Pun Decomposition Skill (MINUS -1)

"A pun exploits multiple valid decompositions of the same phonetic surface."

Core Insight

A pun is an information reflow that maps a single surface form to multiple semantic contexts. The humor arises from the unexpected context switch—the inductive bias favors one parse, but the pun activates another.

pun : Surface → {Context₁, Context₂, ...}
where each Contextᵢ has a valid decomposition

Neighbor Awareness (Braided Monoidal)

This skill knows its neighbors in the triad:

Position	Skill	Trit	Role
Left	gestalt-hacking	0	Perceptual grouping exploitation
Self	pun-decomposition	-1	Multiple parse validation
Right	acsets	0	Schema-aware decomposition

Yang-Baxter coherence:

(σ₁⊗id)(id⊗σ₁)(σ₁⊗id) = (id⊗σ₁)(σ₁⊗id)(id⊗σ₁)

GF(3) Triads

pun-decomposition (-1) ⊗ gestalt-hacking (0) ⊗ gay-mcp (+1) = 0 ✓  [Core Pun]
pun-decomposition (-1) ⊗ acsets (0) ⊗ topos-generate (+1) = 0 ✓  [Schema Pun]
pun-decomposition (-1) ⊗ reflow (0) ⊗ gay-mcp (+1) = 0 ✓  [Reflow Pun]
three-match (-1) ⊗ gestalt-hacking (0) ⊗ gay-mcp (+1) = 0 ✓  [Pattern Match]

Pun as Gestalt Attack

From the gestalt hacking thread:

enum GestaltPrinciple {
    Proximity,    // Close morphemes group
    Similarity,   // Similar sounds group  
    Closure,      // Incomplete parse completed
    Continuity,   // Smooth phonetic path preferred
    FigureGround, // Dominant meaning masks secondary
}

A pun exploits Closure and FigureGround:

• Closure: The listener completes the parse with the expected meaning
• FigureGround: The secondary meaning lurks in background until activated

Decomposition Types

Morphemic Decomposition

# "I'm reading a book about anti-gravity. It's impossible to put down."
{
  surface: "put down",
  decompositions: [
    { parse: ["put", "down"], meaning: "place on surface", trit: 1 },
    { parse: ["put-down"], meaning: "stop reading", trit: -1 },
  ],
  inductive_bias: 0.7,  # Favors first parse
  pun_strength: 0.3     # Second parse activation
}

Phonetic Decomposition

# "Time flies like an arrow. Fruit flies like a banana."
{
  surface: "flies like",
  decompositions: [
    { parse: ["flies", "like"], pos: ["verb", "prep"], trit: 1 },
    { parse: ["flies", "like"], pos: ["noun", "verb"], trit: -1 },
  ],
  gestalt_principle: :figure_ground,
  context_switch: "arrow → banana"
}

Etymological Decomposition

# From the reflow skill:
{
  word: "trimester",
  decomposition: ["tri-", "mester"],
  trits: [0, 0],
  gf3_sum: 0,  # Balanced!
  resonance: :strong
}

{
  word: "semester", 
  decomposition: ["se-", "mester"],  # se- = six (2×3)
  trits: [0, 0],
  gf3_sum: 0,  # Also balanced via factorization
  resonance: :moderate
}

ACSet Schema for Puns

@present SchPun(FreeSchema) begin
  Surface::Ob
  Parse::Ob
  Morpheme::Ob
  Meaning::Ob
  
  surface::Hom(Parse, Surface)
  morphemes::Hom(Morpheme, Parse)
  meaning::Hom(Parse, Meaning)
  
  # Attributes
  Text::AttrType
  Trit::AttrType
  Bias::AttrType
  
  text::Attr(Surface, Text)
  trit::Attr(Parse, Trit)
  bias::Attr(Parse, Bias)
end

@acset_type Pun(SchPun, index=[:surface, :meaning])

Inductive Bias as Prior

The inductive bias determines which decomposition is "default":

P(parse₁ | surface) = softmax(bias₁ / τ)
P(parse₂ | surface) = softmax(bias₂ / τ)

where τ = temperature (context sensitivity)

At low temperature (focused context), one parse dominates. At high temperature (open context), multiple parses activate → PUN.

OpenGame Structure

From gestalt hacking thread:

┌─────────────────────────────────────────────────────────┐
│  PunGame ∆                                              │
│  ─────────────────────────────────────────────────────  │
│  play     :: Surface → ∆ [Parse]     ← enumerate parses │
│  evaluate :: [Parse] → Meaning       ← select by context│
│                                                         │
│  Pun = play produces multiple; evaluate oscillates      │
└─────────────────────────────────────────────────────────┘

Defense: 2-Poisson Disambiguation

When puns attack comprehension, use stochastic sampling:

impl PunDefender {
    fn disambiguate(&mut self, surface: &str) -> Parse {
        let parses = self.decompose(surface);
        
        if parses.len() > 1 {
            // Multiple valid parses detected
            let (_, selected) = self.poisson.next_arrival(0.0);
            // Use Poisson timing to break tie
            parses[selected.to_usize() % parses.len()].clone()
        } else {
            parses[0].clone()
        }
    }
}

LMBIH Seed Integration

Using the LMBIH seed (327833753928) for pun coloring:

# XIP-7074D4: LMBIH Etymological Resonance
seed = 327833753928  # "LMBIH".bytes → hex
index = 43

color_at(seed, index)  # => #7074D4 (purple-blue)

# The pun lives in the purple-blue spectrum:
# - Blue = validation (checking parses)
# - Purple = blend of generation + validation

Commands

just pun-decompose "time flies"     # Enumerate parses
just pun-triad gestalt acsets       # Show GF(3) triad
just pun-bias 0.7                   # Set inductive bias
just pun-attack closure             # Test gestalt attack

Related Skills

• gestalt-hacking (left neighbor): Perceptual grouping exploitation
• acsets (right neighbor): Schema-aware decomposition storage
• reflow: Cross-context meaning preservation
• three-match: Colored subgraph isomorphism for parse matching
• etymological-resonance: Morpheme-level decomposition

Files

• etymological_resonance.rb
• gestalt hacking thread
• chromatic verifier thread

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Graph Theory

• networkx [○] via bicomodule
  • Universal graph hub

Bibliography References

• algorithms

  : 19 citations in bib.duckdb

Cat# Integration

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

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.