracks 𝐾, not the nominal resource supply. Accept reasoned alternatives.) ## Page 67 35 QUESTION BANK — BUILDING BLOCKS 66 35 Question Bank — Building Blocks Linked chapter: sec. 9. 35.1 Recall 1. TODO. (Answer: ) 2. TODO. (Answer: ) 35.2 Application 3. TODO. (Answer: ) 4. TODO. (Answer: ) 35.3 Synthesis 5. TODO. (Answer: ) ## Page 68 36 QUESTION BANK — STRUCTURE AND FORM 67 36 Question Bank — Structure and Form Linked chapter: sec. 10. 36.1 Recall 1. TODO. (Answer: ) 2. TODO. (Answer: ) 36.2 Application 3. TODO. (Answer: ) 4. TODO. (Answer: ) 36.3 Synthesis 5. TODO. (Answer: ) ## Page 69 37 QUESTION BANK — SYSTEMS OVERVIEW 68 37 Question Bank — Systems Overview Linked chapter: sec. 12. 37.1 Recall 1. TODO. (Answer: ) 2. TODO. (Answer: ) 37.2 Application 3. TODO. (Answer: ) 4. TODO. (Answer: ) 37.3 Synthesis 5. TODO. (Answer: ) ## Page 70 38 QUESTION BANK — DYNAMICS AND CHANGE 69 38 Question Bank — Dynamics and Change Linked chapter: sec. 13. 38.1 Recall 1. TODO. (Answer: ) 2. TODO. (Answer: ) 38.2 Application 3. TODO. (Answer: ) 4. TODO. (Answer: ) 38.3 Synthesis 5. TODO. (Answer: ) ## Page 71 39 QUESTION BANK — REGULATION AND CONTROL 70 39 Question Bank — Regulation and Control Linked chapter: sec. 14. 39.1 Recall 1. TODO. (Answer: ) 2. TODO. (Answer: ) 39.2 Application 3. TODO. (Answer: ) 4. TODO. (Answer: ) 39.3 Synthesis 5. TODO. (Answer: ) ## Page 72 40 QUESTION BANK — APPLIED MODELS 71 40 Question Bank — Applied Models Linked chapter: sec. 16. 40.1 Recall 1. TODO. (Answer: ) 2. TODO. (Answer: ) 40.2 Application 3. TODO. (Answer: ) 4. TODO. (Answer: ) 40.3 Synthesis 5. TODO. (Answer: ) ## Page 73 41 QUESTION BANK — CASE STUDIES 72 41 Question Bank — Case Studies Linked chapter: sec. 17. Answers follow each question in italics. 41.1 Recall 1. What two summary numbers does the chapter report for each condition group, and which function computes them? (Answer: the per-group mean — e.g. 2.20, 3.50, 4.95 — plus an overall spread from textbook.models.descriptive_statistics, which returns mean, std, min, max, and count.) 2. What do the slope and intercept of the fitted line eq. 12 represent? (Answer: the slope (≈1.375) is the response added per dose step; the intercept (≈2.175) is the predicted response at dose 0, which should match the control mean.) 41.2 Application 3. The intercept (2.175) is close to the control mean (2.20). Why is this a useful check rather than a coincidence to ignore? (Answer: a fit whose dose-0 prediction matches the measured control is internally consistent; a large mismatch would signal a coding error or a poor model.) 4. The line predicts ̂𝑦(3) = 6.3. Why should this prediction be flagged? (Answer: dose 3 is outside the measured range [0, 2] — it is an extrapolation, and real dose–response curves usually saturate, so a line will overpredict.) 41.3 Synthesis 5. With only three averaged points the fit reports 𝑅2 = 0.999. Explain why this is weak evidence and describe one experiment that would strengthen — or overturn — the linear conclusion. (Answer: 𝑅2 near 1 on three points mostly reflects that a line can pass through three dots; it says little about prediction. Collecting more doses, especially higher ones, would reveal curvature/saturation and test whether the linear model generalises. Accept reasoned alternatives.) ## Page 74 42 QUESTION BANK — FRONTIERS AND OPEN PROBLEMS 73 42 Question Bank — Frontiers and Open Problems Linked chapter: sec. 18. 