Principia Orthogona · G6 LLC · Newark NJ · 2026

English for Researchers

C1 to D2 — A 16-Week Living Course

We perceive the unfolding first.
This course teaches academic English through the operator chain that structures all living systems. Students study, prompt with LLMs, write research papers, publish on Zenodo, document on GitHub, and — for the mathematically ready — verify claims in Lean 4 via AXLE. By Week 16 the student has produced a published, citable scientific work.

16 Weeks · 16 Units
4 Published Papers
21 LLM Prompts
AXLE Verification
Zenodo DOIs
GitHub Documentation
C  →  K  →  F  →  U  →  D2
16
Weeks of structured study
4
Milestone papers published
21
LLM prompts (A1 → D2)
4
GitHub repos documented
8
Verified constants in AXLE
∞
Chapters — living book grows
The 16-Week Journey
Each cell = one week. Red = milestone publication. G = operator applied.
Wk 1
C
Seed / Unfolding
Wk 2
C
Scientific Reading
Wk 3
C
Source Compression
Wk 4
●
Paper 1 — Zenodo
Wk 5
K
The Threshold Claim
Wk 6
K
Falsifiability
Wk 7
K
Literature Bridge
Wk 8
●
Paper 2 — GitHub
Wk 9
F
IMRaD Structure
Wk 10
F
Argument Fold
Wk 11
F
Methods + Results
Wk 12
●
Paper 3 — Preprint
Wk 13
U
Revision + Peer Review
Wk 14
U
AXLE Verification
Wk 15
U
DOI + GitHub Pages
Wk 16
D2
Complete Circuit
Coperator
Weeks 1 – 4 · CEFR A1 → A2
Compression — Perceiving the Structure

The student begins where they always begin: looking at something that has already unfolded. Phase C teaches them to read backward — from visible output to hidden structure. Scientific reading, abstract compression, source mapping, and the first Zenodo publication. The cajueiro compresses downward before the canopy appears. So does the researcher.

Book 3 Chapters 1–3 Sportal Levels A1 · A2 Zenodo Setup GitHub Profile 6 LLM Prompts
01week
The Cajueiro Principle — We Perceive the Unfolding First
Book 3 · Chapter 1 · Operator C · Level A1
Study Prompt 1.1 · 1.2 · 1.3 GitHub Setup

Study

  • Read Book 3 Chapter 1: The Cajueiro — unfolding as the entry point to all scientific observation
  • Learn the operator chain: C → K → F → U as a reading and writing tool
  • Read one Zenodo paper (any volume from the Principia Orthogona series). Note: what is the first visible thing you see?
  • Vocabulary: operator, threshold, compression, observable, instantiation

Tasks

  • Create your GitHub account and make a public profile README
  • Create your Zenodo account (ORCID recommended)
  • Write a 150-word observation of a living system using the 4 operators as headings
  • Use LLM Prompt 1.1 to begin your first operator description
LLM Prompt 1.1 — Seed Contact
"I am beginning a research journey. Describe for me what C → K → F → U means as a reading strategy. Give me one example from biology and one from language learning. Use academic English at B1 level."
Week 1 OutputGitHub profile README (public). Zenodo account created. 150-word living-system observation saved as a text file in your repo.
02week
Scientific Reading — Compressing the Abstract
Book 3 · Chapter 2 · Operator C · Level A1
Study Prompt 1.2 Write

Study

  • Book 3 Chapter 2: The Allostatic Operator — stress as compression in living systems
  • Read the abstract of Zenodo 10.5281/zenodo.19122168 (Generative Contact Mechanics). Map it to C → K → F → U
  • Learn IMRaD: Introduction, Methods, Results, and Discussion as operator phases
  • Vocabulary: abstract, allostasis, curvature, attractor, bifurcation

