---

name: time-crystal-scheduling description: Time crystal-inspired schedule stability analysis. Use when analyzing schedule churn, detecting natural periodicities, or optimizing for minimal disruption.

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

Copyscore = (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

Copybackend/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

Copyfrom 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

Copyfrom 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

Copyfrom 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

Copyfrom 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

Copyfrom 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