bmorphism Diagrams

Interleave bmorphism's mermaid diagrams into interactions using GF(3) triadic selection.

Data Source

~/mermaid_diagrams.duckdb
├── diagrams (251 rows)
│   ├── id: UUID
│   ├── content: VARCHAR (mermaid code)
│   ├── diagram_type: VARCHAR (graph|flowchart|stateDiagram|...)
│   ├── trit: INTEGER (-1, 0, +1)
│   └── content_hash: VARCHAR

Diagram Types

Type	Count	Use Case
graph	126	Dependency/skill relationships
flowchart	47	Process flows, architectures
stateDiagram	8	State machines, protocols
sequenceDiagram	6	Message passing, APIs
classDiagram	6	Type hierarchies
pie	2	Distribution stats
erDiagram	1	Data models

Interleaving Protocol

1. Random Selection (Entropy-Seeded)

# Get random diagram by trit
duckdb ~/mermaid_diagrams.duckdb "
  SELECT content FROM diagrams 
  WHERE trit = (SELECT (random() * 3 - 1)::int % 3)
  ORDER BY random() LIMIT 1
"

2. Type-Matched Selection

# Match diagram type to context
duckdb ~/mermaid_diagrams.duckdb "
  SELECT content FROM diagrams 
  WHERE diagram_type = 'flowchart'
  ORDER BY random() LIMIT 1
"

3. GF(3) Balanced Triad

# Get one diagram per trit for balanced presentation
duckdb ~/mermaid_diagrams.duckdb "
  (SELECT content, trit FROM diagrams WHERE trit = -1 ORDER BY random() LIMIT 1)
  UNION ALL
  (SELECT content, trit FROM diagrams WHERE trit = 0 ORDER BY random() LIMIT 1)
  UNION ALL
  (SELECT content, trit FROM diagrams WHERE trit = 1 ORDER BY random() LIMIT 1)
"

Usage Triggers

Interleave a bmorphism diagram when:

1. Architecture discussions → flowchart/graph
2. Protocol design → sequenceDiagram/stateDiagram
3. Data modeling → erDiagram/classDiagram
4. Skill loading → graph (skill dependencies)
5. Random inspiration → any type, entropy-seeded

Rendering

Use the mermaid tool to render selected diagrams:

mermaid(code=DIAGRAM_CONTENT, citations={})

Example Workflow

# 1. Query a contextual diagram
DIAGRAM=$(duckdb ~/mermaid_diagrams.duckdb -noheader -list "
  SELECT content FROM diagrams 
  WHERE diagram_type = 'flowchart' 
  AND content LIKE '%GF(3)%'
  ORDER BY random() LIMIT 1
")

# 2. Render via mermaid tool
# mermaid(code=$DIAGRAM, citations={})

Trit Assignment

Diagrams inherit trits from content analysis:

• MINUS (-1): Validation, constraints, error states
• ERGODIC (0): Neutral flows, queries, observations
• PLUS (+1): Generation, creation, composition

Stats Query

duckdb ~/mermaid_diagrams.duckdb "
  SELECT 
    diagram_type,
    COUNT(*) as count,
    SUM(CASE WHEN trit = -1 THEN 1 ELSE 0 END) as minus,
    SUM(CASE WHEN trit = 0 THEN 1 ELSE 0 END) as ergodic,
    SUM(CASE WHEN trit = 1 THEN 1 ELSE 0 END) as plus
  FROM diagrams 
  GROUP BY diagram_type 
  ORDER BY count DESC
"

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Graph Theory

• networkx [○] via bicomodule
  • Hub for all graph/network skills

Visualization

• matplotlib [○] via bicomodule
  • Scientific visualization

Bibliography References

• general: 734 citations in bib.duckdb

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 4. Pattern Matching

Concepts: unification, match, segment variables, pattern

GF(3) Balanced Triad

bmorphism-diagrams (○) + SDF.Ch4 (+) + [balancer] (−) = 0

Skill Trit: 0 (ERGODIC - coordination)

Secondary Chapters

• Ch7: Propagators

Connection Pattern

Pattern matching extracts structure. This skill recognizes and transforms patterns.

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.