Calendar ACSet Skill

Transform Google Calendar into an ANIMA-condensed system with GF(3) conservation.

Trit: +1 (PLUS - generator/executor)
Principle: Balanced Calendar = Condensed Equilibrium State
Implementation: CalendarACSet + TriadicQueues + SaturationDetector

Overview

Calendar ACSet applies the ANIMA framework to scheduling:

1. Transform - Events → GF(3)-typed Interactions
2. Route - Interactions → Triadic queue fibers (MINUS/ERGODIC/PLUS)
3. Detect - Saturation → Balanced calendar state
4. Verify - Narya proofs for scheduling consistency

CalendarACSet Schema

┌────────────────────────────────────────────────────────────────────┐
│                     CalendarACSet Schema                           │
├────────────────────────────────────────────────────────────────────┤
│                                                                    │
│  Interaction ─────┬────▶ Event                                     │
│  ├─ verb: String  │      ├─ event_id: String                       │
│  ├─ timebin: Int  │      ├─ summary: String                        │
│  ├─ trit: Trit    │      ├─ start_time: DateTime                   │
│  └─ calendar ─────┼──▶   ├─ end_time: DateTime                     │
│                   │      ├─ has_conflicts: Bool                    │
│  QueueItem ───────┼──▶   └─ saturated: Bool                        │
│  ├─ interaction ──┘                                                │
│  └─ agent ───────────▶ Agent3                                      │
│                        ├─ fiber: Trit {-1, 0, +1}                  │
│  Attendee ◀────────────┤                                           │
│  ├─ email: String      └─ name: String                             │
│  ├─ response: Enum                                                 │
│  └─ event ─────────▶ Event                                         │
│                                                                    │
│  Reminder ─────────▶ Event                                         │
│  ├─ method: Enum                                                   │
│  └─ minutes: Int                                                   │
└────────────────────────────────────────────────────────────────────┘

Objects

Object	Description	Trit Role
Event	Calendar event with time bounds	Data
Calendar	Container calendar (primary/secondary)	Aggregate
Attendee	Event participant with response status	Edge
Reminder	Notification configuration	Node
Agent3	Queue fiber (MINUS/ERGODIC/PLUS)	Router
QueueItem	Links Interaction → Agent3	Edge

GF(3) Verb Typing

Calendar actions are assigned trits based on information flow:

VERB_TRIT_MAP = {
    # MINUS (-1): Consumption/Query
    "get_events": -1,      "list_calendars": -1,
    "get_event": -1,       "check_availability": -1,
    
    # ERGODIC (0): Coordination/Modification
    "modify_event": 0,     "update_attendees": 0,
    "reschedule": 0,       "change_reminder": 0,
    "update_location": 0,
    
    # PLUS (+1): Generation/Creation
    "create_event": +1,    "add_google_meet": +1,
    "invite_attendee": +1, "schedule_recurring": +1,
    "delete_event": +1,    # Deletion generates state change
}

MCP Tool → Trit Mapping

Tool	Trit	Description
get_events	-1	Query calendar events (MINUS)
list_calendars	-1	List available calendars (MINUS)
modify_event	0	Update event details (ERGODIC)
create_event	+1	Create new event (PLUS)
delete_event	+1	Remove event (PLUS)

Event-Thread Morphism

Calendar events link to Gmail threads via meeting invites:

def event_thread_morphism(event: Event, thread: Thread) -> Morphism:
    """Morphism from CalendarACSet → GmailACSet"""
    return {
        'source': ('Event', event.event_id),
        'target': ('Thread', thread.thread_id),
        'relation': 'invite_thread',
        'trit_effect': 0,  # ERGODIC - coordination
    }

# Example: Meeting invite creates Gmail thread
event = create_event(summary="Standup", attendees=["team@example.com"])
thread = search_gmail(f"subject:'{event.summary}' from:calendar-notification")
link_event_thread(event, thread)

