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

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

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

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

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()

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")

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,
}