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feat: scaffold OpenLearn course structure
Directory tree + module-0 placeholder + bibliography stub for an OpenLearn-style free course introducing the KRL stack. 8-module outline covers: resolution as central op, TangleIR, stack layers, construct/transform/resolve/retrieve, and (blocked on user notes) Verisim octadic framework + Katagoria/TypeLL/tropical types. Content itself is pending; this commit is structural scaffolding only. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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openlearn/README.md

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# KRL — OpenLearn Course
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An OpenLearn-style free course introducing the KRL stack: what it is, why it
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exists, and how to use it.
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## Status
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**Scaffold.** Directory structure is in place. Content is pending.
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## Intended audience
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- Mathematicians new to computational knot theory
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- Programmers curious about domain-specific query languages grounded in algebra
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- Open University OpenLearn browsers looking for a worked example of
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formal/algebraic DSL design
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## Intended scope
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### Module 0 — Why "Resolution"?
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Knot theory's skein relations, how resolution is the central operation,
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why "query" would undersell it.
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### Module 1 — Tangles and TangleIR
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Open tangles, closed tangles, ports, crossings, PD codes, composition.
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Introduce TangleIR as the canonical interchange object.
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### Module 2 — The KRL Stack
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Stack layers: KRL surface → TanglePL → TangleIR → Skein.jl + KnotTheory.jl
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via KRLAdapter.jl → QuandleDB semantic fingerprints.
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### Module 3 — Constructing Knots in KRL
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Walkthrough: trefoil, figure-eight. Running a KRL program through the stack.
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### Module 4 — Transforming (Reidemeister)
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R1, R2, R3 moves. Simplification. Isotopy invariants.
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### Module 5 — Resolving (Equivalence)
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Quandle presentations. Fundamental quandle as a functor. Colouring counts.
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### Module 6 — Retrieving (Query + Persistence)
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Skein.jl as the store; query by invariant.
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### Module 7 — Where KRL Fits in the Verisim Framework (optional advanced)
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Octadic structure, observation functors, KRL as a resolution system.
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### Module 8 — Towards Types (advanced)
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Tropical types, Katagoria/TypeLL integration. (Requires user's notes to be
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written first.)
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## Directory layout
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```
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openlearn/
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├── README.md (this file)
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├── modules/ (module content — markdown/adoc/notebook)
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├── exercises/ (interactive exercises, worksheets)
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└── references/ (bibliography, links, pre-reqs)
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```
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## Prerequisites (candidates for pre-reqs / "If you already know..." boxes)
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- Basic linear algebra
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- Undergraduate abstract algebra (groups, modules — not strictly required)
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- Ability to read Julia or follow pseudocode
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- No prior knot theory required (covered from scratch)
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## Target duration
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~8–12 hours of study (typical OpenLearn course length).
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## Contribution notes
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Each module should include:
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1. Learning outcomes (3–5 bullet points)
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2. Narrative explanation with diagrams (SVG preferred)
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3. Interactive exercises that can run in the KRL playground
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4. "Reflection" prompt at the end
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5. References to further reading
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Modules 7 and 8 are blocked on the user's own notes crystallising
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(Verisim octadic framework, Katagoria, TypeLL, tropical types).
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# Module 0 — Why "Resolution"?
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**Draft placeholder. Content to be written.**
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## Learning outcomes
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After this module you will be able to:
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1. State what the skein relation is in knot theory
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2. Explain what "resolving a crossing" means algebraically
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3. Describe why "query" undersells what the KRL language does
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4. Give the four operations KRL supports and how each relates to resolution
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## Content (to be written)
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- The skein relation
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- Crossing resolution as the algebraic heart of invariant computation
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- From "resolve a crossing" to "resolve structure, equivalence, and queries"
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- The four KRL operations: Construct, Transform, Resolve, Retrieve
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## Exercises
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- To be added
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## Reflection
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- To be added
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## References
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- To be added
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# Bibliography — KRL OpenLearn Course
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Key references for the KRL stack.
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## Knot theory
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- Kauffman, L. H. — *On Knots* (foundational)
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- Manturov, V. O. — *Knot Theory*
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- Lickorish, W. B. R. — *An Introduction to Knot Theory*
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## Quandles
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- Joyce, D. — "A classifying invariant of knots, the knot quandle" (1982)
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- Carter, J. S. — *A Survey of Quandle Ideas*
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## Skein relations
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- Jones, V. F. R. — the Jones polynomial papers
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- HOMFLY — Freyd, Yetter, Hoste, Lickorish, Millett, Ocneanu
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## Computational knot theory
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- KnotInfo (knotinfo.math.indiana.edu)
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- SnapPy
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## Category theory for knot theory
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- Baez, J. and Dolan, J. — "Higher-dimensional algebra and topological quantum field theory"
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## Tangle algebras and compositional diagrams
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- Turaev, V. — *Quantum Invariants of Knots and 3-Manifolds*
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## (To be added) Verisim octadic framework
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- User's own notes — not yet written
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## (To be added) Katagoria, TypeLL, tropical types
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- User's own notes — not yet written

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