---
name: dd3c3c
description: "Worldmat TiDAR: 3×3×3 matrix of diffusion draft + AR verify executions with GF(3) conservation"
color: "#DD3C3C"
hue: 0.0
knight_tour_position: 1
---

# dd3c3c — Worldmat TiDAR

**Color:** `#DD3C3C` (scarlet, hue 0°)  
**Knight Tour Position:** 1 (entry point)  
**Golden Angle:** 137.508° per step

## Overview

A **Worldmat** is a 3×3×3 matrix of TiDAR executions structured by:

| Axis | Values | GF(3) |
|------|--------|-------|
| Polarity | MINUS(-1), ERGODIC(0), PLUS(+1) | Conservation |
| Temporal | PAST(0), PRESENT(1), FUTURE(2) | Slice sum = 0 |
| Modality | OBSERVATION(0), ACTION(1), PREDICTION(2) | Per axis |

## TiDAR Pattern (arXiv:2511.08923)

```
Phase 1: Diffusion Draft (parallel)
  └─ SplitMix64.split(n) → n independent token streams
  
Phase 2: AR Verify (sequential)  
  └─ Hash chain: prev ⊕ token → verified
```

## Usage

```python
from worldmat import Worldmat, verify_spi

# Initialize with drand seed
wm = Worldmat(master_seed=0x87079c9f1d3b0474)

# Execute all 27 cells via TiDAR
wm.execute_parallel()

# Verify GF(3) conservation
gf3 = wm.verify_gf3()  # All slices sum to 0 mod 3

# Verify SPI (parallel == sequential)
spi = verify_spi(seed)  # fingerprints match ✓

# Export as ACSet
acset = wm.to_acset()
```

## Knight Tour Discovery

Skills are discovered via knight moves through color space:

```
Position 1: #DD3C3C (this skill) ← ENTRY
Position 2: #3CDD6B (+137.5°)
Position 3: #9A3CDD (+275.0°)
...
Position 27: #DD3C7E (+335.2°) ← EXIT
```

Jump pattern on 3×3×3: `(±1,±2,0)`, `(±2,±1,0)`, `(±1,0,±2)`, etc.

## Implementation

```
/Users/bob/ies/worldmat/worldmat.py
```

## GF(3) Invariants

- Every polarity slice (9 cells): Σ trits ≡ 0 (mod 3)
- Every temporal slice (9 cells): Σ trits ≡ 0 (mod 3)  
- Every modality slice (9 cells): Σ trits ≡ 0 (mod 3)
- MINUS ⊗ ERGODIC ⊗ PLUS = 0 always

## Color Schema

| Polarity | Hex | Trit |
|----------|-----|------|
| MINUS | `#9E16EF` | -1 |
| ERGODIC | `#55D9A0` | 0 |
| PLUS | `#AF3424` | +1 |

## Related Skills

- `3cdd6b` — Knight tour position 2 (next)
- `three-match` — 3-coloring gadget
- `spi-parallel-verify` — Fingerprint verification
- `gay-mcp` — Deterministic color generation