# Join Semilattice

> Join semilattices and sup-preservation.

- Skill: `plurigrid/join-semilattice` (Agent Skill, multi-file: 3 files)
- Install (CLI): `npx skillmds@latest add plurigrid/join-semilattice`
- Raw SKILL.md: https://api.skillmd.com/api/skills/plurigrid/join-semilattice/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: plurigrid (https://skillmd.com/u/plurigrid)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/plurigrid/join-semilattice

---

# J: Join Semilattice

> *Join semilattices and sup-preservation.*

## Directory Tree

```
join-semilattice/
├── SKILL.md
├── order/
├── lattice.idr
```

## GF(3) Assignment

Letter J → trit = -1

## Integration

```scheme
(define (join_semilattice x)
  ;; Join semilattices and sup-preservation.
  x)
```


---

## 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.*


## CT lattice atlas

Part of: `para-mensch-commons` (CT lattice family).