42.1 Recall 1. TODO. (Answer: ) 2. TODO. (Answer: ) 42.2 Application 3. TODO. (Answer: ) 4. TODO. (Answer: ) 42.3 Synthesis 5. TODO. (Answer: ) ## Page 75 43 APPENDIX A — AUTHORING GUIDE: FILLING THE STUBS 74 43 Appendix A — Authoring Guide: Filling the Stubs Reference appendix ⋅For authors and contributors ⋅Read this first. This is the most important file in the template. It explains how to turn the empty scaffold into a finished book by filling stubs and growing structure from a single source of truth. Read it once end-to-end, then keep it open while you work. 43.1 The Big Idea: One Source of Truth The book is data-driven from config.yaml. The list of parts, chapters, labs, question banks, and reference appendices lives there and nowhere else. The Python engine in src/textbook/ reads that file and the scaffolding scripts in scripts/ materialise the matching markdown files. You never hand-number a chapter, figure, equation, or section — pandoc-crossref does that at render time from the labels you write. The flow is always the same: edit config.yaml -> scaffold_chapter.py -> fill blocks -> add figures / glossary terms / references -> audit + tests 43.2 Step 1 — Decide the Structure in config.yaml Open config.yaml. To add or rename a chapter, edit the parts: tree (each chapter has a stem and a title); to add a lab or question bank, add an entry under appendices.labs / appendices.questions for the matching part. The stem drives every downstream name: • chapter file →manuscript//_.md, label {#sec:_} • lab file →manuscript/labs//lab_.md, label {#sec:lab__} • question bank →manuscript/questions//q_.md, label {#sec:q__} Keep stems short, lowercase, and snake_case. Do not invent a numbering scheme; the table of contents and labels are derived in src/textbook/toc.py. 43.3 Step 2 — Materialise the Stubs Run the scaffolder. It only creates files that are missing, so it is safe to re-run after every config change: uv run python scripts/scaffold_chapter.py This writes a chapter (or lab, or question bank) pre-populated with every required structural element as markers. Your job is to replace the stubs with real prose, never to delete the structure. 43.4 Step 3 — Fill the Content Contract Every chapter must carry these elements (enforced by validate_chapter in src/textbook/content.py and by the integrity tests). Fill each, keep the markers’ surrounding structure: • a labelled H1: # Title {#sec:_} • a metadata badge line: • a Study Blueprint: • Learning Objectives • one figure with alt text and a crossref label {#fig:...} • a worked formalism: an equation {#eq:...} plus a parameter table {#tbl:...} ## Page 76 43 APPENDIX A — AUTHORING GUIDE: FILLING THE STUBS 75 • an inline ```mermaid diagram • Summary, Key Terms, Further Reading, Practice sections Cross-reference syntax is pandoc-crossref: [@fig:..], [@tbl:..], [@eq:..], [@sec:..]. Stub markers the audit counts are , TODO:, and TKTK — drive these to zero as the chapter matures. 43.5 Step 4 — Add a Figure Figures are deterministic matplotlib output. Each chapter expects a placeholder named _.png. To make it real, add or edit a function in src/visualization/plots.py (the four worked figures show the pattern), then regenerate: uv run python scripts/generate_figures.py For diagrams, edit src/mermaid/diagram_specs.yaml and run scripts/generate_diagrams.py (PNG, or .mmd fallback). Reference the figure in prose with [@fig:_] and give it alt text. 43.6 Step 5 — Add a Glossary Term Glossary anchors are a closed contract. To add a term you must update both: 1. GLOSSARY_ANCHORS in src/textbook/constants.py 2. the matching entry in glossary.md Link a term in prose as [**term**](#gl:). The current anchors are system, model, paramete r, variable, equilibrium, feedback, gradient, threshold, network, dynamics, emergence, re gulation, boundary, state, observable. 43.7 Step 6 — Add a Reference Citations are [@key] and must resolve in references.bib. Add a BibTeX entry, then cite it. Keep CITATION_KEYS in constants.py in sync if you add a key that the structural contract should track. 