recursive-string-diagrams

Recursive random string diagram generation with white trapezoid as the atomic skill primitive.

Primitives

Symbol	Name	Meaning
◁═══▷	White Trapezoid	Skill = morphism with typed ports
∘	Compose	Sequential skill chaining
⊗	Tensor	Parallel skill execution
↺	Trace	Feedback loop / recursion

GF(3) Trit Assignment

Each white trapezoid carries a trit:

• MINUS (-1): Constraining/validating skill
• ERGODIC (0): Neutral/transforming skill
• PLUS (+1): Generating/expanding skill

Conservation: Σ trits ≡ 0 (mod 3) across diagram

Usage

;; Generate random diagram depth 4
(random-diagram 0 4)

;; Render ASCII
(render-ascii diagram 0)

Example Output

⊗ tensor
  ↺ trace[1]
    ◁═══▷ [3→2] ergodic
  ∘ compose
    ◁═══▷ [2→2] minus
    ◁═══▷ [3→3] plus

Semantics (Rama Connection)

String Diagram	Rama Primitive
White Trapezoid	ETL topology
Compose (∘)	Depot chain
Tensor (⊗)	Parallel PStates
Trace (↺)	Recursive query

DisCoPy Integration

from discopy import Ty, Box, Diagram

# White trapezoid as Box
skill = Box('skill', Ty('in'), Ty('out'))

# Compose
d1 >> d2

# Tensor
d1 @ d2

# Trace
d.trace(n)

Skill Creation Protocol

1. Seed: White trapezoid with [inputs → outputs]
2. Recurse: Apply random {∘, ⊗, ↺} up to depth
3. Color: Assign GF(3) trits, verify conservation
4. Render: ASCII or DisCoPy SVG
5. Save: Write to ~/.claude/skills/<name>/SKILL.md

Related

• discopy - String diagram library
• acsets - Algebraic databases
• rama-gay-clojure - Rama + GF(3) colors