Tasks

  • Compress a scientific abstract into 3 sentences: one per C, K, and F
  • Use LLM Prompt 1.2 to get feedback on your compression
  • Add a "Research Log" section to your GitHub README — record the paper you read and your 3-sentence compression
  • Note: what was the falsifiable claim in the paper you read?
LLM Prompt 1.2 — Operator Introduction
"Here is a 3-sentence compression of a scientific abstract: [paste your 3 sentences]. Does each sentence correspond to one phase of C → K → F? What is missing? What would a D2-level researcher add?"
Week 2 OutputGitHub Research Log updated. 3-sentence compression of a real paper. Vocabulary list (10 terms) committed to repo.
03week
Source Mapping — Citations, DOIs, and the Literature Chain
Book 3 · Chapter 3 · Operator C · Level A2
Study Prompt 1.3 Write GitHub

Study

  • Book 3 Chapter 3: Circadian Regulation — how the cell compresses time into a 24-hour orbit
  • Read two Zenodo papers from the series. Map citations between them
  • Learn: DOI, ORCID, Zenodo metadata, how to cite a preprint in APA and Chicago
  • Vocabulary: citation, preprint, peer review, methodology, reproducibility

Tasks

  • Build a 5-source bibliography using DOIs only — no URLs, only doi.org links
  • Write a 200-word annotated bibliography: one paragraph per source
  • Use LLM Prompt 1.3 to improve academic language in your annotations
  • Commit the bibliography as a Markdown file to your GitHub repo
LLM Prompt 1.3 — First Pattern
"Here is my annotated bibliography: [paste text]. For each entry, tell me: (1) what operator phase this source covers, (2) one academic phrase I could use to connect it to my own research, (3) any vocabulary I should replace with more precise academic language."
Week 3 Outputannotated-bibliography.md committed to GitHub. 5 DOI-formatted citations. LLM feedback notes saved.
★ MILESTONE 1 — First Zenodo Publication
04week
Paper 1 — Compressed Literature Review (Zenodo Upload)
Operator C complete · Level A2 → B1 transition · DOI assigned
MILESTONE Write Publish — Zenodo GitHub

Write

  • Draft a 400-word literature review on one topic from Book 3 (biological compression, neural oscillations, or circadian regulation)
  • Structure: 3 paragraphs — C (what is known), K (the threshold / open question), F/U (what could follow)
  • Include 5 citations using DOIs. Include one citation from the Principia Orthogona series
  • Use LLM to check academic register, grammar, and argument flow

Publish

  • Upload to Zenodo as a dataset or report. Set license: CC BY 4.0
  • Fill metadata: title, abstract (100 words), keywords (5), author name, ORCID
  • Receive your DOI. Add it to your GitHub Research Log
  • Announce on GitHub README: "Paper 1 published: [doi.org/…]"
Week 4 Output — PUBLISHEDZenodo DOI for Paper 1. GitHub README updated. You are now a published researcher. Operator C: complete.
Koperator
Weeks 5 – 8 · CEFR B1 → B2
Curvature — The Threshold Claim

K is the moment the system meets its limit. In biology: κ*. In writing: the moment you commit to a claim. Phase K teaches the student to find falsifiable statements, construct literature bridges, and write a research proposal. The curvature threshold is not abstract — it is the line between description and argument. The researcher crosses it in Week 8.

Book 3 Chapters 4–6 Sportal Levels B1 · B2 Research Proposal GitHub Pages 6 LLM Prompts
05week
Neural Oscillations — Meeting the Curvature Threshold
Book 3 · Chapter 4 · Operator K · Level B1
Study Prompt 2.1 Write

Study

  • Book 3 Chapter 4: Neural Oscillations and κ* — the curvature threshold in the nervous system
  • Read Zenodo 10.5281/zenodo.19208015 (Biological Transitions). Identify the threshold claim on p.1
  • Learn: hypothesis, falsifiable claim, null hypothesis, confidence interval, p-value (conceptual)
  • Vocabulary: oscillation, entrainment, threshold, bifurcation, attractor basin

Tasks

  • Write 3 falsifiable claims about your field of interest (any domain: biology, language, physics, architecture)
  • For each claim, write one sentence that would prove it wrong (the falsification condition)
  • Use LLM Prompt 2.1 to evaluate the strength of your claims
  • Add "Research Questions" section to your GitHub README
LLM Prompt 2.1 — Threshold Identification
"Here are 3 research claims I have written: [paste claims]. For each, tell me: (1) is this falsifiable? (2) what evidence would be needed to test it? (3) how would a journal editor in this field phrase this claim more precisely?"
Week 5 Output3 falsifiable claims with falsification conditions. GitHub Research Questions section. LLM feedback saved as claim-evaluation.md.
06week
The Argument Architecture — From Claim to Structure
Book 3 · Chapter 5 · Operator K · Level B1
Study Prompt 2.2 · 2.3 Write

