dd3c3c — Worldmat TiDAR Skill

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 gadget
spi-parallel-verify — Fingerprint verification
gay-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.

Agent Skills: dd3c3c — Worldmat TiDAR

Install this agent skill to your local

Skill Files