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)

Tool	Description
search_gmail_messages	Search with Gmail query syntax
get_gmail_message_content	Get full message content
get_gmail_messages_content_batch	Batch get (max 25)
get_gmail_thread_content	Get full conversation thread
send_gmail_message	Send email (supports replies)
draft_gmail_message	Create draft (supports replies)
modify_gmail_message_labels	Add/remove labels (archive, delete)
batch_modify_gmail_message_labels	Bulk label operations
list_gmail_labels	List all labels with IDs
manage_gmail_label	Create/update/delete labels

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)

Tool	Description
search_drive_files	Search files by query
list_drive_items	List folder contents
get_drive_file_content	Get file content (text extraction)
get_drive_file_download_url	Get download URL
create_drive_file	Create new file
update_drive_file	Update metadata
share_drive_file	Share with users/groups/anyone
batch_share_drive_file	Bulk sharing
get_drive_file_permissions	Check permissions
get_drive_shareable_link	Get shareable link
remove_drive_permission	Revoke access
transfer_drive_ownership	Transfer file ownership

📅 Calendar (PLUS +1: Executor)

Tool	Description
list_calendars	List user's calendars
get_events	Get events (by ID or time range)
create_event	Create new event
modify_event	Update existing event
delete_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)

Tool	Description
search_docs	Search Google Docs
list_docs_in_folder	List docs in folder
create_doc	Create new document
get_doc_content	Get document content
modify_doc_text	Insert/replace/format text
find_and_replace_doc	Find and replace
insert_doc_image	Insert image
insert_doc_elements	Insert table/list/page break
create_table_with_data	Create populated table
inspect_doc_structure	Get document structure
debug_table_structure	Debug table layout
update_doc_headers_footers	Update headers/footers
batch_update_doc	Multiple operations
export_doc_to_pdf	Export to PDF

📊 Sheets (ERGODIC 0)

Tool	Description
list_spreadsheets	List spreadsheets
create_spreadsheet	Create new spreadsheet
get_spreadsheet_info	Get spreadsheet metadata
create_sheet	Add new sheet
read_sheet_values	Read cell range
modify_sheet_values	Write/update/clear cells

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

📽️ Slides (PLUS +1)

Tool	Description
create_presentation	Create new presentation
get_presentation	Get presentation details
get_page	Get slide details
get_page_thumbnail	Get slide thumbnail
batch_update_presentation	Apply updates

📋 Forms

Tool	Description
create_form	Create new form
get_form	Get form details
list_form_responses	List responses
get_form_response	Get specific response
set_publish_settings	Update publish settings

✅ Tasks

Tool	Description
list_task_lists	List all task lists
get_task_list	Get task list details
create_task_list	Create new list
update_task_list	Rename list
delete_task_list	Delete list
list_tasks	List tasks in list
get_task	Get task details
create_task	Create task
update_task	Update task
delete_task	Delete task
move_task	Move task (position/list)
clear_completed_tasks	Clear completed

💬 Chat

Tool	Description
list_spaces	List Chat spaces
get_messages	Get messages from space
search_messages	Search messages
send_message	Send message to space

🔍 Custom Search

Tool	Description
search_custom	Programmable Search Engine
search_custom_siterestrict	Site-restricted search
get_search_engine_info	Get search engine config

💬 Comments (All Doc Types)

Tool	Description
read_document_comments	Read doc comments
create_document_comment	Add doc comment
reply_to_document_comment	Reply to comment
resolve_document_comment	Resolve comment
read_spreadsheet_comments	Read sheet comments
create_spreadsheet_comment	Add sheet comment
read_presentation_comments	Read slide comments
create_presentation_comment	Add slide 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)

Skill	Trit	Integration
finder-color-walk	0	Drive files ↔ local Finder GF(3) coloring via drive_color_walk.py
gay-mcp	+1	SplitMix64 deterministic colors for file organization
triad-interleave	+1	Schedule Drive operations in GF(3)-balanced triplets
bisimulation-game	-1	Verify Drive state equivalence across agents

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

Invariant	Definition	Verification
NoDuplication	Each item (message, event, file) resides in exactly one triadic queue	Queue intersection = ∅
RouteInvariance	route(item) = agent_of(trit(item)) always	For all items, routing is deterministic
ThreadConservation	Thread trit sum ≡ 0 (mod 3) at cycle close	verify_h1_obstruction() returns no violations
ClosedWorkflowBalance	Any complete workflow has Σ trits = 0	GF(3) conservation check

Narya Compatibility

Field	Definition	Example
before	Raw input from Google APIs	{"messages": [...], "files": [...]}
after	Transformed interactions with GF(3) trits	[{id, trit, verb, thread_id}]
delta	Change in triadic queue state	{added: 3, removed: 1, trit_sum_delta: +1}
birth	Initial unprocessed state	Empty queues, no interactions
impact	1 if equivalence class changed, 0 otherwise	Used for ANIMA detection

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.