43.8 Step 7 — Audit and Test Two gates decide whether the book is healthy: # Quality gate: counts stubs, checks the content contract per file uv run python scripts/audit_textbook_quality.py # Full test suite (engine + manuscript integrity) uv run --extra dev python -m pytest tests/test_manuscript_integrity.py verifies that every chapter satisfies the content contract, that labels are unique, that citations resolve, and that glossary links point at real anchors. Green tests with remaining stubs mean the structure is correct but the content is unfinished — that is the normal state of a freshly scaffolded chapter. 43.9 Growing the Book To add a whole new chapter end-to-end: 1. add its stem/title under the right part in config.yaml; ## Page 77 43 APPENDIX A — AUTHORING GUIDE: FILLING THE STUBS 76 2. add matching lab and question-bank entries under appendices; 3. run scripts/scaffold_chapter.py; 4. fill the stubs (Steps 3–6); 5. run the audit and tests until the contract passes. See also: Appendix B — Notation, Appendix C — Mathematical Review, and the appendices README. ## Page 78 44 APPENDIX B — NOTATION AND SYMBOLS 77 44 Appendix B — Notation and Symbols Reference appendix ⋅Symbol glossary for the worked models. This appendix lists the symbols used by the worked formalisms in src/textbook/models.py. Keep it in sync with the parameter tables ({#tbl:...}) in the chapters: every symbol that appears in an equation {#eq:...} should have a row here. 44.1 Conventions • Scalars are italic lowercase (e.g. r, t); sets and spaces are uppercase. • Subscript 0 denotes an initial value (e.g. N 0 at t = 0). • Units are stated in SI / metric unless a chapter declares otherwise. 44.2 Symbol Table Symbol Name Appears in Units Notes t time / independent variable all dynamic models s (or chapter unit) N state quantity / population logistic_growth dimensionless N 0 initial state logistic_growth, exponential_deca y dimensionless r intrinsic growth rate logistic_growth 1/time K carrying capacity logistic_growth dimensionless 𝜆(lambda) decay constant exponential_deca y, half_life 1/time t½ half-life half_life time Vmax maximum response saturating_respo nse response unit Km half-saturation constant saturating_respo nse input unit x, y paired observations linear_fit data unit m, b slope, intercept linear_fit derived 𝜇, 𝜎 mean, standard deviation descriptive_stat istics data unit See also: Appendix C — Mathematical Review. ## Page 79 45 APPENDIX C — MATHEMATICAL REVIEW 78 45 Appendix C — Mathematical Review Reference appendix ⋅Just-enough mathematics for the worked models. A brief refresher on the mathematics the book relies on. Each section ties directly to a function in src/tex tbook/models.py so you can move from formula to tested code without a gap. Replace the stubs with the depth your audience needs. 45.1 Functions and Variables A function maps an input to an output; here state quantities depend on a variable such as time, tuned by parameters. See normalize_unit_interval for rescaling inputs to [0, 1]. 45.2 Growth and Decay Logistic growth (logistic_growth) rises then saturates at the carrying capacity K; exponential decay (exp onential_decay) falls by a fixed fraction per unit time, summarised by the half-life t½ (half_life). These are the canonical examples of dynamics. 45.3 Saturating Responses The saturating (Michaelis–Menten-style) response (saturating_response) climbs toward Vmax with half- maximum at Km — a recurring shape whenever a resource or signal becomes limiting near a threshold. 45.4 Linear Fits Least-squares fitting (linear_fit) returns a slope m and intercept b for paired data, the simplest way to summarise a trend before reaching for a richer model. 