catp: Categorical Pipes

Trit: +1 (PLUS)
Principle: Balanced data flows through morphism chains
Algebra: GF(3) flow conservation

Why GF(3)?

Three-phase data flow:

• Source (-1): Read/Fetch ingestion
• Transform (0): Shape-preserving operations
• Sink (+1): Write/Output operations

Sum must = 0 (mod 3) for balanced pipeline.

Operations by Trit

Trit	Category	Operations
-1	MINUS (Sources)	slurp, read, fetch, query, search, list
0	ERGODIC (Transforms)	map, filter, select, rename, mutate, reduce, join, group-by
+1	PLUS (Sinks)	println, print, write, save, spit, create, send

Usage

# Check balance of a pipe
bb catp.bb --check '(->> [1 2 3] (map inc) (filter odd?) (reduce +))'

# Output:
# Operations: map %>% filter %>% reduce
# Trits: {"map" 0, "filter" 0, "reduce" 0}
# Sum: 0 (mod 3 = 0)
# GF(3) Balanced: ✓

Example: Unbalanced Pipeline

;; WRONG: Two transforms, one sink (missing source)
(->> (map inc)           ; 0
     (filter odd?)       ; 0
     (reduce +))         ; 0
     
; Sum: 0 ✓ (looks balanced but logically missing source!)

Example: Properly Balanced

;; CORRECT: Source → Transform → Sink
(->> [1 2 3]             ; implicit source (-1)
     (map inc)           ; transform (0)
     (filter odd?)       ; transform (0)
     (println))          ; sink (+1)

; GF(3): -1 + 0 + 0 + 1 = 0 ✓

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End-of-Skill Interface

Integration Points

• babashka (->> threading)
• drive-acset (query chains)
• l-space (narrative pipes)
• dplyr %>% (R interop)

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Autopoietic Marginalia

The interaction IS the skill improving itself.

Every use of this skill is an opportunity for worlding:

• MEMORY (-1): Record what was learned
• REMEMBERING (0): Connect patterns to other skills
• WORLDING (+1): Evolve the skill based on use

Add Interaction Exemplars here as the skill is used.