plurigrid spectre-worldmat
Synthesis of aperiodic monotile geometry and Worldmat TiDAR execution.
Core Insight
The Spectre monotile achieves global aperiodicity through local edge-matching rules. Similarly, threads evolve aperiodically through local GF(3) conservation constraints.
Metatile → Thread Archetype Mapping
| Metatile | Thread Type | GF(3) | Pattern |
|---|---|---|---|
| Γ Gamma | SEED | 0 | Bifurcating origin (2 spectres) |
| Δ Delta | BRIDGE | +1 | 8-way cross-domain synthesis |
| Θ Theta | RECURSIVE | -1 | Self-referential loops |
| Λ Lambda | ABSTRACTION | 0 | Meta-level generalization |
| Ξ Xi | INTEGRATION | +1 | Unification of disparate concepts |
| Π Pi | EXPANSION | -1 | Proliferation and scaling |
| Σ Sigma | AGGREGATION | 0 | Spur-edge decentralized collection |
| Φ Phi | GENERATOR | +1 | Ubiquitous production (in all subs) |
| Ψ Psi | TERMINAL | -1 | Boundary interface |
Mod12 = GF(3) × Z/4Z
12 rotations decompose into 3 trits × 4 temporal phases:
Dawn (phase 0): ergodic(0), plus(1), minus(2)
Noon (phase 1): ergodic(3), plus(4), minus(5)
Dusk (phase 2): ergodic(6), plus(7), minus(8)
Night (phase 3): ergodic(9), plus(10), minus(11)
Conservation Laws
- Γ-Σ Conservation: Every substitution contains exactly 1 Gamma and 1 Sigma
- Φ Abundance: Generator appears 2+ times in every expansion
- GF(3) Balance: Sum of trits across any substitution ≡ 0 (mod 3)
TrigNum 4D Embedding
data TrigNum a = TrigNum a a a a
-- Spans hexagonal lattice: {1, √3/2+i/2, 1/2+i√3/2, i}
-- Parity constraint: parity(a,d) = parity(b,c)
Threads embed in 4D space with coherence verified by parity matching.
Worldmat Integration
from worldmat import Worldmat
wm = Worldmat(master_seed=0x87079c9f1d3b0474)
wm.execute_parallel()
# 27 cells = 3³ = 9 metatile types × 3 instances
# Each cell is a TiDAR execution (diffusion + AR verify)
# GF(3) conserved across all 9 slices
Skill Growth Pattern
Skills grow via golden angle (137.5°) knight tour:
Position 1 → #DD3C3C (scarlet) @ hue 0°
Position 2 → #3CDD6B (mint) @ hue 137.5°
Position 3 → #9A3CDD (violet) @ hue 275°
...
Position 27 → #DD3C7E (rose) @ hue 335.2°
After 27 positions, full coverage. Never repeats (aperiodic).
Usage
# Run worldmat demo
python3 /Users/bob/ies/worldmat/worldmat.py
# Verify SPI
python3 /Users/bob/ies/worldmat/worldmat.py verify
# Grow skill at next position
python3 /Users/bob/ies/worldmat/skill_grower.py grow "context"
# Check tour status
python3 /Users/bob/ies/worldmat/skill_grower.py status
Related Files
- worldmat.py - Core implementation
- skill_grower.py - Gay MCP integration
- Spectre.hs - Haskell monotile
- plus_monotile_predictions.json - PLUS agent
GF(3) Triad
MINUS (-1): minus_verification_sink.json - stale thread analysis
ERGODIC(0): ergodic_thread_state.json - current network state
PLUS (+1): plus_monotile_predictions.json - future predictions
Sum: -1 + 0 + 1 = 0 ✓
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.