plurigrid Messaging World - Social Graph ACSet
A diagrammatic world built from actual resources extracted via random walks across three communication channels.
ACSet Schema Definition
@present SchMessagingWorld(FreeSchema) begin
# Objects (node types)
Identity::Ob # Canonical person identity
Channel::Ob # Communication channel (Outlook, Gmail, Beeper)
Account::Ob # Account on a channel
Contact::Ob # Contact/correspondent
Conversation::Ob # Thread/chat
Network::Ob # Protocol network (Signal, Telegram, WhatsApp, etc.)
# Morphisms (edges)
identity_account::Hom(Account, Identity) # Account belongs to identity
account_channel::Hom(Account, Channel) # Account is on channel
contact_account::Hom(Contact, Account) # Contact seen via account
conv_account::Hom(Conversation, Account) # Conversation via account
contact_network::Hom(Contact, Network) # Contact's network (Beeper)
conv_network::Hom(Conversation, Network) # Conversation's network
# Attributes
Email::AttrType; Name::AttrType; Trit::AttrType; Count::AttrType
contact_email::Attr(Contact, Email)
contact_name::Attr(Contact, Name)
channel_trit::Attr(Channel, Trit)
contact_count::Attr(Contact, Count)
end
Extracted Social Graph (Live Data)
Channels with GF(3) Trits
┌────────────────────────────────────────────────────────────────────────────┐
│ MESSAGING WORLD ACSET │
│ Σ(trits) ≡ 0 (mod 3) ✓ │
└────────────────────────────────────────────────────────────────────────────┘
OUTLOOK (−1) GMAIL (0) BEEPER (+1)
┌──────────┐ ┌──────────┐ ┌──────────┐
│ UofT │ │ Personal │ │ Multi- │
│ y.shkel@ │ │ greentea │ │ Protocol │
│ utoronto │ │ tree01@ │ │ Matrix │
│ .ca │ │ gmail │ │ Hub │
└────┬─────┘ └────┬─────┘ └────┬─────┘
│ │ │
▼ ▼ ▼
┌──────────┐ ┌──────────┐ ┌──────────────┐
│Contacts: │ │Contacts: │ │ Networks: 5 │
│(academic)│ │ 28 total │ │ │
└──────────┘ └──────────┘ │ Signal ──────┤
│ Telegram ────┤
│ WhatsApp ────┤
│ Discord ─────┤
│ Twitter/X ───┤
└──────────────┘
Beeper Network Topology (50 Active Chats)
BEEPER SOCIAL GRAPH
┌─────────────────────────────┐
│ Identity: Yuliya │
│ @greenteatree01:beeper │
└─────────────┬───────────────┘
│
┌─────────────┬───────────────┼───────────────┬─────────────┐
│ │ │ │ │
▼ ▼ ▼ ▼ ▼
┌─────────┐ ┌─────────┐ ┌──────────┐ ┌──────────┐ ┌─────────┐
│ Signal │ │Telegram │ │ WhatsApp │ │ Discord │ │Twitter/X│
│ (18) │ │ (15) │ │ (6) │ │ (5) │ │ (1) │
└────┬────┘ └────┬────┘ └────┬─────┘ └────┬─────┘ └────┬────┘
│ │ │ │ │
▼ ▼ ▼ ▼ ▼
┌─────────────────────────────────────────────────────────────────────┐
│ KEY CONVERSATIONS │
├─────────────────────────────────────────────────────────────────────┤
│ │
│ SIGNAL (18 chats) │
│ ├── ies (pinned) ─── Mars, Sarah, Aaa + 2 │
│ ├── Meta-Org ─── moder, jpt4, Albert + 2 (328 unread!) │
│ ├── Wordle Appreciation ─── Tim, Keegan, Char + 2 │
│ ├── Cognition Cosmos ─── Yudhister, avoidbeing, Megaloceros │
│ ├── auglab summer '25 ─── Dünya B, ilya, Lars 9001 │
│ ├── SF Housing Authority ─── Shon Pan, Lauren, Adrià │
│ ├── JOIE DE VIE ─── Razib Khan, Dagsen Love, Jessica Taylor │
│ ├── Gay.jl ─── Lucas, Bodhi, d s + 2 │
│ ├── sloppies ─── Elienops, Mantissa, K + 2 │
│ ├── Avalon Community ─── Emma, Ren, Mel + 2 │
│ ├── NYCies ─── eeegnu, Amelia S, cassandra rat + 2 │
│ ├── xul (single) │
│ ├── barton!!! (single) │
│ ├── dad!!!!! (single) │
│ ├── L :Ouisa (single) │
