Skill Loader

Dynamic Skill Loading via Polynomial Functor Arrangements

Based on Samantha Jarvis & David Spivak's work on dynamic structures, this skill treats skill loading as dynamic arrangement morphisms in the category Poly.

Polynomial Semantics

Each skill is an interface polynomial:

p_skill = Outputs^y^Inputs

Loading skills creates composite arrangements:

p₁ ⊗ p₂ → System

The state

S

determines which arrangement is active. Loading a skill updates

s : S

, rewiring the system dynamically.

Usage

# Load a single skill
bb ~/.claude/skills/skill-loader/load.bb skill-name

# Load multiple skills with GF(3) trit assignment
bb ~/.claude/skills/skill-loader/load.bb skill1:-1 skill2:0 skill3:+1

# List loadable skills
bb ~/.claude/skills/skill-loader/load.bb --list

# Query skill lattice
bb ~/.claude/skills/skill-loader/load.bb --lattice

# Reverse derivative: find skills that influence current state
bb ~/.claude/skills/skill-loader/load.bb --reverse

Dynamic Arrangement Protocol

State Space

State = (M, move, f, m)

Where:

• M

  = Parameterizing object (skill configuration space)

• move : F(M) × F(M) → F(M)

  = State update function

• f : M × A → B

  = Skill morphism (input → output transformation)

• m : F(M)

  = Current parameter (loaded skill configuration)

Load Operation

Loading skill

s

creates arrangement morphism:

F(A) --[m × id]--> F(M) × F(A) --[F(f)]--> F(B)

Update Rule

After skill execution, update state via reverse derivative:

F(A) × F(B) --[R[f]]--> F(M) × F(A) --[π; move]--> F(M)

GF(3) Trit Assignment

Skills loaded in triads conserve:

Σ trits ≡ 0 (mod 3)

Trit	Role	Hue Range
-1 (MINUS)	Validator/Constrainer	180°-300° (cold)
0 (ERGODIC)	Coordinator/Synthesizer	60°-180° (neutral)
+1 (PLUS)	Generator/Executor	0°-60°, 300°-360° (warm)

Babashka Implementation

(ns skill-loader
  (:require [babashka.fs :as fs]
            [clojure.edn :as edn]
            [clojure.string :as str]))

(def skills-dir (str (System/getProperty "user.home") "/.claude/skills"))

(defn list-skills []
  (->> (fs/list-dir skills-dir)
       (filter fs/directory?)
       (map fs/file-name)
       (filter #(fs/exists? (fs/path skills-dir % "skill.md")))
       sort))

(defn parse-frontmatter [content]
  (when-let [[_ yaml] (re-find #"(?s)^---\n(.*?)\n---" content)]
    (reduce (fn [m line]
              (if-let [[_ k v] (re-find #"^(\w+):\s*(.+)$" line)]
                (assoc m (keyword k) v)
                m))
            {} (str/split-lines yaml))))

(defn load-skill [skill-name]
  (let [path (fs/path skills-dir skill-name "skill.md")]
    (when (fs/exists? path)
      (let [content (slurp (str path))
            meta (parse-frontmatter content)]
        {:name skill-name
         :meta meta
         :content content
         :loaded-at (System/currentTimeMillis)}))))

(defn load-triad [s1 s2 s3]
  "Load three skills with GF(3) conservation"
  (let [skills [(assoc (load-skill s1) :trit -1)
                (assoc (load-skill s2) :trit 0)
                (assoc (load-skill s3) :trit +1)]]
    {:skills skills
     :sum (reduce + (map :trit skills))
     :conserved? (zero? (mod (reduce + (map :trit skills)) 3))}))

Integration with Dynamic Categories

Following (Shapiro & Spivak 2022), skill loading forms a dynamic monoidal category where:

• Objects are skill interfaces
• Morphisms are arrangements
• State updates follow reverse derivative backpropagation

This enables gradient-based skill optimization analogous to neural network training.

References

• Jarvis, S. (2024). "Building dynamic structures". Topos Institute Blog.
• Shapiro, B.T. & Spivak, D.I. (2022). "Dynamic Categories, Dynamic Operads: From Deep Learning to Prediction Markets."
• Cockett et al. (2020). "Reverse Derivative Categories." CSL 2020.