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

Services Overview

📧 Gmail (MINUS -1: Validator)

search_gmail_messages

get_gmail_message_content

get_gmail_messages_content_batch

get_gmail_thread_content

send_gmail_message

draft_gmail_message

modify_gmail_message_labels

batch_modify_gmail_message_labels

list_gmail_labels

manage_gmail_label

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)

search_drive_files

list_drive_items

get_drive_file_content

get_drive_file_download_url

create_drive_file

update_drive_file

share_drive_file

batch_share_drive_file

get_drive_file_permissions

get_drive_shareable_link

remove_drive_permission

transfer_drive_ownership

📅 Calendar (PLUS +1: Executor)

list_calendars

get_events

create_event

modify_event

delete_event

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)

search_docs

list_docs_in_folder

create_doc

get_doc_content

modify_doc_text

find_and_replace_doc

insert_doc_image

insert_doc_elements

create_table_with_data

inspect_doc_structure

debug_table_structure

update_doc_headers_footers

batch_update_doc

export_doc_to_pdf

📊 Sheets (ERGODIC 0)

list_spreadsheets

create_spreadsheet

get_spreadsheet_info

create_sheet

read_sheet_values

modify_sheet_values

Range syntax:

Sheet1!A1:D10

A1:Z1000

📽️ Slides (PLUS +1)

create_presentation

get_presentation

get_page

get_page_thumbnail

batch_update_presentation

📋 Forms

create_form

get_form

list_form_responses

get_form_response

set_publish_settings

✅ Tasks

list_task_lists

get_task_list

create_task_list

update_task_list

delete_task_list

list_tasks

get_task

create_task

update_task

delete_task

move_task

clear_completed_tasks

💬 Chat

list_spaces

get_messages

search_messages

send_message

🔍 Custom Search

search_custom

search_custom_siterestrict

get_search_engine_info

💬 Comments (All Doc Types)

read_document_comments

create_document_comment

reply_to_document_comment

resolve_document_comment

read_spreadsheet_comments

create_spreadsheet_comment

read_presentation_comments

create_presentation_comment

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)

drive_color_walk.py

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

NoDuplication

RouteInvariance

route(item) = agent_of(trit(item))

ThreadConservation

verify_h1_obstruction()

ClosedWorkflowBalance

Narya Compatibility

before

{"messages": [...], "files": [...]}

after

[{id, trit, verb, thread_id}]

delta

{added: 3, removed: 1, trit_sum_delta: +1}

birth

impact

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

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.