Time Crystal Scheduling

Time Crystal Scheduling Skill

Use this skill when working with schedule stability, churn analysis, or periodicity detection.

When to Use

• Analyzing schedule changes between regenerations
• Detecting natural cycles (weekly, biweekly, ACGME 4-week)
• Optimizing schedules for minimal disruption
• Checking stroboscopic checkpoint status
• Troubleshooting schedule instability

Key Concepts

Time Crystal Objective Function

score = (1-α-β)·constraint_score + α·rigidity_score + β·fairness_score

Weight Guidelines:

• α = 0.0: Pure constraint optimization (may cause large reshuffles)
• α = 0.3: Balanced - satisfy constraints with minimal disruption (RECOMMENDED)
• α = 0.5: Conservative - prefer stability over minor improvements
• α = 1.0: Pure stability (no changes even if suboptimal)

Rigidity Score

Measures schedule stability (0.0-1.0):

• ≥0.95: Minimal changes (safe to publish)
• 0.85-0.94: Low churn (review recommended)
• 0.70-0.84: Moderate churn (review carefully)
• <0.50: Critical churn (investigate root cause)

Subharmonic Periods

Natural cycles detected via autocorrelation:

• 7 days: Weekly structure
• 14 days: Alternating weekends
• 28 days: ACGME 4-week averaging window
• 84 days: Quarterly rotation

Module Location

backend/app/scheduling/periodicity/
├── __init__.py              # Module exports
├── anti_churn.py            # Rigidity scoring, time crystal objective
├── subharmonic_detector.py  # Cycle detection via autocorrelation
└── stroboscopic_manager.py  # Checkpoint-based state management

Key Functions

Anti-Churn Analysis

from app.scheduling.periodicity import (
    calculate_schedule_rigidity,
    time_crystal_objective,
    estimate_churn_impact,
    hamming_distance,
)

# Compare two schedules
rigidity = calculate_schedule_rigidity(new_schedule, current_schedule)
# Returns 0.0-1.0 (1.0 = identical)

# Get detailed impact
impact = estimate_churn_impact(current, proposed)
# Returns: total_changes, affected_people, severity, recommendation

Periodicity Detection

from app.scheduling.periodicity import (
    detect_subharmonics,
    analyze_periodicity,
)

# Find natural cycles
cycles = detect_subharmonics(assignments, base_period=7)
# Returns: [7, 14, 28] - detected cycle lengths in days

# Full analysis
report = analyze_periodicity(assignments)
# Returns: PeriodicityReport with strength, patterns, recommendations

Stroboscopic State Management

from app.scheduling.periodicity import (
    StroboscopicScheduleManager,
    CheckpointBoundary,
)

manager = StroboscopicScheduleManager()

# Propose draft changes
await manager.propose_draft(new_assignments)

# Advance checkpoint (makes draft authoritative)
await manager.advance_checkpoint(CheckpointBoundary.WEEK_START)

# Get stable state (what observers see)
state = await manager.get_observable_state()

MCP Tools

5 MCP tools available:

1. analyze_schedule_rigidity_tool - Compare schedule stability
2. analyze_schedule_periodicity_tool - Detect natural cycles
3. calculate_time_crystal_objective_tool - Combined optimization score
4. get_checkpoint_status_tool - Stroboscopic state info
5. get_time_crystal_health_tool - Component health monitoring

Common Tasks

Check if Schedule Regeneration is Safe

from app.scheduling.periodicity import estimate_churn_impact, ScheduleSnapshot

current = ScheduleSnapshot.from_assignments(current_assignments)
proposed = ScheduleSnapshot.from_assignments(proposed_assignments)

impact = estimate_churn_impact(current, proposed)

if impact["severity"] in ["high", "critical"]:
    print(f"WARNING: {impact['affected_people']} people affected")
    print(f"Recommendation: {impact['recommendation']}")
else:
    print("Safe to publish")

Preserve Natural Patterns

from app.scheduling.periodicity import analyze_periodicity

report = analyze_periodicity(assignments)

# Configure optimizer to preserve detected patterns
optimizer_config = {
    "preserve_cycles": report.subharmonic_periods,
    "rigidity_weight": 0.3 if report.periodicity_strength > 0.7 else 0.5,
}

Documentation

• Architecture: docs/architecture/TIME_CRYSTAL_ANTI_CHURN.md
• Research: docs/SYNERGY_ANALYSIS.md Section 11
• Integration Guide: backend/app/scheduling/periodicity/INTEGRATION_GUIDE.md

References

• Shleyfman et al. (2025). Planning with Minimal Disruption. arXiv:2508.15358
• Time Crystal Physics: Discrete time crystals (Wilczek 2012)
• docs/explorations/boolean-algebra-parallels.md