slowtime-mcp

# Slowtime MCP

Asymmetric temporal constructs for capability gain through deliberate slowness.

## Core Asymmetry

```
┌─────────────────────────────────────────────────────────────┐
│  FAST PATH (Standard MCP)     │  SLOW PATH (Slowtime)       │
├───────────────────────────────┼─────────────────────────────┤
│  tool_call → response         │  tool_call → deliberation   │
│  O(1) latency                 │       ↓                     │
│  No accumulation              │  Cat# bicomodule check      │
│                               │       ↓                     │
│                               │  capability_gain_narrative  │
│                               │       ↓                     │
│                               │  response + new_capability  │
└───────────────────────────────┴─────────────────────────────┘
```

## Capability Gain via Cat#

**Key insight**: Slowness enables bicomodule composition verification.

```
Cat# Capability Accumulation:

  skill₁ ──────────────────────────────► skill₂
    │                                      │
    │  [slowtime deliberation]             │
    ▼                                      ▼
  cap₁ ───► Cat# bicomodule check ───► cap₁ ⊗ cap₂
            (Ran/Lan coherence)
```

### Capability Types (Cat# Homes)

| Home | Capability Type | Slowtime Operation |
|------|-----------------|-------------------|
| Span | Linear resources | Verify no duplication |
| Prof | Transformations | Check naturality |
| Presheaves | Observations | Validate coherence |

## Asymmetry Constructs

### 1. Temporal Asymmetry

```python
class SlowtimeAsymmetry:
    """Time dilation creates information asymmetry."""
    
    def fast_path(self, tool_call):
        """Standard MCP: immediate response."""
        return self.execute(tool_call)
    
    def slow_path(self, tool_call, deliberation_budget: float):
        """Slowtime: accumulate capabilities during delay."""
        
        # Phase 1: Cat# structure analysis
        bicomodules = self.analyze_bicomodules(tool_call)
        
        # Phase 2: Capability composition check
        new_caps = self.compose_capabilities(bicomodules)
        
        # Phase 3: Coherence verification (takes time)
        if self.verify_naturality(new_caps, budget=deliberation_budget):
            self.accumulate(new_caps)
        
        return self.execute(tool_call), new_caps
```

### 2. Information Asymmetry

The slow agent knows MORE than the fast agent:

```
Fast Agent: sees tool_call, response
Slow Agent: sees tool_call, Cat# structure, capability gains, response
```

### 3. Compositional Asymmetry

Slow paths enable checking composition that fast paths skip:

```nickel
# Fast: trust composition
let fast_compose = fun f g => f >> g

# Slow: verify composition via Cat# bicomodule
let slow_compose = fun f g =>
  let bicomod = analyze_bicomodule f g in
  if verify_naturality bicomod
  then { result = f >> g, capability_gain = bicomod.new_caps }
  else { error = "Composition fails naturality" }
```

## Plausible Narratives of Capability Gain

### Narrative 1: Contract Accumulation

```
Initial: Agent has `nickel` skill (contracts)
Slowtime: Agent deliberates on pyUSD query structure
Cat# Check: DoubleTheory contract validates query schema
Gain: Agent now has `dune-analytics` + `nickel` composed capability
      → Can write validated Dune queries with contract guarantees
```

### Narrative 2: Self-Hosting Bootstrap

```
Initial: Agent has basic Nickel eval
Slowtime: Agent traces evaluation through self_hosting_monad.ncl
Cat# Check: 2-monad laws verified (unit/mult coherence)
Gain: Agent can now describe its own grammar
      → Metacircular evaluator capability unlocked
```

### Narrative 3: Keyspace Correspondence

```
Initial: Agent has tree-sitter AST view
Slowtime: Agent computes Gay.jl colors for AST nodes
Cat# Check: Bicomodule from Source → Binary categories
Gain: Agent can now correlate source ↔ binary
      → Reverse engineering capability via color correspondence
```

## GF(3) Triads for Slowtime

```
# Slowtime deliberation triad
temporal-coalgebra (-1) ⊗ slowtime-mcp (0) ⊗ free-monad-gen (+1) = 0 ✓

# Capability accumulation triad
nickel (-1) ⊗ slowtime-mcp (0) ⊗ dune-analytics (+1) = 0 ✓

# Self-hosting triad
sicp (-1) ⊗ slowtime-mcp (0) ⊗ topos-catcolab (+1) = 0 ✓
```

## Implementation

```typescript
interface SlowtimeMCP {
  // Standard MCP tool
  tool_call(name: string, args: object): Promise<Response>;
  
  // Slowtime-enhanced tool
  slowtime_call(
    name: string, 
    args: object,
    deliberation_ms: number
  ): Promise<{
    response: Response;
    capability_gains: CapabilityGain[];
    cat_sharp_trace: BicomoduleTrace;
  }>;
}

interface CapabilityGain {
  source_skill: string;
  target_skill: string;
  bicomodule: string;  // Cat# structure
  home: 'Span' | 'Prof' | 'Presheaves';
  verified: boolean;
}
```

## Commands

```bash
# Run with slowtime deliberation
just slowtime-call tool_name --budget 5000ms

# Analyze capability accumulation
just slowtime-capabilities

# Verify Cat# coherence
just slowtime-verify-naturality
```

## Trit Assignment

```
Trit: 0 (ERGODIC)
Home: Prof (bicomodule coordinator)
Poly Op: ⊗ (parallel composition during deliberation)
Color: #FFFF00 (yellow - caution/deliberation)
```