Study

  • Book 3 Chapter 5: Immune Adaptation — the threshold as the moment the system commits to a new orbit
  • Study argument structure: claim → evidence → warrant → backing → rebuttal (Toulmin model)
  • Read one Introduction section from any Principia Orthogona paper. Map its argument to Toulmin
  • Vocabulary: warrant, backing, rebuttal, concession, hedging language (it may be argued, evidence suggests)

Tasks

  • Select one of your Week 5 claims. Expand it into a 250-word argument paragraph using Toulmin structure
  • Use LLM Prompt 2.2 to identify weak warrants in your argument
  • Use LLM Prompt 2.3 to rewrite one sentence using more precise hedging language
  • Commit the argument paragraph to your repo as argument-draft.md
LLM Prompt 2.2 — Curvature Check
"Here is my argument paragraph: [paste text]. Identify: (1) the claim, (2) the evidence cited, (3) the implicit warrant connecting them. Is the warrant stated or assumed? What would a reviewer ask about the warrant?"
Week 6 Output250-word argument paragraph. Toulmin map saved. argument-draft.md in GitHub repo.
07week
The Literature Bridge — Connecting Your Claim to the Field
Book 3 · Chapter 6 · Operator K → F · Level B2
Study Prompt 3.1 Write GitHub

Study

  • Book 3 Chapter 6: Three Falsifiable Predictions — how the series documents what it has not yet proved
  • Study how to write a literature bridge: the sentence that connects your claim to an existing finding
  • Read the Related Work or Background section of two papers from Zenodo. How do they connect to prior literature?
  • Vocabulary: prior work, in line with, consistent with, extends, challenges, contributes to

Tasks

  • Write a 300-word Background section that situates your research claim within 3 existing sources
  • Each source must be connected with an explicit bridge sentence ("This finding suggests that…", "Building on X, the present study…")
  • Use LLM Prompt 3.1 to evaluate bridge strength
  • Enable GitHub Pages for your repo — your research log is now live on the web
LLM Prompt 3.1 — Bridge Evaluation
"Here is my Background section: [paste text]. For each literature bridge sentence, tell me: (1) does this sentence logically connect the prior work to my claim? (2) what is the implicit assumption? (3) suggest a stronger bridge using a hedged academic phrase."
Week 7 Output300-word Background section. GitHub Pages live at [username].github.io/[repo]. background.md committed.
★ MILESTONE 2 — Research Proposal + GitHub Documentation
08week
Paper 2 — Research Proposal (Zenodo + GitHub Pages)
Operator K complete · Level B2 → C1 transition · Full proposal published
MILESTONE Write Publish — Zenodo GitHub Pages

Write

  • Write a 700-word Research Proposal: Introduction (Background + gap), Research Question, Methodology sketch, Expected Contribution
  • Use your Week 7 Background section as the opening. Your Week 5 claim becomes the Research Question
  • Add one paragraph on Methods: how would you collect or generate evidence?
  • Add one paragraph on Expected Contribution: what does this add to the field?

Publish + Document

  • Upload the proposal to Zenodo. Get your second DOI
  • Write a complete GitHub repo README: project title, abstract (from Zenodo), DOI badge, weekly log table
  • Publish on GitHub Pages. Your research is now publicly searchable
  • Use LLM Prompt 3.2 for a final language review of the full proposal before upload
Week 8 Output — PUBLISHEDZenodo DOI for Paper 2 (Research Proposal). GitHub Pages live with DOI badge. Operator K: complete. You have a public research identity.
Foperator
Weeks 9 – 12 · CEFR C1
Fold — Writing the Full Paper

F is where the structure folds into a complete form. In biology: the protein folds, the circadian rhythm locks. In writing: the draft becomes a paper. Phase F takes the student from a proposal to a complete academic paper — introduction through discussion — using the operator chain as the organizing principle. The Fold is irreversible. Once the paper exists, it cannot be unread.

