GF(3) PR Verification

Enforces skill coloring requirements on all contributions. PRs without valid GF(3) manifests will be rejected.

Why GF(3) Conservation?

Every contribution uses skills. Recording which skills were used:

1. Provenance: Track how code was created
2. Balance: Ensure generator/validator equilibrium
3. Reproducibility: Others can use same skill triads
4. Attribution: Credit skill authors

Required PR Format

Every PR body or comment MUST include:

## GF(3) Skill Coloring

| Skill | Trit | Color | Role |
|-------|------|-------|------|
| skill-name-1 | ⊕ (+1) | #RRGGBB | Generator |
| skill-name-2 | ○ (0) | #RRGGBB | Coordinator |
| skill-name-3 | ⊖ (-1) | #RRGGBB | Validator |

**Conservation**: Σ = (+1) + (0) + (-1) = 0 ✓

Thread: ⟨xxxx⟩

Trit Definitions

Trit	Symbol	Value	Role	Hue Range	Examples
PLUS	⊕	+1	Generator/Executor	0-60°, 300-360° (warm)	gay-mcp, gaymove, depth-search
ERGODIC	○	0	Coordinator/Synthesizer	60-180° (neutral)	acsets, aptos-agent, ducklake-walk
MINUS	⊖	-1	Validator/Constrainer	180-300° (cold)	code-review, narya-proofs, three-match

Conservation Rules

Rule 1: Single PR Conservation

Σ trits ≡ 0 (mod 3)

Valid combinations:

• ⊕ ⊗ ○ ⊗ ⊖ → 1 + 0 + (-1) = 0 ✓
• ⊕ ⊗ ⊕ ⊗ ⊖ ⊗ ⊖ → 1 + 1 + (-1) + (-1) = 0 ✓
• ○ ⊗ ○ ⊗ ○ → 0 + 0 + 0 = 0 ✓

Invalid:

• ⊕ ⊗ ○ → 1 + 0 = 1 ≠ 0 (mod 3) ✗
• ⊕ ⊗ ⊕ → 1 + 1 = 2 ≠ 0 (mod 3) ✗

Rule 2: Cross-PR Triads

PRs can form balanced triads across the repository:

PR#23○ ⊗ PR#24⊕ ⊗ PR#25⊖ ⊢ Σ = 0 ✓

Document cross-PR links:

### Cross-PR Triad
This PR (⊕) balances with:
- PR#XX (○) - coordinator
- PR#YY (⊖) - validator

Rule 3: Thread Linkage

Include thread ID for provenance:

Thread: ⟨6d21⟩

Verification Commands

Check PR Body

# Extract and verify GF(3) from PR
gh pr view $PR --json body | jq -r '.body' | \
  grep -oE '[⊕○⊖]' | \
  awk 'BEGIN{s=0} {if($0=="⊕")s+=1; if($0=="⊖")s-=1}
       END{m=(s%3+3)%3; print "Σ="s" mod3="m; exit(m!=0)}'

Check All Open PRs

# Verify all open PRs have GF(3) manifests
for pr in $(gh pr list --json number -q '.[].number'); do
  echo -n "PR#$pr: "
  gh pr view $pr --json body | jq -r '.body' | \
    grep -q 'GF(3)' && echo "✓" || echo "✗ MISSING"
done

Generate Skill Manifest

# List skills used in this session
cat << 'EOF'
## GF(3) Skill Coloring

| Skill | Trit | Color | Role |
|-------|------|-------|------|
| gf3-pr-verify | ⊖ (-1) | #3541C7 | Validator |
| code-review | ⊖ (-1) | #3541C7 | Validator |
| gay-mcp | ⊕ (+1) | #FFD700 | Generator |

**Conservation**: Σ = (-1) + (-1) + (+1) = -1 ≡ 2 (mod 3) ⚠️
Need 1 more ⊕ or 2 more ⊖ to balance
EOF

CI/CD Integration

Add to .github/workflows/validate.yml:

- name: Verify PR GF(3) Conservation
  if: github.event_name == 'pull_request'
  run: |
    PR_BODY=$(gh pr view ${{ github.event.pull_request.number }} --json body -q '.body')

    # Check for GF(3) section
    if ! echo "$PR_BODY" | grep -q 'GF(3)'; then
      echo "::error::PR missing GF(3) Skill Coloring section"
      exit 1
    fi

    # Verify conservation
    SUM=$(echo "$PR_BODY" | grep -oE '[⊕○⊖]' | \
      awk 'BEGIN{s=0} {if($0=="⊕")s+=1; if($0=="⊖")s-=1} END{print s}')
    MOD=$((($SUM % 3 + 3) % 3))

    if [ "$MOD" -ne 0 ]; then
      echo "::error::GF(3) not conserved: Σ=$SUM (mod 3)=$MOD"
      exit 1
    fi

    echo "✓ GF(3) conserved: Σ=$SUM (mod 3)=0"

Common Triads

Development

code-review⊖ ⊗ aptos-agent○ ⊗ gaymove⊕ ⊢ 0

Research

narya-proofs⊖ ⊗ acsets○ ⊗ depth-search⊕ ⊢ 0

Infrastructure

three-match⊖ ⊗ ducklake-walk○ ⊗ gay-mcp⊕ ⊢ 0

This PR

gf3-pr-verify⊖ ⊗ code-review⊖ ⊗ autopoiesis⊕ ⊗ gay-mcp⊕ ⊢ 0
  = (-1) + (-1) + (+1) + (+1) = 0 ✓

Error Messages

Error	Meaning	Fix
PR missing GF(3) section	No skill manifest	Add ## GF(3) Skill Coloring section
GF(3) not conserved	Σ ≠ 0 (mod 3)	Add balancing skills
Invalid trit value	Not in {-1, 0, +1}	Use ⊖/○/⊕ symbols
Missing thread ID	No ⟨xxxx⟩	Link to ampcode thread

Operator Algebra

Skills combine via tensor product (⊗):

⟦s₁ ⊗ s₂⟧ = (trit₁ + trit₂, mix(color₁, color₂), xor(seed₁, seed₂))

Conservation law:

∀ PR: Σᵢ tritᵢ ≡ 0 (mod 3)

This ensures the skill lattice remains balanced across all contributions.

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

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.