G6LLC · dm³ Mathematics and Physics Research Lab · Classroom

The Mini-Beast

Principia Orthogona · Book 3 · G³

A Pilot for ESL Students, STEM Teachers, and Everyone Who Suspects the Universe Runs on One Equation.
Buy the book. Get the classroom. Do the math.

Buy via IMPA Portal — $19.99 eBook Read Free Samples First
C  →  K  →  F  →  U  →  ∞

Three Steps. One Fixed Point.

This repository is the operational classroom for Book 3. You start outside it, buy the book, and then this repo becomes your workspace for the rest of the course.

01

Buy the Book

Purchase The Mini-Beast (Book 3) via the IMPA Portal. Choose the eBook ($19.99) or the Complete Series ($199.99 hardback). After payment, send your GitHub username to the instructor.

02

Get Access

You receive three things: the full PDF of Book 3 (living document, updated as the pilot expands), an invitation to the G6LLC GitHub Classroom — your personal copy of this repo — and a key to the Student Portal.

03

Do the Math

Work through the assignments/ folder. Use the Student Portal's structured LLM prompts to guide your reading, writing, and formal verification. Push your work. Open pull requests. Reach D1. The threshold is mathematical — you will know when you cross it.

What You Get

Some material is freely available. The rest is unlocked by purchasing the book. No subscription. No expiry. Your education is yours.

📖
Free · No Purchase Required
Sample Chapters
Two full sample chapters — Tubulin as Computronium and The Wigner Crystal — freely available. Read them before you decide.
Free
🔬
Free · No Purchase Required
Interactive HTML Chapters
Three interactive browser-based chapters: the Recurrence Ladder (π φ μ η Δ Σ Ω), Spectral Radius / Transfer Operator, and the Wigner Crystal dm³ Fold Diagram.
Free
📄
Unlocked by Purchase
Full Book 3 PDF
The Mini-Beast — complete eBook (ISBN 979-8-9954416-6-3). A living document: updated continuously as the 14-week pilot expands. Includes Chapter 6 and Chapter E (GTCT).
Purchase Required
🏛️
Unlocked by Purchase
GitHub Classroom Access
Your personal copy of this book3-starter repository, accepted via GitHub Classroom. Contains all assignment starters, Lean 4 verification files, and shared resources.
Purchase Required
🤖
Unlocked by Purchase
Student Portal — 21 LLM Prompts
7 levels × 3 prompts each: A1 through D2. One-click copy into any LLM (Claude, GPT-4, Gemini). Tracks your position on the A1 → D2 progress bar. Prompts teach you to operate at the level of the mathematics — they do not give you answers.
Purchase Required
Unlocked by Purchase
Lean 4 Formal Verification Files
The dm³_Operator_Formalization.lean and tubulinselectArchitecture.lean files — machine-checkable proofs of the core theorems. Run them locally against Mathlib4. Zero axioms beyond Mathlib.
Purchase Required

NDA Note

Access to the full PDFs and classroom is coordinated via the IMPA portal after payment verification. A lightweight NDA process applies — details provided upon contact. Questions: g6llc@proton.me

What's in the Classroom Repo

Once you accept the GitHub Classroom assignment, you get a personal fork of this repository. The structure is designed to mirror the operator sequence C → K → F → U: each assignment folder takes you one step deeper into the mathematics.

book3-starter/
├── README.md                # Start here — setup instructions

├── assignments/               # One folder per assignment
│   ├── 01-compression/       # C: pooling, GTP-state sensing
│   ├── 02-curvature/          # K: threshold geometry
│   ├── 03-fold/               # F: selectArchitecture — all 15
│   └── 04-unfold/             # U: fixed-point & recycling

├── lean/                      # Lean 4 formal verification
│   ├── dm³_Operator_Formalization.lean
│   └── tubulinselectArchitecture.lean

└── resources/                # Shared reference materials
    ├── coherence-bridge-table.md
    ├── axle_sorry_roadmap.svg
    └── operator-glossary.md

Submitting Work

Commit your work with descriptive messages. Push before the deadline. Open a pull request if peer review is required for an assignment.