Triadic Queue Routing

                    ┌─────────────────────────────────────────┐
                    │           TRIADIC QUEUES                │
                    ├─────────────────────────────────────────┤
                    │                                         │
   Interaction ────▶│  route(trit) ───▶ Agent3 Fiber         │
                    │                                         │
                    │  MINUS (-1)  ────▶ [get_events, ...]    │
                    │  ERGODIC (0) ────▶ [modify_event, ...]  │
                    │  PLUS (+1)   ────▶ [create_event, ...]  │
                    │                                         │
                    └─────────────────────────────────────────┘

Saturation Detection

Calendar saturation = no conflicts, all events responded, balanced time:

def is_calendar_saturated(calendar_id: str) -> bool:
    """Calendar is saturated when:
    1. No conflicting events in range
    2. All attendee responses received
    3. GF(3) cycle closure: sum(trits) ≡ 0 (mod 3)
    4. Time blocks balanced (no overload)
    """
    events = get_events(calendar_id)
    
    conflicts = detect_conflicts(events)
    pending_responses = [e for e in events if has_pending_rsvp(e)]
    gf3_sum = sum(event.trit_history) % 3
    
    return (
        len(conflicts) == 0 and
        len(pending_responses) == 0 and
        gf3_sum == 0
    )

def detect_anima() -> Dict:
    """System at ANIMA when all calendars saturated."""
    return {
        "at_anima": all(is_calendar_saturated(c) for c in calendars),
        "condensed_fingerprint": sha256(sorted_event_hashes),
        "conflict_free": True,
    }

Source Files

File	Description	Trit
calendar_acset.py	ACSet schema + GF(3) event tracking	+1
calendar_saturation.py	Conflict detection + saturation	+1
calendar_mcp_bridge.py	MCP tool wiring with guards	0

Workflows

Workflow 1: Meeting Creation with GF(3) Balance

from calendar_mcp_bridge import create_calendar_bridge

bridge = create_calendar_bridge("user@gmail.com")

# MINUS: Check availability first
bridge.get_events(time_min="2025-01-01", time_max="2025-01-07")  # trit=-1

# PLUS: Create meeting
bridge.create_event(
    summary="Project Sync",
    start_time="2025-01-06T10:00:00",
    end_time="2025-01-06T11:00:00",
    attendees=["team@example.com"],
    add_google_meet=True
)  # trit=+1

# Conservation: -1 + 1 = 0 ✓

Workflow 2: Event Response with GF(3) Guard

# MINUS: Read event details
bridge.get_events(event_id=event_id)  # trit=-1

# ERGODIC: Modify response
bridge.modify_event(
    event_id=event_id,
    attendees=[{"email": "me@example.com", "responseStatus": "accepted"}]
)  # trit=0

# PLUS: Add reminder
bridge.modify_event(
    event_id=event_id,
    reminders=[{"method": "popup", "minutes": 15}]
)  # Would need balancing

# Balance with read
bridge.get_events(event_id=event_id)  # -1 + 0 + 1 - 1 = -1... add +1

Workflow 3: Weekly Review with Saturation

detector = CalendarSaturationDetector()

# Review week
events = bridge.get_events(time_min="2025-01-06", time_max="2025-01-13")

for event in events:
    detector.update_event(event.event_id, trit=Trit.MINUS)
    
    if has_conflicts(event):
        bridge.modify_event(event.event_id, reschedule=True)
        detector.update_event(event.event_id, trit=Trit.ERGODIC)

# Check saturation
if detector.is_saturated():
    say("Calendar at equilibrium. No conflicts detected.")

Integration

Skill	Trit	Integration
gmail-anima	0	Event↔Thread morphisms
google-workspace	0	MCP tool provider
gay-mcp	+1	SplitMixTernary RNG
tasks-acset	-1	Event→Task deadline links

GF(3) Triadic Conservation

calendar-acset (+1) ⊗ gmail-anima (0) ⊗ tasks-acset (-1) = 0 ✓
get_events (-1) ⊗ modify_event (0) ⊗ create_event (+1) = 0 ✓

---

Skill Name: calendar-acset
Type: Calendar Management / ANIMA Framework
Trit: +1 (PLUS - generator/executor)
GF(3): Conserved via triadic queue routing
ANIMA: Balanced Calendar = Condensed Equilibrium State

Scientific Skill Interleaving

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

Annotated Data

• anndata [○] via bicomodule

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.