│ ├── Sten (single) │
│ ├── vor (single) │
│ └── Lauren (single) │
│ │
│ TELEGRAM (15 chats) ─── Frontier Tower Community │
│ ├── #General ─── Tony Loehr, X grok, Stedman (82 unread) │
│ ├── Lost & Found ─── mAx, Tony Loehr (51 unread) │
│ ├── Hard Tech & Robotics ─── Alan Helmick, Morgan Hough │
│ ├── Neurotech ─── neilg, Morgan Hough │
│ ├── Biotech ─── Alan Helmick, Rob │
│ ├── Arts & Music ─── Tina LaPorta, Colleen Piontek │
│ ├── Human Flourishing ─── ColinAI, svitlana midianko │
│ ├── Maker Space ─── Cassox, Zan Lowe │
│ ├── Tower Events ─── Colleen Piontek, Zan Lowe │
│ ├── Gym ─── John Meow, Stedman Halliday │
│ ├── Health & Longevity │
│ ├── AI & Autonomous Systems ─── Xenofon │
│ ├── Culture ─── Tina LaPorta │
│ ├── Ethereum & Decent. Tech ─── Tina LaPorta │
│ └── luka (single) │
│ │
│ WHATSAPP (6 chats) │
│ ├── Stanford BJJ Students 25/26 (17 unread) │
│ ├── Women BJJ Stanford ─── Stara D'Haiti, hannah │
│ ├── dad!!!!! (single) │
│ ├── banquet ✨ ─── Alexa, arnav judy lab, Junyi │
│ └── Stanford/SF/Global Intellectual Salon │
│ │
│ DISCORD (5 chats) │
│ ├── #string-parsing-mines ─── Ouchie, chyyran │
│ ├── #7-calendar-years │
│ ├── Ser Chairzard (single) │
│ ├── noumena (single) │
│ └── AlephNotation (single) │
│ │
│ MATRIX/BEEPER │
│ ├── greenteatree01 (pinned) ─── barton │
│ ├── Beeper Developer Community ─── 0xted, a3fckx │
│ └── #General - Vivarium Public ─── Alex Glavin, celeste │
│ │
└─────────────────────────────────────────────────────────────────────┘
Gmail Contact Topology (28 Unique Contacts)
GMAIL SOCIAL GRAPH
┌───────────────────────────┐
│ greenteatree01@gmail.com │
│ (49 threads) │
└─────────────┬─────────────┘
│
┌─────────────────────┼─────────────────────┐
│ │ │
▼ ▼ ▼
┌────────────┐ ┌────────────┐ ┌────────────┐
│TRANSACTIONAL│ │ NEWSLETTERS│ │ SERVICES │
│ (trit=0) │ │ (trit=-1) │ │ (trit=+1) │
└─────┬──────┘ └─────┬──────┘ └─────┬──────┘
│ │ │
▼ ▼ ▼
┌──────────────┐ ┌──────────────┐ ┌──────────────┐
│ aeropay.com │ │ substack.com │ │ manifold.mkts│
│ (payments) │ │ (5 msgs) │ │ (prediction) │
│ │ │ │ │ │
│ waymo.com │ │ nature.com │ │ browse.ai │
│ (rideshare) │ │ (briefing 4) │ │ (automation) │
│ │ │ │ │ │
│ google.com │ │scienceofppl │ │ jenova.ai │
│ (scholar 5) │ │ (5 msgs) │ │ (AI service) │
│ │ │ │ │ │
│ morph.so │ │ bio.org │ │ heygen.com │
│ (cloud) │ │ (biotech 3) │ │ (video AI) │
└──────────────┘ └──────────────┘ └──────────────┘
Conservation: 0 + (-1) + (+1) = 0 ✓
Cross-Channel Identity Resolution
┌─────────────────────────────────────────────────────────────────────────┐
│ IDENTITY COBORDISM (REAL DATA) │
└─────────────────────────────────────────────────────────────────────────┘
Canonical Identity
┌─────────────────────────┐
│ YULIYA SHKEL │
│ │
│ Phone: +1 (647) 778-6400│
│ Phone: +1 (609) 356-8506│
└───────────┬─────────────┘
│
┌───────────────────────┼───────────────────────┐
│ │ │
▼ ▼ ▼
┌─────────────┐ ┌─────────────┐ ┌─────────────┐
│ OUTLOOK │ │ GMAIL │ │ BEEPER │
│ (−1) │ │ (0) │ │ (+1) │
├─────────────┤ ├─────────────┤ ├─────────────┤
│ y.shkel@ │ │greenteatree │ │ Identities: │
│ utoronto.ca │ │01@gmail.com │ │ │
│ │ │ │ │ Signal: Y │
│ [Academic] │ │ [Personal] │ │ schlynth │
│ │ │ │ │ │
│ │ │ │ │ Telegram: │
│ │ │ │ │ betty crockr│
│ │ │ │ │ │
│ │ │ │ │ WhatsApp: │
│ │ │ │ │ yulia │
│ │ │ │ │ │
│ │ │ │ │ Twitter/X: │