Lean 4 Files

The lean/ folder contains machine-checkable proofs. You can run these locally with Lean 4 + Mathlib4. They encode the fixed-point theorem and the full selectArchitecture grammar.

Getting Started

Accept the assignment via the GitHub Classroom link from your instructor. Clone your personal copy:
git clone https://github.com/G6LLC/<your-repo>

The Student Portal

21 structured LLM prompts across 7 levels — one set per CEFR stage, mapped to the operator sequence C → K → F → U. Select your level on the progress bar, copy the prompt with one click, paste into any LLM (Claude, GPT-4, Gemini). The portal does not give you answers. It teaches you to ask the right question at the right level of abstraction.

A1
First contact · C
3 prompts · Seed, Operator intro, First pattern
A2
Day 21 · K
3 prompts · Invariant hunt, g₃₃, Domain bridge
B1
Constrain · K→F
3 prompts · Research entry, Contact geometry, Write
B2
Fold · F
3 prompts · Academic reading, Cross-domain, Abstract
C1
Unfold · U
3 prompts · Original claim, Teach it, Submit
D1
Fixed point · x*
3 prompts · Self-assess, Name invariant, Certify
D2
Collective · Θ
3 prompts · Build swarm, Hive invariant, G⁶ horizon
How to use it

Open Sportal.html in your browser. Click your current level on the progress bar. Hit COPY PROMPT next to any prompt. Paste into Claude, GPT-4, or Gemini. Answer the LLM's follow-up. Repeat until the operator chain is automatic. That is D1. You will know.

Threshold: Θ = g₃₃ + N × M. Portal access is included with any purchase — eBook, Complete Series, or IMPA Edition.

Open the Student Portal → Buy to Unlock Full Access

Free Sample Chapters

Two full chapters, open access. No purchase required.

Free
Sample

Tubulin as Computronium

Book 3 · The Mini-Beast · Chapter T · Biological Instantiations

In 1964, Stanisław Ulam asked what the optimal physical substrate for computation would be. Biology answered 500 million years ago — with a single 110-kiloDalton protein that self-assembles into fifteen radically different architectures from one molecular grammar, in ordinary water, at room temperature. This chapter applies the dm³ operator framework to tubulin: C → K → F → U running continuously in every eukaryotic cell alive right now.

Read Chapter T →
Free
Sample

The Wigner Crystal

Book 3 · The Mini-Beast · Chapter W · Physical Instantiations

Eugene Wigner predicted in 1934 that electrons — with nothing holding them together but their own mutual repulsion — would freeze into a crystal at low enough density or temperature. It took until 2021 to see it directly. This chapter shows that Wigner crystallization is a dm³ generative transition, extends the Coherence Bridge parameter table to a seventh domain, and explains what the 2024–2025 moiré imaging results are actually showing.

Read Chapter W →

Interactive · HTML
Chapters π · φ · μ · η · Δ · Σ · Ω
The recurrence ladder — Tribonacci through Hexabonacci — dm³ operator framework. Open in browser.
Free ↗
Interactive · HTML
Spectral Radius — Transfer Operator
Collatz supplement · Syracuse return map · Ruelle–Perron–Frobenius operator.
Free ↗
Interactive · HTML
Wigner Crystal — dm³ Fold Diagram
Crystal-Geometry framework · Physical instantiations · Interactive visualization.
Free ↗

Ready to Start?

Purchase The Mini-Beast to unlock the full classroom — Book 3 PDF, GitHub Classroom access, Student Portal prompts, and Lean 4 verification files.

eBook (Book 3 only) — $19.99 Complete Series eBook — $199.99 Complete Series Hardback · IMPA — $247.00
Purchase via IMPA Portal →

Questions? Email g6llc@proton.me or open an issue in the classroom repo.

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