45.5 Basic Statistics Descriptive statistics (descriptive_statistics) report the mean 𝜇and standard deviation 𝜎— the first numbers to compute on any observable before inference. See also: Appendix B — Notation and the Authoring Guide. ## Page 80 46 APPENDIX — FORMALISMS 79 46 Appendix — Formalisms A worked example of every formal element a technical book uses: definitions, theorems with proofs, lem- mas, algorithms in pseudocode, step-by-step derivations, systems of numbered equations, and dimensioned quantities. Each maps to a tested function in src/textbook/models.py, so the prose and the code stay in agreement. Convention. Theorem-like environments below use a portable bold-label block-quote form that renders in every target. If your render profile loads amsthm (the preamble does), you may instead use native LaTeX theorem, lemma, definition, and proof environments. 46.1 1. Definitions Definition 1 (Equilibrium). A state 𝑁∗of a dynamical system ̇ 𝑁= 𝑓(𝑁) is an equilibrium if 𝑓(𝑁∗) = 0. See equilibrium. Definition 2 (Carrying capacity). For logistic dynamics, the carrying capacity 𝐾is the non-zero equilibrium toward which trajectories converge. 46.2 2. A theorem with proof Theorem 1 (Logistic limit). For the logistic model in eq. 14 with 𝑟> 0 and 0 < 𝑁0 ≤𝐾, the trajectory satisfies lim𝑡→∞𝑁(𝑡) = 𝐾. 𝑁(𝑡) = 𝐾 1 + 𝐴𝑒−𝑟𝑡, 𝐴= 𝐾−𝑁0 𝑁0 . (14) Proof. Because 𝑟> 0, the term 𝑒−𝑟𝑡→0 as 𝑡→∞. Hence the denominator 1 + 𝐴𝑒−𝑟𝑡→1, and therefore 𝑁(𝑡) →𝐾/1 = 𝐾. The constant 𝐴≥0 follows from 0 < 𝑁0 ≤𝐾, so 𝑁(𝑡) is increasing and the limit is approached from below. ■ This is exactly the asymptotic behaviour the test tests/test_models.py::test_logistic_growth_star ts_at_initial_and_approaches_capacity verifies numerically — the proof and the test assert the same fact. 46.3 3. A lemma Lemma 1 (Half-life). For exponential decay 𝑦(𝑡) = 𝑦0𝑒−𝜆𝑡with 𝜆> 0, the time at which 𝑦 falls to half its initial value is 𝑡1/2 = ln 2/𝜆, independent of 𝑦0. Proof. Set 𝑦(𝑡1/2) = 𝑦0/2. Then 𝑒−𝜆𝑡1/2 = 1/2, so −𝜆𝑡1/2 = −ln 2, giving 𝑡1/2 = ln 2/𝜆. The result does not depend on 𝑦0. ■ Implemented as textbook.models.half_life. ## Page 81 46 APPENDIX — FORMALISMS 80 46.4 4. Algorithms (pseudocode) Where the preamble provides an algorithm package, use it; otherwise this fenced form renders everywhere. Algorithm 1: Ordinary least-squares line fit Input : points (x_i, y_i), i = 1..n, n >= 2 Output: slope m, intercept b, coefficient of determination R^2 1 x_bar <- mean(x); y_bar <- mean(y) 2 m <- sum((x_i - x_bar)(y_i - y_bar)) / sum((x_i - x_bar)^2) 3 b <- y_bar - m * x_bar 4 SS_res <- sum((y_i - (m x_i + b))^2) 5 SS_tot <- sum((y_i - y_bar)^2) 6 R^2 <- 1 - SS_res / SS_tot (define R^2 = 1 when SS_tot = 0) 7 return (m, b, R^2) This is textbook.models.linear_fit; Step 6’s degenerate case is covered by tests/test_models.py::te st_linear_fit_constant_y_gives_r_squared_one. 46.5 5. A step-by-step derivation Starting from the logistic differential equation and separating variables: 𝑑𝑁 𝑑𝑡= 𝑟𝑁(1 −𝑁 𝐾) ∫ 𝑑𝑁 𝑁(1 −𝑁/𝐾) = ∫𝑟𝑑𝑡 ln( 𝑁 𝐾−𝑁) = 𝑟𝑡+ 𝐶 𝑁(𝑡) = 𝐾 1 + 𝐴𝑒−𝑟𝑡, 𝐴= 𝑒−𝐶, which recovers eq. 14. Each line is one algebraic move; show your work at this granularity so readers can follow without gaps. 46.6 6. A system of numbered equations A simple predator–prey system, with each equation individually referenceable (eq. 15, eq. 16): 𝑑𝑥 𝑑𝑡= 𝛼𝑥−𝛽𝑥𝑦 (15) 𝑑𝑦 𝑑𝑡= 𝛿𝑥𝑦−𝛾𝑦 (16) The vector-field figure style for such systems is demonstrated by the quiver plot in the format gallery (sec. 47). ## Page 82 46 APPENDIX — FORMALISMS 81 46.7 7. Dimensioned quantities State parameters with units explicitly, in math mode so they render in every target: Table 13. Worked-model parameters with representative dimensioned values. Symbol Quantity Example value 𝑟 intrinsic rate 0.8 s−1 𝜆 decay constant 0.5 s−1 𝑡1/2 half-life 1.386 s 𝐾 carrying capacity 100 individuals 46.8 8. Notation summary Symbols used throughout are collected in the notation appendix (sec. 44); glossary definitions for narrative terms such as gradient and threshold are in