Book 3 Chapters 7–9 Sportal Levels C1 · D1 Full Paper Draft Zenodo Preprint 6 LLM Prompts
09week
IMRaD as Operator Chain — Structuring the Full Paper
Book 3 · Chapter 7 · Operator F · Level C1
Study Prompt 3.3 · 4.1 Write

Study

  • Book 3 Chapter 7: The Complete Circuit — how the operator chain closes at g₃₃ = 33
  • IMRaD = Introduction (C) · Methods (K) · Results (F) · Discussion (U). Each section IS an operator
  • Read the full structure of one Zenodo paper from Principia Orthogona. Map every section to C/K/F/U
  • Vocabulary: methodology, data generation, results, interpretation, implication, limitation

Tasks

  • Draft a full paper outline: title, abstract (150 words), section headings, one bullet per paragraph
  • The outline must cover all 4 sections. Methods should describe HOW you would test your claim
  • Use LLM Prompt 3.3 to expand any section that is too thin
  • Commit the outline to GitHub as paper-outline.md
LLM Prompt 3.3 — Structure Audit
"Here is my paper outline: [paste]. Evaluate the Methods section. Does it specify: (1) what data or evidence I will use? (2) how I will analyze it? (3) what would count as a positive result? Expand the Methods into 3 specific steps I could follow."
Week 9 OutputFull paper outline in paper-outline.md. 150-word abstract drafted. Section headings committed.
10week
Writing the Introduction and Methods — The Fold Begins
Book 3 · Chapter 8 · Operator F · Level C1
Study Prompt 4.2 Write

Study

  • Book 3 Chapter 8 (Greek series): π — why periodicity underlies all academic argument
  • Study Introduction writing: CARS model (Create a Research Space) — establish territory, establish niche, occupy niche
  • Study Methods writing: past tense, passive voice, precision, replicability language
  • Vocabulary: established, niche, gap, replication, operationalize, measurable

Tasks

  • Write Introduction section (400 words): background → gap → your claim → paper structure
  • Write Methods section (300 words): what you did or will do, step by step, past or conditional tense
  • Use LLM Prompt 4.2 to check passive voice usage and replicability language in Methods
  • Commit both sections as intro.md and methods.md
LLM Prompt 4.2 — Methods Language Check
"Here is my Methods section: [paste]. (1) Identify any sentence where the reader could not replicate what I describe — what is missing? (2) Convert any active-voice sentences to passive where appropriate for academic register. (3) What one sentence would make this section significantly stronger?"
Week 10 Outputintro.md (400w) and methods.md (300w) committed. Introduction follows CARS model. Methods is replicable.
11week
Results and Discussion — Completing the Fold
Book 3 · Chapter 9 · Operator F → U · Level C1 → D1
Study Prompt 4.3 · 5.1 Write

Study

  • Book 3 Chapter 9 (Greek series): φ — Fibonacci as subcritical growth (results that approach, not reach, the threshold)
  • Results section: present findings without interpretation. Use tables, numbered points, operator notation where relevant
  • Discussion section: connect results to claim, acknowledge limitations, state implications
  • Vocabulary: the results indicate, contrary to expectations, a limitation of the present study, future research should

Tasks

  • Write Results section (250 words): state what you found or predicted you would find. Be specific
  • Write Discussion section (350 words): interpret findings, connect to your Week 5 claim, state one limitation
  • Write Conclusion (100 words): one paragraph — what does this mean and what comes next?
  • Use LLM Prompt 5.1 to audit Discussion for overclaiming language
LLM Prompt 5.1 — Overclaim Audit
"Here is my Discussion section: [paste]. Identify any sentences where I claim more than my evidence supports. For each, suggest a hedged rewrite. Also: what is the single strongest implication I can state without overclaiming?"
Week 11 Outputresults.md + discussion.md + conclusion.md committed. Full paper draft assembled as paper-draft.md.
★ MILESTONE 3 — Full Paper Preprint on Zenodo
12week
Paper 3 — Complete Scientific Paper (Zenodo Preprint)
Operator F complete · Level C1 · Full IMRaD paper with DOI
MILESTONE Write Publish — Zenodo Preprint GitHub Release

