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cat Skill: Derivational Pipe Chaining
Based on SOC occupation classification
| name | cat |
| description | cat Skill: Derivational Pipe Chaining |
| version | 1.0.0 |
Trit: 0 (ERGODIC - coordinator) Color: #26D826 (Green) Principle: Chain operations via derivational succession, not temporal
The cat skill implements the |> pipe operator using derivational chaining instead of temporal succession. Each pipe stage advances a seed: seed_{n+1} = f(seed_n, trit_n).
pipe_chain: A |> f |> g |> h
seed₀ → f(seed₀, trit_f) → seed₁
seed₁ → g(seed₁, trit_g) → seed₂
seed₂ → h(seed₂, trit_h) → seed₃
GF(3) conservation: Σ(trit_f + trit_g + trit_h) ≡ 0 (mod 3)
(ns cat.pipe
(:require [clojure.string :as str]))
(def GAMMA 0x9E3779B97F4A7C15)
(def MIX 0xBF58476D1CE4E5B9)
(def MASK64 0xFFFFFFFFFFFFFFFF)
(defn chain-seed [seed trit]
(bit-and (unchecked-multiply
(bit-xor seed (* trit GAMMA))
MIX)
MASK64))
(defmacro |>
"Derivational pipe with GF(3) tracking"
[seed & forms]
(reduce (fn [acc [f trit]]
`(let [result# (~f ~acc)
new-seed# (chain-seed (:seed ~acc) ~trit)]
(assoc result# :seed new-seed# :trit ~trit)))
`{:value ~seed :seed 0x42D :trit 0}
(partition 2 forms)))
# Pipe with GF(3) conservation
bb -e "(require '[cat.pipe :refer [|>]])
(|> 'input'
[read-fn -1] ; MINUS: validate
[transform-fn 0] ; ERGODIC: coordinate
[write-fn +1]) ; PLUS: generate
; => GF(3) sum = 0 ✓"
# Run pipe chain
just cat-pipe 'input' -1 0 +1
# Verify GF(3) conservation
just cat-verify-gf3 chain.edn
Forms triads with temporal-coalgebra (-1) and synthetic-adjunctions (+1):
temporal-coalgebra (-1) ⊗ cat (0) ⊗ synthetic-adjunctions (+1) = 0 ✓
Skill Name: cat
Type: Pipe Coordinator
Trit: 0 (ERGODIC)
Replaces: dypler-mcp (not found in npm)
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
category-theory: 139 citations in bib.duckdbThis skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):
Concepts: generic arithmetic, coercion, symbolic, numeric
cat (−) + SDF.Ch3 (○) + [balancer] (+) = 0
Skill Trit: -1 (MINUS - verification)
Generic arithmetic crosses type boundaries. This skill handles heterogeneous data.
This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:
Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.
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