the master glossary. ## Page 83 47 APPENDIX — FORMAT GALLERY 82 47 Appendix — Format Gallery This appendix is a kitchen-sink demonstration: a working example of every content primitive this tem- plate supports. Copy any block into a chapter and adapt it. Each example is real and renders through the standard pipeline; figures are produced deterministically by src/visualization/ and embedded from ../figures/. How to read this appendix. Headings group primitives by kind: text, lists, callouts, tables, math, figures, diagrams, code, cross-references, media, and pedagogy blocks. The Markdown source is the example — view it next to the rendered output. 47.1 1. Text and inline formatting Plain paragraph text wraps and flows normally. Inline styles: bold, italic, bold italic, inline code, strikethrough, H2O with a subscript, E = mc2 with a superscript, and a footnote.1 You can hard-break a line with two trailing spaces, or separate paragraphs with a blank line. Escape literal Markdown with a backslash: *not italic*. 47.2 2. Lists Unordered, with nesting: • First item • Second item – Nested item – Another nested item ∗Third level • Third item Ordered: 1. Step one 2. Step two 1. Sub-step a 2. Sub-step b 3. Step three Task list (renders as checkboxes in many targets): ⊠Scaffold the chapter ⊠Generate figures □Fill the prose □Write the assessment answers Definition list: Parameter A fixed quantity that configures a model (see parameter). 1Footnotes collect at the end of the document (or page, in PDF). Use them for asides that would interrupt the sentence. ## Page 84 47 APPENDIX — FORMAT GALLERY 83 Variable A quantity that changes across states (see variable). 47.3 3. Block quotes and callouts A plain block quote: “Form follows function.” Use quotes for epigraphs and primary-source extracts. Portable callouts (a bold label inside a block quote — renders in every target): Note. A neutral aside that adds context. Tip. A practical suggestion the reader can act on. Warning. A caveat, common error, or safety note. Example. A short worked illustration inline in the text. Definition. A precise statement of a term, often paired with a glossary entry such as equilib- rium. Pandoc fenced-div callout (richer styling where supported; falls back gracefully): This is a Pandoc fenced div. If your render profile styles .callout-note, it appears as a boxed admonition; otherwise it renders as a normal block. 47.4 4. Tables A simple table with column alignment and a cross-referencable caption (tbl. 14): Table 14. Column alignment — left, centre, right. Left Centre Right alpha 1 10.0 beta 22 2.5 gamma 333 0.125 A multi-line / grid table (cells may contain longer wrapped text): Symbol Meaning Typical range 𝑟 intrinsic rate of change 0.1 – 2.0 𝐾 carrying capacity / saturation level the system approaches problem- dependent ## Page 85 47 APPENDIX — FORMAT GALLERY 84 47.5 5. Mathematics and units Inline math: the half-life is 𝑡1/2 = ln 2/𝜆. A numbered display equation, cross-referenced as eq. 17: 𝑁(𝑡) = 𝐾 1 + (𝐾−𝑁0 𝑁0 ) 𝑒−𝑟𝑡 (17) Multi-line aligned derivation: 𝑑𝑁 𝑑𝑡= 𝑟𝑁(1 −𝑁 𝐾) = 𝑟𝑁−𝑟 𝐾𝑁2. A matrix and a piecewise definition: A = [𝑎11 𝑎12 𝑎21 𝑎22 ] , 𝑓(𝑥) = {0 𝑥< 0 1 𝑥≥0. Physical quantities with units, written in math mode so they render in every target (PDF, HTML, slides): a rate of 0.5 s−1, a length of 2.0 m, and a concentration of 1.5 mol L−1. (For PDF-only builds you may instead use siunitx macros such as \SI{0.5}{\per\second}, which the preamble loads — but math-mode units are the portable choice.) 47.6 6. Figures A single figure with caption, label, and alt text, cross-referenced as fig. 25: Two figures side by side (Pandoc fenced div; falls back to stacked): A multi-panel composite (fig. 28): The full plot-type gallery lives in ../figures/gallery/ and includes: line, scatter-with-fit, bar, grouped bar, horizontal bar, histogram, box, violin, heatmap, contour, quiver field, step, stacked area, error bars, log-log, pie, annotated, and multi-panel. 