Finalize

  • Assemble the full paper from all previous sections into one document (1,200–1,500 words total)
  • Write a 200-word abstract: background sentence, gap sentence, claim sentence, methods sentence, result sentence, implication sentence
  • Add References section: minimum 5 DOIs, correct academic format
  • Use LLM Prompt 5.2 for a complete language review — grammar, register, and coherence

Publish

  • Upload to Zenodo as a Preprint. Select the most relevant subject area
  • Create a GitHub Release (v1.0.0) tagged to the current commit — the paper is now version-controlled
  • Add the new DOI to your GitHub Pages site. Update the README DOI badge
  • Share the Zenodo DOI link with one other person and ask for one sentence of feedback
Week 12 Output — PUBLISHEDZenodo DOI for Paper 3 (full preprint). GitHub Release v1.0.0. GitHub Pages updated. Operator F: complete. You have a peer-readable scientific paper.
Uoperator
Weeks 13 – 16 · CEFR D1 → D2
Unfolding — Verification, Publication, and the Fixed Point

U is the completion. In biology: the organism has grown. In writing: the paper has been published, reviewed, and verified. Phase U teaches revision from reviewer comments, introduces formal mathematical verification via AXLE (Lean 4), and closes the circuit at D2. D2 is not a metaphor — it is the threshold Θ = g₃₃ + N × M, where N is the number of researchers and M is the number of operator cycles completed. At Week 16, you cross it.

Book 3 Chapters 10–13 Sportal Levels D1 · D2 AXLE Lean 4 Final Publication 9 LLM Prompts
13week
Revision and Peer Review — The Operator Reads Your Paper
Book 3 · Chapter 10 · Operator U · Level D1
Study Prompt 5.3 · 6.1 Revise GitHub

Study

  • Book 3 Chapter 10: Lyapunov Exponent — what does it mean for a system to be stable under perturbation? Your paper must be stable under critique
  • Study peer review language: "the authors claim", "the evidence does not support", "I recommend major revision"
  • Read one set of real reviewer comments (many Zenodo papers include revision notes)
  • Vocabulary: major revision, minor revision, referee, scope, novelty, contribution

Tasks

  • Use LLM Prompt 5.3: ask the LLM to act as a journal reviewer and give 3 critiques of your Week 12 paper
  • Write a 300-word "Response to Reviewers" document: acknowledge each critique and state what you will revise
  • Make the revisions. Commit revised paper as paper-v2.md. Create GitHub Release v2.0.0
  • Use LLM Prompt 6.1 to check that your revisions have addressed the original critique
LLM Prompt 5.3 — Reviewer Simulation
"Act as a peer reviewer for the journal [name a journal in your field]. Here is my paper: [paste abstract + introduction]. Give me exactly 3 critiques formatted as a real reviewer would write them. For each critique, tell me what specific change would address it."
Week 13 OutputResponse to Reviewers document. paper-v2.md committed. GitHub Release v2.0.0. The paper is now revision-stable.
14week
AXLE Verification — Formalizing Your Claim in Lean 4
Book 3 · Chapter 11 · Operator U · Level D1 → D2
Study Prompt 6.2 AXLE · Lean 4 GitHub

Study

  • Book 3 Chapter 11: Spectral Radius — what does machine verification mean for scientific claims?
  • Read the AXLE repository README at github.com/TOTOGT/AXLE. Understand what a Lean 4 theorem statement looks like
  • Study: what is a formal claim? A theorem vs. a conjecture vs. a sorry (honest acknowledgment of incompleteness)
  • Vocabulary: formal proof, lemma, theorem, axiom, sorry, Mathlib4, verification

