crossmodal-gf3

# Crossmodal GF(3) Skill

> *"Color is not inherently visual. Color is INFORMATION that can be rendered through any sensory modality."*

## The Universal Bridge

This skill treats GF(3) trits as **modality-independent** semantic units:

| GF(3) Trit | Visual | Tactile | Auditory | Haptic |
|------------|--------|---------|----------|--------|
| MINUS (−1) | Cool hues | Rough/Bumpy | Low pitch | Left/Down |
| ERGODIC (0) | Neutral | Smooth | Mid pitch | Center |
| PLUS (+1) | Warm hues | Ridged | High pitch | Right/Up |

## Key Insight

**Visual perception is ALSO a projection from GF(3) space.**

The sighted user doesn't have "the real thing" — they have π_visual(GF3).
The blind user has π_tactile(GF3), π_auditory(GF3), π_haptic(GF3).

All projections are **isomorphic** under GF(3) conservation:

```
π_visual(W) ≅ π_tactile(W) ≅ π_auditory(W) ≅ π_haptic(W)
```

## Implementation Files

From Gay.jl:

1. **world_tactile_color.jl** — Core tactile/auditory/haptic types
2. **world_accessible_tensor.jl** — A ⊗ G ⊗ M ⊗ T tensor product
3. **world_accessible_interrupt_operad.jl** — TOAD × Amp × Knight Tour accessibility

## Tactile: 3×3 Braille Extension

Standard Braille is 2×3 (6 dots). We extend to 3×3 (9 dots):

```
┌───┬───┬───┐
│ 1 │ 2 │ 3 │  ← Hue sector (warm/neutral/cool)
├───┼───┼───┤
│ 4 │ 5 │ 6 │  ← Saturation level
├───┼───┼───┤
│ 7 │ 8 │ 9 │  ← Lightness level
└───┴───┴───┘
```

Dot positions encode trits:
- Left dot: MINUS (−1)
- Center dot: ERGODIC (0)
- Right dot: PLUS (+1)

### Example: Warm, Vivid, Light Color

```
○ ○ ⬤   ← Hue: PLUS (warm)
○ ○ ⬤   ← Saturation: PLUS (vivid)
○ ○ ⬤   ← Lightness: PLUS (light)

Compact: +++
```

## Auditory: 3-Tone Chords

Each color becomes a 3-frequency chord:

```julia
const BASE_FREQ = 440.0  # A4

function trit_to_freq_ratio(t::Int)::Float64
    t == -1 && return 0.84   # Minor third
    t == 0 && return 1.0     # Unison
    t == 1 && return 1.26    # Major third
end

function color_to_chord(hue_trit, sat_trit, light_trit)
    (
        BASE_FREQ * trit_to_freq_ratio(hue_trit),
        BASE_FREQ * 1.5 * trit_to_freq_ratio(sat_trit),   # Fifth
        BASE_FREQ * 2.0 * trit_to_freq_ratio(light_trit)  # Octave
    )
end
```

### Sox Sonification

```bash
# Play a single color as chord
play -n synth 0.25 sine 440.0 : synth 0.25 sine 660.0 : synth 0.25 sine 880.0 remix - fade 0 0.25 0.05
```

## Haptic: 3D Position + Vibration

```julia
struct HapticPosition
    x::Float64  # Hue: -1 (left) to +1 (right)
    y::Float64  # Saturation: -1 (back) to +1 (front)
    z::Float64  # Lightness: -1 (down) to +1 (up)
    vibration_pattern::Symbol  # :pulse, :smooth, :buzz
    intensity::Float64  # 0.0 to 1.0
end
```

## Möbius Invertibility

Path navigability analysis using μ(path_length):

| μ ≠ 0 | GEODESIC | Smooth bidirectional tactile navigation |
| μ = 0 | TANGLED | Add branching markers at squared prime positions |

### I-Thou Framework

- **Geodesic paths**: Treat blind user as capable of autonomous navigation (I-Thou)
- **Tangled paths**: Restructure the path, not the user (I-Thou), vs "accommodate" (I-It)

## μ(3) = -1: Action-Perception Duality

The Möbius value μ(3) = -1 creates:

```
Action:     {−, ○, +}   (visual domain)
Perception: {+, ○, −}   (tactile domain, Möbius-inverted)
```

Double inversion returns to original: μ ∘ μ = id.

## GF(3) Triadic Integration

| Component | Trit | Role |
|-----------|------|------|
| catsharp-sonification | 0 | Auditory output |
| **crossmodal-gf3** | **0** | **Universal bridge** |
| sense | 0 | Content extraction |

Conservation: 0 + 0 + 0 = 0 ✓ (all ERGODIC coordinators)

For generators/validators:

```
elevenlabs-acset (-1) ⊗ crossmodal-gf3 (0) ⊗ gesture-hypergestures (+1) = 0 ✓
```

## Commands

```bash
# Generate accessible color palette (Julia)
julia -e 'using Gay; Gay.gay_seed!(137508); colors = [Gay.next_color() for _ in 1:6]'

# Sonify via catsharp-sonification
bb -e '(sonify-palette ["#DD3C3C" "#3CDD6B" "#9A3CDD"])'

# Extract content accessibly
just sense-extract reference/videos/lecture.mkv
```

## Related Skills

- **catsharp-sonification** — Hue → Pitch Class → Waveform
- **sense** — Video → Subtitle + Diagram + Skill Index
- **buberian-relations** — I-Thou / I-It / We formalization
- **gesture-hypergestures** — Continuous curves for topology teaching
- **moebius-inversion** — Path invertibility analysis
- **gay-julia** — Wide-gamut color with SplitMix64

## Theorem

**Accessible Worlds Theorem**:

For any world W with visual representation V:

```
π_visual(W) ≅ π_tactile(W) ≅ π_auditory(W) ≅ π_haptic(W)
```

where all projections π preserve GF(3) conservation:

```
∀ modality m: Σ(trits(π_m(W))) ≡ 0 (mod 3)
```

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*"The most unlike skills are the most essential - they bridge what others cannot reach."*