47.7 7. Diagrams (Mermaid) The pipeline renders fenced mermaid blocks to figures (and falls back to the .mmd source if the Mermaid CLI is absent). One worked example of each kind the builders in src/mermaid/diagrams.py support: Flowchart: Sequence: State: Class: ## Page 86 47 APPENDIX — FORMAT GALLERY 85 Figure 25. A multi-series line plot of three sine waves, produced by visualization.gallery.line_plot. Figure 26. Bar chart. ## Page 87 47 APPENDIX — FORMAT GALLERY 86 Figure 27. Pie chart. Figure 28. A 2×2 composite: line, scatter, bar, and histogram panels. ## Page 88 47 APPENDIX — FORMAT GALLERY 87 Figure 29. Mermaid diagram Figure 30. Mermaid diagram ## Page 89 47 APPENDIX — FORMAT GALLERY 88 Figure 31. Mermaid diagram Entity-relationship: Pie, Gantt, mindmap, timeline, quadrant, and user-journey diagrams are also supported — see src/mermai d/diagram_specs.yaml for a worked spec of each. 47.8 8. Code Inline code: call textbook.models.logistic_growth(t, r=..., ...). A fenced code block with a language (syntax-highlighted) and a caption (lst. 1): Listing 1 Calling the tested computational backbone. from textbook import models import numpy as np t = np.linspace(0, 10, 100) n = models.logistic_growth(t, r=0.8, carrying_capacity=100.0, initial=5.0) print(n[-1]) # -> approaches the carrying capacity A shell example: uv run python scripts/generate_figures.py uv run --extra dev python -m pytest tests/ --cov=src ## Page 90 47 APPENDIX — FORMAT GALLERY 89 Figure 32. Mermaid diagram 47.9 9. Cross-references and citations Cross-references resolve by label: figure fig. 25, table tbl. 14, equation eq. 17, and section sec. 46. Never hand-number — Pandoc fills these in. Citations resolve against references.bib: a single source [Smith, 2020], multiple sources [Doe, 2019, Lee, 2021], and an in-text form — Garcia [2022] showed the effect first. A locator narrows the reference [Patel, 2018, pp. 12–14]. 47.10 10. Media and data Embedded raster image (any PNG/JPG works the same way as a figure): Audio and video embed in HTML targets (PDF shows the caption + link). Syntax: ![Caption for an audio clip.](../assets/media/clip.mp3) ![Caption for a video.](../assets/media/demo.mp4){width=70%} A downloadable data file lives at assets/data/sample_dataset.csv; its contents as a table: ## Page 91 47 APPENDIX — FORMAT GALLERY 90 Figure 33. Mermaid diagram Figure 34. A generated heatmap embedded as a raster image. ## Page 92 47 APPENDIX — FORMAT GALLERY 91 Table 15. Sample dataset (mirrors assets/data/sample_dataset.csv). condition replicate measurement standard_error control 1 2.10 0.20 control 2 2.30 0.18 treatment_low 1 3.60 0.25 treatment_high 1 4.80 0.35 The error-bar figure fig. 35 visualises this kind of data: Figure 35. Means with standard-error bars. 47.11 11. Pedagogical blocks These are the reusable teaching elements chapters draw on. Learning objective. After this section a reader can identify which Markdown primitive to use for a given purpose. Worked example. Given 𝑟= 0.8, 𝐾= 100, 𝑁0 = 5, evaluate 𝑁(10) via eq. 17 using textbook .models.logistic_growth. The result approaches 𝐾. Try it. Change 𝑟to 1.5 and predict, then check, how the curve shifts. Key terms. model, parameter, state. Summary. This appendix demonstrated text, lists, callouts, tables, math and units, figures, diagrams, code, cross-references, media, and pedagogy blocks — the complete primitive set. ## Page 93 47 APPENDIX — FORMAT GALLERY 92 47.12 12. Miscellany A horizontal rule separates major shifts in topic (three or more dashes): Raw inline HTML is supported only inside
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