docs(readme): convert README.adoc -> Markdown README.md (#26)

README must be real Markdown to render in GitHub community-health, the GitHub
profile, and external MCP directories (Glama) — AsciiDoc shows as raw markup
there. pandoc asciidoc->GFM, badges fixed to clickable, SPDX header kept as an
HTML comment, duplicate README.adoc removed.

Co-authored-by: Claude Opus 4.8 <noreply@anthropic.com>

Author: hyperpolymath

README.adoc

@@ -0,0 +1,119 @@
+<!--
+SPDX-License-Identifier: CC-BY-SA-4.0
+SPDX-FileCopyrightText: 2025-2026 Jonathan D.A. Jewell <j.d.a.jewell@open.ac.uk>
+-->
+
+[![OpenSSF Best Practices](https://img.shields.io/badge/OpenSSF-Best_Practices-green?logo=opensourcesecurity)](https://www.bestpractices.dev/en/projects/new?repo_url=https://github.com/hyperpolymath/frayed-knot-toolkit)
+[![License: PMPL-1.0](https://img.shields.io/badge/License-MPL--2.0-blue.svg)](https://github.com/hyperpolymath/palimpsest-license) <embed
+src="https://api.thegreenwebfoundation.org/greencheckimage/github.com"
+data-link="https://www.thegreenwebfoundation.org/green-web-check/?url=github.com" />
+
+This directory contains the formalization of **Frayed Knot** theory
+using the dependently typed programming language and proof assistant
+**Agda**. It provides foundational definitions, topological states, and
+structural facts regarding knot crossings, resolutions, and strand
+choreographies.
+
+This project provides a comprehensive toolkit for formalizing Frayed
+Knot Theory.
+
+<div id="toc">
+
+</div>
+
+# Overview
+
+The project explores the mathematics and topology of "frayed" knots. It
+models knots mathematically by defining strands, orientations, crossing
+signs (Positive, Negative), and resolutions (A-Smooth, B-Smooth). The
+toolkit is designed to formally verify and prove structural properties
+about knot crossings and the choreographic interactions of their
+strands.
+
+# Project Structure
+
+The project primarily consists of Agda (`.agda`) files that construct
+the formal proofs and definitions, alongside an empty Julia (`.jl`) file
+intended for future numerical or programmatic implementation.
+
+## Core Modules
+
+- `FrayedKnot.agda` Defines the basic topological objects including:
+
+  - `Resolution` (`A-Smooth`, `B-Smooth`)
+
+  - `CrossingSign` (`Positive`, `Negative`)
+
+  - `BranchKind` (`Split`, `Preserve`)
+
+  - `TopologicalState` (Tracking component counts and resolution
+    history)
+
+  - Logic for resolving crossings and fraying nodes, including
+    structural lemmas and successor-state proofs.
+
+<!-- -->
+
+- `ChoreographicFrayedKnot.agda` Focuses on the choreographic aspects of
+  strands. It defines `Strand` types, `Orientation` (`Over`, `Under`),
+  `Distinct` proofs for strands, and projects knot paths, capturing
+  navigation over and under crossings.
+
+<!-- -->
+
+- `FrayedKnotDiagram.agda` & `FrayedKnotLabeled.agda` (Core internal
+  modules) Define the structures for constructing diagrams from
+  crossings and applying labels to track crossing signs and topological
+  states across a full diagram.
+
+<!-- -->
+
+- `FrayedKnotExamples.agda` Contains practical examples and theorems.
+  For instance, it provides diagrams (`allPositive₂`, `mixed₂`),
+  constructs explicit toy signatures/profiles, and formally proves
+  distinction theorems (e.g., `profiles-differ`) which show that
+  different crossing configurations yield mathematically distinct
+  profiles.
+
+<!-- -->
+
+- `FrayedKnotUniformity.agda` Explores uniformity properties and lemmas
+  across the knot formalization.
+
+<!-- -->
+
+- `frayed_knot.jl` A placeholder Julia script indicating planned support
+  for numerical analysis, simulation, or algorithm execution related to
+  frayed knots.
+
+# Getting Started
+
+To verify the proofs in this project, you need to have **Agda**
+installed along with the **Agda Standard Library**.
+
+1.  **Install Agda:** Follow the instructions on the [Agda
+    Wiki](https://wiki.portal.chalmers.se/agda/pmwiki.php) or your
+    package manager.
+
+2.  **Type-check the project:** You can load the root files in your
+    editor (e.g., using Emacs with `agda-mode`) to verify all proofs, or
+    run: `` `bash `` `agda` `FrayedKnotExamples.agda`\`
+
+# Theory and Architecture
+
+The theoretical foundation builds on basic knot theory concepts (like
+the Kauffman bracket’s A/B smoothings) and extends them to "frayed"
+interpretations. It tracks how local resolutions affect the global
+topological state (e.g., the number of components) and uses dependent
+types to statically guarantee structural facts—such as the binary nature
+of fraying and the impossibility of profile equalities between distinct
+knot configurations.
+
+# Status
+
+The Agda formalization is currently in active development with several
+foundational lemmas and main distinction theorems already proven. The
+Julia script represents planned numerical support, reflecting the
+hyperpolymath architectural preference for cross-language workflows (in
+this case, Agda for proofs and Julia for high-performance scientific
+computing).