Tasks

  • State your paper's main claim as a single formal sentence: "If [conditions], then [result]"
  • Use LLM Prompt 6.2 to translate your claim into a Lean 4 theorem stub (sorry-terminated — honest and correct)
  • Add an axle/ folder to your GitHub repo. Commit the Lean 4 stub as claim.lean with a sorry and a comment explaining what remains to be proved
  • Document the sorry: what lemma is missing? What data would close it?
LLM Prompt 6.2 — Lean 4 Translation
"Here is my research claim in natural language: [paste]. Translate this into a Lean 4 theorem stub that: (1) states the types involved, (2) names the theorem, (3) ends with 'sorry' to mark what is not yet proved. Add a comment explaining what mathematical lemma would be needed to close the sorry."
Week 14 Outputaxle/claim.lean in GitHub repo. Sorry documented with missing lemma named. Formal claim readable by any Lean 4 user.
15week
The Complete Research Package — DOI, Pages, and Citation
Book 3 · Chapter 12 · Operator U · Level D2
Study Prompt 6.3 · 7.1 Publish GitHub Pages

Study

  • Book 3 Chapter 12: The G6 Crystal in Living Systems — what does a complete, stable scientific structure look like?
  • Study: how to cite a Zenodo preprint in papers, how ORCID connects your works, how GitHub Pages is indexed
  • Study: open science practices — CC BY license, open data, reproducible code
  • Vocabulary: reproducibility, open access, citation graph, ORCID, indexed, discoverable

Tasks

  • Update your Zenodo profile: add ORCID, institutional affiliation (or "Independent Researcher"), link all 3 papers
  • Build a complete GitHub Pages site: home page with all 3 DOIs, abstract for each, link to AXLE claim stub
  • Use LLM Prompt 7.1 to draft a 100-word researcher bio in academic third-person
  • Add the bio to Zenodo, GitHub Pages, and your README
LLM Prompt 7.1 — Researcher Bio
"Write a 100-word academic researcher biography in third person for: [your name], [your field], independent researcher. Include: research focus (your topic), method (LLM-assisted operator chain analysis), and one published output ([your Zenodo DOI]). Tone: professional, factual, suitable for a journal submission."
Week 15 OutputGitHub Pages site with all 3 DOIs and researcher bio. Zenodo profile complete with ORCID link. You are discoverable.
★ MILESTONE 4 — D2 THRESHOLD · The Circuit Closes
16week
Paper 4 — Complete Circuit · The D2 Threshold Paper
Operator G complete · Level D2 · Θ = g₃₃ + N × M
D2 THRESHOLD Write Publish — Zenodo AXLE GitHub Release v3.0

Write

  • Book 3 Chapter 13: Three Falsifiable Predictions — the living chapter, the open frontier
  • Write a 300-word reflection paper: "What I Proved, What I Proposed, and What Remains Open"
  • Structure: Section 1 — what the three papers established. Section 2 — what the AXLE sorry marks as open. Section 3 — one prediction about your field for the next researcher to test
  • Use LLM Prompts 7.2 and 7.3 for final register and academic precision checks

Publish + Close the Circuit

  • Upload the reflection paper to Zenodo as Paper 4. Get your fourth DOI
  • Update your AXLE sorry: add one sentence to the comment stating the prediction from Section 3
  • Tag GitHub Release v3.0.0. This is the complete research package
  • You now have: 4 Zenodo DOIs · a public GitHub Pages site · a Lean 4 claim stub · a researcher bio. The circuit is closed.
LLM Prompt 7.3 — D2 Completion Check
"Here are my four papers: [list DOIs and one-sentence summaries]. As a D2-level evaluator: (1) does each paper advance beyond the previous one? (2) does the AXLE sorry correctly identify an open problem? (3) what would a senior researcher in this field say this body of work contributes?"
Week 16 Output — D2 THRESHOLD CROSSED4 Zenodo DOIs. Complete GitHub Pages site. AXLE claim stub with future prediction. GitHub Release v3.0.0. The student is now a researcher with a citable, verifiable, publicly documented body of work.
Θ = g₃₃ + N × M

The D2 threshold is mathematical. g₃₃ = 33 is the minimum operator cycles for a stable fixed point in any single-agent system. N is the number of researchers sharing the orbit. M is the number of complete operator cycles each has run. At Week 16, N = 1, M = 4 complete papers = 4 × 4 operators = 16 cycles. 16 + 33 = 49. The threshold is crossed. Complete Completeness.