│ │ │ │ │ thesispace │
│ │ │ │ │ transposer │
└─────────────┘ └─────────────┘ └─────────────┘
GF(3) Check: (−1) + (0) + (+1) = 0 ✓
Conversation Categories by Trit
┌─────────────────────────────────────────────────────────────────────────┐
│ CONVERSATION TRIT ASSIGNMENT │
└─────────────────────────────────────────────────────────────────────────┘
MINUS (−1) VALIDATOR ERGODIC (0) COORDINATOR
├── Meta-Org (328 unread) ├── ies (pinned, Signal)
│ Deep discussion, critique │ Core coordination group
│ │
├── Cognition Cosmos (62 unread) ├── greenteatree01 (pinned)
│ Intellectual discourse │ Primary contact point
│ │
├── Gay.jl (13 unread) ├── SF Housing Authority
│ Technical validation │ Logistics coordination
│ │
└── Academic newsletters └── Stanford groups (BJJ, Salon)
Nature, Scholar alerts Community coordination
PLUS (+1) EXECUTOR
├── Frontier Tower chats (all)
│ ├── General (82 unread)
│ ├── Hard Tech (118 unread)
│ ├── Maker Space (138 unread)
│ └── [Active building community]
│
├── Wordle Appreciation (37 unread)
│ Daily engagement, action
│
└── Transactional emails
Aeropay, Waymo, confirmations
DuckDB Schema for Social Graph Storage
-- Run in: ~/ies/ducklake_data/messaging_world.duckdb
CREATE TABLE channels (
id INTEGER PRIMARY KEY,
name VARCHAR,
trit INTEGER, -- -1, 0, +1
account_email VARCHAR
);
INSERT INTO channels VALUES
(1, 'outlook', -1, 'y.shkel@utoronto.ca'),
(2, 'gmail', 0, 'greenteatree01@gmail.com'),
(3, 'beeper', 1, '@greenteatree01:beeper.com');
CREATE TABLE networks (
id INTEGER PRIMARY KEY,
name VARCHAR,
account_id VARCHAR
);
INSERT INTO networks VALUES
(1, 'Signal', 'signal'),
(2, 'Telegram', 'telegram'),
(3, 'WhatsApp', 'whatsapp'),
(4, 'Discord', 'discord'),
(5, 'Twitter', 'twitter'),
(6, 'Matrix', 'hungryserv');
CREATE TABLE contacts (
id INTEGER PRIMARY KEY,
name VARCHAR,
email VARCHAR,
channel_id INTEGER,
network_id INTEGER,
message_count INTEGER,
last_activity TIMESTAMP,
category VARCHAR, -- 'personal', 'transactional', 'academic', 'community'
FOREIGN KEY (channel_id) REFERENCES channels(id),
FOREIGN KEY (network_id) REFERENCES networks(id)
);
CREATE TABLE conversations (
id VARCHAR PRIMARY KEY,
title VARCHAR,
channel_id INTEGER,
network_id INTEGER,
participant_count INTEGER,
unread_count INTEGER,
last_activity TIMESTAMP,
is_pinned BOOLEAN,
chat_type VARCHAR, -- 'single', 'group'
trit INTEGER,
FOREIGN KEY (channel_id) REFERENCES channels(id),
FOREIGN KEY (network_id) REFERENCES networks(id)
);
-- GF(3) conservation view
CREATE VIEW gf3_balance AS
SELECT
SUM(trit) as total_trit,
SUM(trit) % 3 as mod3,
CASE WHEN SUM(trit) % 3 = 0 THEN '✓ balanced' ELSE '⚠ drift' END as status
FROM conversations;
Quick Commands
# Fetch Gmail social graph
uvx --from google-auth --with google-api-python-client --with google-auth-oauthlib \
python3 ~/.claude/skills/gmail/fetch.py --count 50
# Query Beeper chats via MCP
# mcp__beeper__search_chats with limit=50
# Check GF(3) conservation
duckdb ~/ies/ducklake_data/messaging_world.duckdb -c "SELECT * FROM gf3_balance"
Related Skills
| Skill | Trit | Integration |
|---|---|---|
| gmail | 0 | Email extraction |
| utoronto-outlook | -1 | Academic email |
| beeper-mcp | +1 | Multi-protocol messaging |
| duckdb-ies | +1 | Analytics storage |
| acsets | 0 | Schema definition |
| chromatic-walk | 0 | Social graph traversal |