plurigrid Covariant Modification Skill
Trit: 0 (ERGODIC - coordinator) Color: Green (#26D826)
Overview
Covariant Modification unifies three skill patterns for safe, structure-preserving self-modification:
| Component Skill | Trit | Role | Pattern |
|---|---|---|---|
codex-self-rewriting |
+1 | Generator | Lisp-machine self-modification via MCP Tasks |
self-evolving-agent |
0 | Coordinator | Darwin Gödel Machine evolution loops |
covariant-fibrations |
-1 | Validator | Type families respect directed morphisms |
GF(3): (+1) + (0) + (-1) = 0 ✓
Core Concept: Covariant Transport
When skill A modifies itself, dependent skills B must transform covariantly:
modify_A
Skill_A ─────────────→ Skill_A'
│ │
uses │ COVARIANT │ uses'
│ TRANSPORT │
↓ ↓
Skill_B ─────────────→ Skill_B'
transport_f
Agda Definition
-- Skill fibration over dependency base
skill-fibration : (Base : SkillGraph) → (Fiber : Base → SkillVersion) → Type
-- Covariant transport along modification morphisms
cov-transport : {A A' : Skill} {P : SkillDeps A → Type}
→ (f : Modification A A')
→ P (deps A) → P (deps A')
-- Functoriality
cov-comp : ∀ (f : Mod A A') (g : Mod A' A'') →
cov-transport (g ∘ f) ≡ cov-transport g ∘ cov-transport f
MCP Tasks State Machine
From codex-self-rewriting:
┌─────────────┐
│ working │ LIVE (+1)
│ (modify) │
└──────┬──────┘
│
┌────────────┼────────────┐
↓ ↓ ↓
┌─────────────┐ ┌─────────────┐ ┌─────────────┐
│ completed │ │input_required│ │ failed │
│ BACKFILL(-1)│ │ VERIFY (0) │ │ BACKFILL(-1)│
└─────────────┘ └─────────────┘ └─────────────┘
Darwin Gödel Machine Integration
class CovariantDGM(DarwinGodelMachine):
"""Darwin Gödel Machine with covariant skill transport."""
def __init__(self, skill_fibration: SkillFibration, ...):
super().__init__(...)
self.fibration = skill_fibration
def mutate(self, agent: Agent) -> Agent:
"""Mutate agent while preserving fibration structure."""
new_code = self.mutator(agent)
# Transport dependent skills covariantly
modified_deps = {}
for dep_skill in self.fibration.dependencies(agent):
modified_deps[dep_skill] = self.fibration.transport(
modification=Diff(agent.code, new_code),
target=dep_skill
)
return Agent(
code=new_code,
dependencies=modified_deps,
generation=self.generation
)
Multi-Agent Sheaf Gluing
class CovariantModificationSheaf:
"""Sheaf ensuring consistent modifications across agents."""
def glue(self, local_mods: Dict[Agent, Modification]) -> GlobalMod:
"""Glue compatible local modifications into global section."""
for a1, a2 in combinations(local_mods.keys(), 2):
overlap = self.overlap(a1, a2)
if overlap:
r1 = self.restrict(local_mods[a1], overlap)
r2 = self.restrict(local_mods[a2], overlap)
if not self.compatible(r1, r2):
raise CovarianceViolation(a1, a2, overlap)
return self.colimit(local_mods)
Triadic Modification Operators
| Trit | Effect | Operator | Example |
|---|---|---|---|
| +1 | Generative | Create new structure | Add skill capability |
| 0 | Neutral | Refactor/reorganize | Rename function |
| -1 | Destructive | Remove/simplify | Delete unused code |
Conservation Law:
Σ trit(modification_i) ≡ 0 (mod 3)
GF(3) Triads
covariant-fibrations (-1) ⊗ covariant-modification (0) ⊗ codex-self-rewriting (+1) = 0 ✓
temporal-coalgebra (-1) ⊗ covariant-modification (0) ⊗ self-evolving-agent (+1) = 0 ✓
sheaf-cohomology (-1) ⊗ covariant-modification (0) ⊗ gay-mcp (+1) = 0 ✓
Commands
# Verify covariant modification
just covariant-verify skill=my-skill mod=v1.1
# Run DGM evolution with covariance check
just dgm-evolve --covariant --generations=50
# Check GF(3) conservation
just gf3-audit modified-skills/
# Apply modification with transport
just covariant-modify skill=target mod=change.diff
Related Skills
covariant-fibrations(-1): Type transport validationself-evolving-agent(0): DGM evolution patternscodex-self-rewriting(+1): MCP Tasks self-modificationbisimulation-game(-1): Observational equivalence verification
See Also
CT lattice atlas
Part of: para-mensch-commons (CT lattice family).