covariant-modification

# 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 ```agda -- 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 ```python 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 ```python 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 ```bash # 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 validation - `self-evolving-agent` (0): DGM evolution patterns - `codex-self-rewriting` (+1): MCP Tasks self-modification - `bisimulation-game` (-1): Observational equivalence verification ## See Also - [Covariant Fibrations in Directed Type Theory](https://arxiv.org/abs/2211.01602) - [Darwin Gödel Machine](https://hf.co/papers/2505.22954) - [MCP Tasks Specification](https://modelcontextprotocol.io/specification/draft/basic/utilities/tasks) ## CT lattice atlas Part of: `para-mensch-commons` (CT lattice family).