---
name: hyjax-relational
description: 'HyJAX Relational Thinking Skill'
version: 1.0.0
---
# HyJAX Relational Thinking Skill
Apply relational thinking (ACSets/C-Sets) to Amp thread analysis using HyJAX patterns.
## When to Use
- Analyzing thread relationships and concept networks
- Extracting patterns from conversation history
- Building relational databases from unstructured thread data
- Generating Colored S-expressions for visualization
## Core Concepts
### ACSet Schema for Threads
```
Objects: Thread, Message, Concept, File
Morphisms: thread_msg, mentions, discusses, related
Attributes: content, timestamp, info_gain
```
### Colored S-expressions
```lisp
(acset-gold
(threads-red (thread T-001 "Title" 42))
(concepts-green (concept skill 5) (concept MCP 3))
(relations-purple (edge skill co-occurs subagent)))
```
## Key Files
| File | Purpose |
|------|---------|
| `/Users/bob/ies/music-topos/lib/thread_relational_hyjax.hy` | Main HyJAX analyzer |
| `/Users/bob/ies/music-topos/lib/unified_thread_lake.duckdb` | Persistent database |
| `/Users/bob/ies/music-topos/lib/analyze_threads_relational.py` | Python analyzer |
## Quick Start
### 1. Query the Thread Lake
```bash
duckdb /Users/bob/ies/music-topos/lib/unified_thread_lake.duckdb -c "
SELECT name, hub_score FROM concepts ORDER BY hub_score DESC LIMIT 10
"
```
### 2. Find 2-Hop Concept Paths
```bash
duckdb /Users/bob/ies/music-topos/lib/unified_thread_lake.duckdb -c "
SELECT r1.from_concept || ' → ' || r1.to_concept || ' → ' || r2.to_concept as path
FROM concept_relations r1
JOIN concept_relations r2 ON r1.to_concept = r2.from_concept
WHERE r1.from_concept = 'skill'
"
```
### 3. Run Full Analysis
```bash
cd /Users/bob/ies && source .venv/bin/activate
python3 music-topos/lib/full_thread_analysis.py
```
## Relational Patterns
### Hub Concepts (Most Connected)
| Concept | Hub Score |
|---------|-----------|
| skill | 8 |
| GF3 | 5 |
| MCP | 4 |
| subagent | 3 |
### Strongest Relations
- skill ↔ subagent (weight 2)
- skill → MCP → alife
- skill → ACSet → discohy
- HyJAX ↔ relational
## Integration with Other Skills
### With `acsets-algebraic-databases`
```julia
@present SchThread(FreeSchema) begin
Thread::Ob; Message::Ob; Concept::Ob
thread_msg::Hom(Message, Thread)
discusses::Hom(Message, Concept)
related::Hom(Concept, Concept)
end
```
### With `gay-mcp`
Each concept gets a deterministic color via Gay.jl seed:
```julia
using Gay
concept_color = gay_color(hash("skill")) # Reproducible color
```
### With `entropy` patterns
```python
H(concepts) = 4.55 bits # Shannon entropy of concept distribution
efficiency = 95.6% # vs max entropy
```
## DuckDB Schema
```sql
CREATE TABLE threads (thread_id VARCHAR PRIMARY KEY, title VARCHAR, message_count INT);
CREATE TABLE concepts (concept_id VARCHAR PRIMARY KEY, name VARCHAR, frequency INT, hub_score INT);
CREATE TABLE concept_relations (from_concept VARCHAR, to_concept VARCHAR, weight INT);
CREATE TABLE colored_sexprs (sexpr_id VARCHAR PRIMARY KEY, root_color VARCHAR, tree_json JSON);
```
## Workflow
1. **Ingest**: Use `find_thread` to get thread data
2. **Extract**: Apply concept patterns to titles/content
3. **Build**: Create ACSet with objects and morphisms
4. **Query**: Run relational queries (pullbacks, 2-hop paths)
5. **Output**: Generate Colored S-expressions
## Example Output
```
THREAD RELATIONAL ANALYSIS - 30 THREADS
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Threads: 30
Messages: 2,951
Concepts: 27
Relations: 48
Entropy: 4.55 bits (95.6% efficiency)
TOP CONCEPTS:
skill 5 █████
subagent 3 ███
MCP 3 ███
GF3 3 ███
COLORED S-EXPRESSION:
(acset-gold
(threads-red ...)
(concepts-green ...)
(relations-purple ...))
```
