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:
- Transform - Events → GF(3)-typed Interactions
- Route - Interactions → Triadic queue fibers (MINUS/ERGODIC/PLUS)
- Detect - Saturation → Balanced calendar state
- 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.