ward-identity-checker

name	ward-identity-checker
description	Ward Identity Checker
version	1.0.0

Ward Identity Checker

Verify GF(3) conservation as Ward identities across RG flow with Markov blanket separation.

Seed

741086072858456200

Core Principle

Ward identities express symmetry conservation: Σ trit = 0 (mod 3) at every renormalization group (RG) level. Violations indicate "relevant operators" that break the symmetry.

MCP Calibration Data

markov_blanket:
  internal_states: ["#3FF1A7", "#10B99D", "#DF9811"]
  sensory_indices: [1, 2, 3]
  
active_inference:
  prediction_error: 0.5692
  free_energy: 0.6692
  recommendation: perceptual_inference
  
reafference:
  prediction: "#F7E182"
  sensation: "#3FF1A7"
  result: identity_mismatch

Predicates

GF3Conserved(level)

GF3Conserved(L) := Σᵢ trit(cᵢ) ≡ 0 (mod 3)
  where cᵢ ∈ colors_at_level(L)

BlanketIntact(state)

BlanketIntact(s) := ∀ internal ∈ s.internal_states,
  ∃ blanket ∈ s.sensory_states ∪ s.active_states
  such that internal ⊥ external | blanket

NoLeakage(flow)

NoLeakage(f) := GF3Conserved(f.source) ∧ GF3Conserved(f.target)
  ∧ Σ trit(f.source) = Σ trit(f.target)

Ward Identity Check Protocol

def check_ward_identity(colors: list[str], level: int) -> dict:
    """Verify Σ trit = 0 at RG level."""
    trits = [hex_to_trit(c) for c in colors]
    total = sum(trits) % 3
    
    return {
        "level": level,
        "trit_sum": total,
        "conserved": total == 0,
        "violation_type": None if total == 0 else "relevant_operator",
        "correction_needed": (3 - total) % 3
    }

def hex_to_trit(hex_color: str) -> int:
    """Map hex to GF(3) via hue angle."""
    r, g, b = int(hex_color[1:3], 16), int(hex_color[3:5], 16), int(hex_color[5:7], 16)
    hue = compute_hue(r, g, b)
    return int(hue / 120) % 3  # 0-119 → 0, 120-239 → 1, 240-359 → 2

Markov Blanket Separation

┌─────────────────────────────────────────────┐
│                 EXTERNAL                     │
│   (exafference: world-caused sensations)    │
├─────────────────────────────────────────────┤
│              BLANKET STATES                  │
│  Sensory: idx [1,2,3] → colors observed     │
│  Active:  predictions emitted               │
├─────────────────────────────────────────────┤
│                 INTERNAL                     │
│  #3FF1A7 (trit 1) ─┐                        │
│  #10B99D (trit 1) ─┼─ Σ = 3 ≡ 0 (mod 3) ✓  │
│  #DF9811 (trit 1) ─┘                        │
└─────────────────────────────────────────────┘

Violation Detection

When reafference check shows identity mismatch (prediction ≠ sensation):

Condition	Diagnosis	Action
GF3Conserved ∧ ¬BlanketIntact	Boundary leak	Reseal blanket
¬GF3Conserved ∧ BlanketIntact	Relevant operator	Add counterterm
¬GF3Conserved ∧ ¬BlanketIntact	Full symmetry break	RG flow unstable

Usage

# Via Gay.jl MCP
gay_seed 741086072858456200
gay_markov_blanket --internal-seed 741086072858456200 --sensory-indices "1,2,3"

# Check conservation
just ward-check --level 0 --colors "#3FF1A7,#10B99D,#DF9811"

Integration

• cybernetic-immune: Use Ward violations as non-self markers
• active-inference: Free energy ≈ Ward violation magnitude
• unworld: Color chain derivations must preserve Ward identity

References

• Ward-Takahashi identities in QFT
• Friston's Markov blanket formalism
• GF(3) trit arithmetic for color conservation

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

• general: 734 citations in bib.duckdb

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 3. Variations on an Arithmetic Theme

Concepts: generic arithmetic, coercion, symbolic, numeric

GF(3) Balanced Triad

ward-identity-checker (○) + SDF.Ch3 (○) + [balancer] (○) = 0

Skill Trit: 0 (ERGODIC - coordination)

Secondary Chapters

• Ch4: Pattern Matching
• Ch10: Adventure Game Example

Connection Pattern

Generic arithmetic crosses type boundaries. This skill handles heterogeneous data.

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.