plurigrid semilattice-discovery
Find, compose, and verify skills using the free commutative idempotent semigroup.
Trit: 0 (Ergodic - coordinator)
Bundle: core
The Algebra
Every skill has a SemilatticeFiber: {color, trit, hash}.
- hash:
SplitMix64(name)— deterministic, O(1) - trit:
hash mod 3 - 1∈ {-1, 0, +1} — GF(3) conservation - color:
hash → RGB → OKLAB— perceptual similarity metric
Two skills compose via fiber join:
fiberJoin(a, b) = {
color: OKLAB midpoint (idempotent, commutative)
trit: findBalancer(a.trit, b.trit) — conserves GF(3)
hash: mix64(a.hash + b.hash)
}
Commands
# Compute fiber for a skill
bb skill-semilattice.bb fiber bisimulation-game
# Join two skills — shows conservation
bb skill-semilattice.bb join bisimulation-game sheaf-cohomology
# Find the best third skill to complete a conserved triad
bb skill-semilattice.bb triad bisimulation-game sheaf-cohomology
# Discover skills by fiber proximity to a query
bb skill-semilattice.bb discover "color theory oklab"
# Verify global GF(3) conservation across all 1425 skills
bb skill-semilattice.bb conserved?
# Show skill clusters by trit and color proximity
bb skill-semilattice.bb cluster 5
Semilattice Laws (verified)
| Law | Substrate | Braid | Color |
|---|---|---|---|
| a ⊔ a = a | trit balancer idempotent | merge(v,v) = v | blend(c,c,0.5) = c |
| a ⊔ b = b ⊔ a | + is commutative | merge commutes | blend commutes |
| (a⊔b)⊔c = a⊔(b⊔c) | + is associative | merge associative | blend ≈ associative |
Origin
Three independent discoveries of the same algebra:
- Flavors (Symbolics, 1979): mixin merge
- CRDTs (Kleppmann, 2011): state merge
- OKLAB (Ottosson, 2020): perceptual blend
Jaffer's SLIB contains the three pieces (colorspace.scm, modular.scm, random.scm) never composed.
Gay.jl and nanoclj-zig/src/semilattice.zig are the first known compositions.
Implementation
- Zig:
nanoclj-zig/src/semilattice.zig(211 lines, 9 tests) - Babashka:
asi/skill-semilattice.bb(walks all 1425 skills)
Results (2026-04-05)
Skills: 1425
Trit distribution: +1=478 0=481 -1=466
Trit sum: 12
GF(3) balanced: YES ✓ (sum mod 3 = 0)
Related Skills
join-semilattice— the abstract algebraskill-dispatch— GF(3) triadic task routinggf3-conservation-oracle— conservation verificationbisimulation-game— behavioral equivalenceimplicit-coordination— stigmergic merge (distance 0.0000 from "semilattice crdt merge")