color-envelope-preserving

Files (1)

• SKILL.md

SKILL.md (first lines)

# Color Envelope Preserving

## Core Concept

Every navigation path carries a **color envelope** - a GF(3) ternary assignment that propagates through the path composition. This skill ensures that composed Navigators maintain color conservation (the envelope sums to 0 mod 3) across all compositions.

**GF(3) Color Trits**:
- **-1** (Red/MINUS) - Conservative/filtering paths
- **0** (Green/ERGODIC) - Neutral/structural paths
- **+1** (Blue/PLUS) - Generative/enriching paths

The **envelope invariant**: Any valid Navigator composition must have trits that sum to 0 (mod 3).

## Why Color Envelopes?

### Determinism Through Color

Every navigation operation is seeded with a color value. Same color seed → same traversal order → same results every time.

```julia
# With SplitMix64 seeding from color
nav = @late_nav([ALL, pred(iseven)])
                          ↓ (color=-1)
                    deterministic traversal order
```

### Conservation Law

When two Navigators compose:
```julia
nav1 = @late_nav([ALL, pred(f)])        # trit = -1
nav2 = @late_nav([keypath("x")])        # trit = 0
nav_composed = compose_navigators(nav1, nav2)

# Check: (-1) + 0 = -1 ≠ 0
# => INVALID! Cannot compose these Navigators.
```

A valid composition requires a third Navigator to balance:
```julia
nav3 = @late_nav([keypath("y")])        # trit = +1
# Check: (-1) + 0 + (+1) = 0 ✓
# => VALID! Complete GF(3) triad.
```

## Architecture

### Color Assignment Algorithm

Each Navigator's trit is determined by its **semantic role**:

| Path Type | Trit | Justification |
|-----------|------|---------------|
| `[ALL]` | -1 | Expands cardinality (conservative gate) |
| `[pred(f)]` | -1 | Filters/restricts domain |
| `[keypath(k)]` | 0 | Neutral structural access |
| `[INDEX(i)]` | 0 | Direct indexing (no change) |
| `[APPEND(x)]` | +1 | Adds value (generative) |
| `[TRANSFORM(f)]` | +1 | Enriches/generates new form |
| Composition of above | Sum of trits | Trits compose additively |

### Color Propagation

```
Input structure (color = c_in)
    ↓
Apply Navigator with trit = t_nav
    ↓
Output structure (color = c_in + t_nav mod 3)
    ↓
Apply next Navigator with trit = t_nav2
    ↓
Final color = c_in + t_nav + t_nav2 mod 3
```

### Envelope Invariant Checker

```julia
function verify_envelope(navigator_chain::Vector{Navigator})
    total_trit = sum(nav.trit for nav in navigator_chain) % 3
    return total_trit == 0  # Valid if sums to 0 mod 3
end
```

## API

### Color Assignment

**`assign_trit(navigator::Navigator) :: Int`**
Determines the GF(3) trit for a Navigator.

```julia
nav = @late_nav([ALL, pred(f)])
trit = assign_trit(nav)  # => -1 (filtering/expansion)

nav = @late_nav([keypath("x")])
trit = assign_trit(nav)  # => 0 (structural)

nav = @late_nav([APPEND(value)])
trit = assign_trit(nav)  # => +1 (generative)
```

**`color_seed(navigator::Navigator) :: UInt64`**
Generates a deterministic SplitMix64 seed from the Navigator's trit and structure.

```julia
nav = @late_nav([ALL, pred(iseven)])
seed = color_seed(nav)  # => UInt64 derived from trit=-1, hash(path)

# Same Navigator always produces same seed
seed2 = color_seed(nav)
@assert seed == seed2  # ✓
```

### Envelope Verification

**`verify_envelope(navs::Vector{Navigator}) :: Bool`**
Checks if a chain of Navigators maintains color conservation.

From plurigrid/asi, MIT.

More from plurigrid/asi