plurigrid 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
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 |
End-of-Skill Interface
Related Skills
3cdd6b— Knight tour position 2 (next)three-match— 3-coloring gadgetspi-parallel-verify— Fingerprint verificationgay-mcp— Deterministic color generation
Autopoietic Marginalia
The interaction IS the skill improving itself.
Every use of this skill is an opportunity for worlding:
- MEMORY (-1): Record what was learned
- REMEMBERING (0): Connect patterns to other skills
- WORLDING (+1): Evolve the skill based on use
Add Interaction Exemplars here as the skill is used.