Google Workspace Skill

Comprehensive MCP integration for all Google Workspace services.

Denotation

Google Workspace tasks map to functional invariants, resulting in consistent email, file, calendar, and task states under Narya condensation and GF(3) conservation.

The skill reaches a fixed point when all pending operations complete with no H¹ obstructions (gluing failures), and thread/folder trit sums are conserved modulo 3.

Formal Contract

Effect: Google Workspace → State × Trit
Invariant: ∀ closed workflow: Σ(trit) ≡ 0 (mod 3)
Denotation: ⟦GW⟧ = lim_{n→∞} Condense(Op_n(...Op_1(S_0)))

Required Parameter

All tools require user_google_email - the user's Google email address.

Services Overview

📧 Gmail (MINUS -1: Validator)

Query syntax examples:

• from:user@example.com - From specific sender
• is:unread - Unread messages
• has:attachment - Has attachments
• after:2024/01/01 - Date filters

📁 Drive (ERGODIC 0: Coordinator)

📅 Calendar (PLUS +1: Executor)

Event creation options:

• add_google_meet: true - Add Meet link
• attendees: ["email1", "email2"] - Invite attendees
• reminders: [{"method": "popup", "minutes": 15}] - Custom reminders
• transparency: "transparent" - Show as available

📄 Docs (MINUS -1)

📊 Sheets (ERGODIC 0)

Range syntax: Sheet1!A1:D10 or A1:Z1000

📽️ Slides (PLUS +1)

📋 Forms

✅ Tasks

💬 Chat

🔍 Custom Search

💬 Comments (All Doc Types)

GF(3) Triadic Workflow

MINUS (-1): Validation/Reading
├── search_gmail_messages
├── get_doc_content
├── read_sheet_values
└── list_drive_items

ERGODIC (0): Coordination/Metadata
├── get_spreadsheet_info
├── list_calendars
├── inspect_doc_structure
└── get_drive_file_permissions

PLUS (+1): Execution/Writing
├── send_gmail_message
├── create_event
├── modify_sheet_values
└── create_drive_file

Common Workflows

Email Management

# Search → Read → Reply
messages = search_gmail_messages(query="from:boss is:unread")
content = get_gmail_message_content(message_id=messages[0].id)
send_gmail_message(
    to="boss@company.com",
    subject="Re: " + content.subject,
    body="Response...",
    thread_id=content.thread_id,
    in_reply_to=content.message_id
)

Document Creation

# Create → Inspect → Add Table
doc = create_doc(title="Report")
structure = inspect_doc_structure(document_id=doc.id)
create_table_with_data(
    document_id=doc.id,
    index=structure.total_length,
    table_data=[["Header1", "Header2"], ["Data1", "Data2"]]
)

Calendar Scheduling

# Check availability → Create event with Meet
events = get_events(
    time_min="2024-12-26T09:00:00Z",
    time_max="2024-12-26T17:00:00Z"
)
create_event(
    summary="Team Sync",
    start_time="2024-12-26T14:00:00Z",
    end_time="2024-12-26T15:00:00Z",
    attendees=["team@company.com"],
    add_google_meet=True
)

File Sharing

# Share with expiration
share_drive_file(
    file_id="abc123",
    share_with="contractor@example.com",
    role="writer",
    expiration_time="2025-01-15T00:00:00Z"
)

Authentication

If tools fail with auth errors, use:

start_google_auth(service_name="gmail|drive|calendar|docs|sheets|slides|forms|tasks|chat")

Tips

1. Batch operations - Use batch tools for multiple items
2. Table creation - Always call inspect_doc_structure first to get safe index
3. Email threading - Include thread_id, in_reply_to, references for proper replies
4. Drive shared drives - Use drive_id parameter for shared drive operations
5. Calendar attachments - Use Drive file URLs or IDs for event attachments

Related Skills (Backlinks)

Triadic Integration Pattern

google-workspace (ERGODIC 0) ─── Coordinator
        │
        ├── finder-color-walk (0) ─── File coloring bridge
        │       └── drive_color_walk.py
        │
        ├── gay-mcp (+1) ─── Color generation
        │       └── SplitMix64 seeds → GF(3) trits
        │
        └── bisimulation-game (-1) ─── State verification
                └── Attacker/Defender/Arbiter protocol

GF(3) Check: 0 + 0 + 1 + (-1) = 0 ✓

Invariant Set

Narya Compatibility

Condensation Policy

Trigger: When 10 consecutive operations yield no change in equivalence classes.

def should_condense(history: List[State], threshold: int = 10) -> bool:
    if len(history) < threshold:
        return False
    recent = history[-threshold:]
    return all(equiv(s) == equiv(recent[0]) for s in recent)

Action: Collapse queue state into condensed fingerprint, archive processed items.

Scientific Skill Interleaving

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

Graph Theory

• networkx [○] via bicomodule
  • Universal graph hub

Bibliography References

• general: 734 citations in bib.duckdb

SDF Interleaving

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

Primary Chapter: 10. Adventure Game Example

Concepts: autonomous agent, game, synthesis

GF(3) Balanced Triad

google-workspace (○) + SDF.Ch10 (+) + [balancer] (−) = 0

Skill Trit: 0 (ERGODIC - coordination)

Secondary Chapters

• Ch7: Propagators
• Ch6: Layering
• Ch4: Pattern Matching
• Ch2: Domain-Specific Languages
• Ch1: Flexibility through Abstraction

Connection Pattern

Adventure games synthesize techniques. This skill integrates multiple 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.