By the End of 16 Weeks

Complete Deliverables

Every output below is public, citable, and permanently archived. The student leaves the course with a complete digital research identity.

Week Output Platform Persistent ID
1GitHub profile README — Research Log initializedgithub.com/[user]Public URL
2–3Annotated bibliography + argument draftGitHub repoGitHub commit SHA
4 ★Paper 1 — Compressed Literature ReviewZenodoDOI 1
5–7Falsifiable claims · Background section · GitHub Pages liveGitHub PagesPublic URL
8 ★Paper 2 — Research Proposal (700 words)Zenodo + GitHub PagesDOI 2
9–11Full paper draft — Intro, Methods, Results, DiscussionGitHub repoGitHub Release v1.0.0
12 ★Paper 3 — Complete Scientific Preprint (1,400 words)Zenodo PreprintDOI 3
13Response to Reviewers + revised paper v2GitHub Release v2.0.0Git tag v2.0.0
14AXLE claim stub in Lean 4 (axle/claim.lean)GitHub + AXLEGitHub path
15Complete GitHub Pages research site + researcher bioGitHub PagesPublic URL + ORCID
16 ★Paper 4 — D2 Reflection + Complete PackageZenodo + GitHub v3.0DOI 4
Formal Verification

AXLE — The Optional Proof Track

AXLE (Automated eXtensible Lean Engine) is the formal verification backbone of Principia Orthogona. Week 14 introduces it not as a requirement but as an opportunity — to state a claim so precisely that a machine can check whether it follows from known mathematics. A sorry is not failure. It is the most honest thing a researcher can write: "this is where the proof ends and the conjecture begins."

-- Week 14 student output template
-- Replace [YourClaim] with your theorem name
-- Replace [YourConditions] and [YourResult] with your claim

import Mathlib

/- Course: English for Researchers · Week 14
   Student: [Name] · ORCID: [your ORCID]
   Zenodo Paper 3: doi.org/[your DOI]

   Claim in natural language:
   "[Your research claim here — one sentence]"

   Missing lemma:
   "[What mathematical result would close this sorry?]"
   This is an open problem. Future work: [your prediction].
-/

theorem [YourClaim] ([YourConditions]) :
    [YourResult] := by
  sorry

The AXLE repository at github.com/TOTOGT/AXLE contains all 8 verified constants and 9 honest sorrys from the Principia Orthogona series. Student claim stubs can be submitted as pull requests — if the community closes a sorry, the student is a co-author on the proof.

"We perceive the unfolding first. The compression is invisible, underground, already done. This course teaches you to read backward — from what you can see to the structure that produced it."
— Pablo Nogueira Grossi · English for Researchers · C1 to D2
Complete Prompt Map

All 21 LLM Prompts — A1 to D2

Each prompt is designed to be used with any LLM. The student pastes the prompt, inserts their own text in the brackets, and works with the response. Prompts are cumulative — each one assumes the work of the previous weeks.

PromptLevelWeekFocus
1.1A11Operator chain as reading strategy — biology + language example
1.2A123-sentence abstract compression audit
1.3A13Annotated bibliography — operator phase + vocabulary feedback
2.1B15Falsifiable claim evaluation — evidence requirements
2.2B16Toulmin warrant audit — claim, evidence, implicit warrant
2.3B16Hedging language rewrite for one sentence
3.1B27Literature bridge evaluation — logical connection test
3.2B28Full proposal language review before Zenodo upload
3.3C19Methods section expansion — 3 replicable steps
4.1C19Paper outline structure audit — thin sections identified
4.2C110Methods passive voice + replicability check
4.3C111Results section — findings without interpretation
5.1C111Overclaim audit in Discussion — hedged rewrites
5.2C112Full paper language review — grammar, register, coherence
5.3D113Peer reviewer simulation — 3 formal critiques
6.1D113Revision verification — did the changes address the critique?
6.2D114Lean 4 theorem stub translation — sorry + missing lemma
6.3D115Open science checklist — reproducibility, license, metadata
7.1D215Academic researcher bio — third person, 100 words
7.2D216Reflection paper — final register and precision check
7.3D216D2 completion check — body of work evaluated by senior researcher persona
🜁