Asi semilattice-discovery

Compositional skill discovery via join-semilattice fiber (color × trit × hash)

install

source · Clone the upstream repo

git clone https://github.com/plurigrid/asi

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/plurigrid/asi "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/semilattice-discovery" ~/.claude/skills/plurigrid-asi-semilattice-discovery && rm -rf "$T"

manifest: skills/semilattice-discovery/SKILL.md

source content

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 algebra
```
skill-dispatch
```
— GF(3) triadic task routing
```
gf3-conservation-oracle
```
— conservation verification
```
bisimulation-game
```
— behavioral equivalence
```
implicit-coordination
```
— stigmergic merge (distance 0.0000 from "semilattice crdt merge")