recursive-string-diagrams Skill

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

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

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

Agent Skills: recursive-string-diagrams

Install this agent skill to your local

Skill Files