S-Expression Neighborhood Index (0)

Complete catalog of sexp-using skills with triadic classification.

Trit: 0 (ERGODIC - index/coordinator)

Master Sexp Skill Taxonomy

┌─────────────────────────────────────────────────────────────────────────────┐
│                       SEXP SKILL NEIGHBORHOOD                                │
├─────────────────────────────────────────────────────────────────────────────┤
│                                                                              │
│   PLUS (+1) GENERATIVE              ERGODIC (0) BRIDGE                      │
│   ┌─────────────────────┐          ┌─────────────────────┐                  │
│   │ geb                 │          │ lispsyntax-acset    │                  │
│   │ cue-lang            │          │ nickel              │                  │
│   │ geiser-chicken      │          │ discopy             │                  │
│   │ cider-clojure       │          │ crdt-vterm          │                  │
│   │ borkdude            │          │ og (open-games)     │                  │
│   │ gay-mcp             │          │                     │                  │
│   └─────────────────────┘          └─────────────────────┘                  │
│                                                                              │
│   MINUS (-1) EXTRACTIVE                                                     │
│   ┌─────────────────────┐                                                   │
│   │ slime-lisp          │                                                   │
│   │ hof                 │                                                   │
│   │ intent-sink         │                                                   │
│   │ solver-fee          │                                                   │
│   └─────────────────────┘                                                   │
│                                                                              │
│   GF(3) BALANCED TRIADS:                                                    │
│   geb(+1) + nickel(0) + slime-lisp(-1) = 0 ✓                               │
│   cue-lang(+1) + nickel(0) + hof(-1) = 0 ✓                                 │
│   gay-mcp(+1) + lispsyntax-acset(0) + intent-sink(-1) = 0 ✓                │
│                                                                              │
└─────────────────────────────────────────────────────────────────────────────┘

Complete Skill Index

PLUS (+1) - Generative/Emissive

Skill	Description	Sexp Role
geb	Anoma categorical semantics	S-exp syntax for morphisms
cue-lang	Lattice config language	Exports to JSON (sexp-convertible)
geiser-chicken	Chicken Scheme REPL	Native sexp evaluation
cider-clojure	Clojure nREPL	EDN sexp format
borkdude	Babashka runtime	Clojure sexp scripting
gay-mcp	Deterministic colors	Color sexp nodes
unworld	Derivation chains	Sexp chain serialization

ERGODIC (0) - Bridge/Coordinator

Skill	Description	Sexp Role
lispsyntax-acset	LispSyntax ↔ ACSet	Bidirectional sexp conversion
nickel	Gradual typing config	JSON export, sexp bridge
discopy	String diagrams	Diagram ↔ sexp
crdt-vterm	Terminal CRDT	Sexp-based session recording
og	Open games	Game state as sexp
ombudsman	Neutral arbiter	Verifies sexp-encoded chains

MINUS (-1) - Extractive/Absorptive

Skill	Description	Sexp Role
slime-lisp	SLIME Common Lisp	Consumes sexp, returns values
hof	CUE code generation	Consumes config, emits code
intent-sink	Intent absorption	Nullifies sexp-encoded intents
solver-fee	Fee extraction	Extracts from sexp matches

GF(3) Balanced Triads

Triad 1: Lisp Dialects

geiser-chicken (+1) + lispsyntax-acset (0) + slime-lisp (-1) = 0
     Scheme              Bridge                Common Lisp

Triad 2: Configuration Languages

cue-lang (+1) + nickel (0) + hof (-1) = 0
   Lattice       Gradual      Codegen

Triad 3: Anoma/Intent

geb (+1) + discopy (0) + intent-sink (-1) = 0
  Types     Diagrams      Nullifiers

Triad 4: Color/State

gay-mcp (+1) + crdt-vterm (0) + solver-fee (-1) = 0
  Colors       Sessions         Extraction

Triad 5: Clojure Ecosystem

cider-clojure (+1) + borkdude (+1) + lispsyntax-acset (0) = +2
                    UNBALANCED - needs -2 skill

Fix: Add

clj-kondo-3color

as 0 or create extraction skill.

Bridge Patterns

Sexp → ACSet (lispsyntax-acset)

# Any sexp-producing skill → ACSet
sexp = parse_sexp("(graph (V 1 2 3) (E (1 2) (2 3)))")
acset = acset_of_sexp(GraphSchema, sexp)

Config → Sexp → ACSet

# CUE/Nickel → JSON → Julia
cue export config.cue | jq '.' > config.json
nickel export config.ncl > config.json

# Julia: JSON → Sexp → ACSet
using JSON3
data = JSON3.read("config.json")
sexp = json_to_sexp(data)
acset = sexp_to_acset(ConfigSchema, sexp)

Geb → Vampir → ZK

;; Geb sexp → Vampir IR → ZK proof
(geb-to-vampir 
  (comp (inject-left so1 so1) (terminal so1)))

Neighborhood Graph

graph TD
    subgraph "PLUS +1"
        GEB[geb]
        CUE[cue-lang]
        GEISER[geiser-chicken]
        CIDER[cider-clojure]
        BORK[borkdude]
        GAY[gay-mcp]
    end
    
    subgraph "ERGODIC 0"
        LISP[lispsyntax-acset]
        NICKEL[nickel]
        DISCO[discopy]
        CRDT[crdt-vterm]
    end
    
    subgraph "MINUS -1"
        SLIME[slime-lisp]
        HOF[hof]
        SINK[intent-sink]
        FEE[solver-fee]
    end
    
    GEB --> LISP
    CUE --> NICKEL
    GEISER --> LISP
    CIDER --> LISP
    GAY --> CRDT
    
    LISP --> SLIME
    NICKEL --> HOF
    DISCO --> SINK
    CRDT --> FEE

Usage

# List all sexp skills
grep -l "sexp\|S-expression\|lisp" ~/.claude/skills/*/SKILL.md

# Check GF(3) balance of a triad
python3 -c "
skills = {'geb': 1, 'nickel': 0, 'slime-lisp': -1}
print('Balanced:', sum(skills.values()) % 3 == 0)
"

# Find unbalanced triads
just sexp-audit

Cross-Skill Pipelines

Pipeline 1: Anoma Intent Compilation

Intent (sexp) → Geb (morphism) → Vampir (IR) → ZK (proof)
    +1              +1              0            -1

Pipeline 2: Config-to-Code

CUE (schema) → Nickel (contract) → Hof (template) → Code
    +1              0                  -1            output

Pipeline 3: Collaborative Terminal

Terminal → crdt-vterm (sexp) → localsend → peer
             0                    0         receive

Pipeline 4: Colored Lisp REPL

gay-mcp (color) → geiser (scheme) → display
   +1                 +1             visual

Files

• This index:

  ~/.claude/skills/sexp-neighborhood/SKILL.md

• Core bridge:

  ~/.claude/skills/lispsyntax-acset/SKILL.md

• Geb:

  ~/.claude/skills/geb/SKILL.md

• Config triad:

  ~/.claude/skills/{cue-lang,nickel,hof}/SKILL.md

---

Trit: 0 (ERGODIC - index/coordinator) Purpose: Exhaustive sexp skill awareness GF(3): Multiple balanced triads documented

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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.