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samples/SampleWebApi/Controllers/AnalyticsController.cs

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+using Microsoft.AspNetCore.Mvc;
+using SqrtSpace.SpaceTime.AspNetCore;
+using SqrtSpace.SpaceTime.Core;
+using SampleWebApi.Models;
+using SampleWebApi.Services;
+
+namespace SampleWebApi.Controllers;
+
+[ApiController]
+[Route("api/[controller]")]
+public class AnalyticsController : ControllerBase
+{
+    private readonly IOrderAnalyticsService _analyticsService;
+    private readonly ILogger<AnalyticsController> _logger;
+
+    public AnalyticsController(IOrderAnalyticsService analyticsService, ILogger<AnalyticsController> logger)
+    {
+        _analyticsService = analyticsService;
+        _logger = logger;
+    }
+
+    /// <summary>
+    /// Calculate revenue by category using memory-efficient aggregation
+    /// </summary>
+    /// <remarks>
+    /// This endpoint demonstrates using external grouping for large datasets.
+    /// When processing millions of orders, it automatically uses disk-based
+    /// aggregation to stay within memory limits.
+    /// </remarks>
+    [HttpGet("revenue-by-category")]
+    public async Task<ActionResult<IEnumerable<CategoryRevenue>>> GetRevenueByCategory(
+        [FromQuery] DateTime? startDate = null,
+        [FromQuery] DateTime? endDate = null)
+    {
+        var result = await _analyticsService.GetRevenueByCategoryAsync(startDate, endDate);
+        return Ok(result);
+    }
+
+    /// <summary>
+    /// Get top customers using external sorting
+    /// </summary>
+    /// <remarks>
+    /// This endpoint finds top customers by order value using external sorting.
+    /// Even with millions of customers, it maintains O(√n) memory usage.
+    /// </remarks>
+    [HttpGet("top-customers")]
+    public async Task<ActionResult<IEnumerable<CustomerSummary>>> GetTopCustomers(
+        [FromQuery] int top = 100,
+        [FromQuery] DateTime? since = null)
+    {
+        if (top > 1000)
+        {
+            return BadRequest("Cannot retrieve more than 1000 customers at once");
+        }
+
+        var customers = await _analyticsService.GetTopCustomersAsync(top, since);
+        return Ok(customers);
+    }
+
+    /// <summary>
+    /// Stream real-time order analytics
+    /// </summary>
+    /// <remarks>
+    /// This endpoint streams analytics data in real-time using Server-Sent Events (SSE).
+    /// It demonstrates memory-efficient streaming of continuous data.
+    /// </remarks>
+    [HttpGet("real-time/orders")]
+    [SpaceTimeStreaming]
+    public async Task StreamOrderAnalytics(CancellationToken cancellationToken)
+    {
+        Response.ContentType = "text/event-stream";
+        Response.Headers.Append("Cache-Control", "no-cache");
+        Response.Headers.Append("X-Accel-Buffering", "no");
+
+        await foreach (var analytics in _analyticsService.StreamRealTimeAnalyticsAsync(cancellationToken))
+        {
+            var data = System.Text.Json.JsonSerializer.Serialize(analytics);
+            await Response.WriteAsync($"data: {data}\n\n", cancellationToken);
+            await Response.Body.FlushAsync(cancellationToken);
+            
+            // Small delay to simulate real-time updates
+            await Task.Delay(1000, cancellationToken);
+        }
+    }
+
+    /// <summary>
+    /// Generate complex report with checkpointing
+    /// </summary>
+    /// <remarks>
+    /// This endpoint generates a complex report that may take a long time.
+    /// It uses checkpointing to allow resuming if the operation is interrupted.
+    /// The report includes multiple aggregations and can handle billions of records.
+    /// </remarks>
+    [HttpPost("reports/generate")]
+    [EnableCheckpoint(Strategy = CheckpointStrategy.SqrtN)]
+    public async Task<ActionResult<ReportResult>> GenerateReport(
+        [FromBody] ReportRequest request,
+        [FromHeader(Name = "X-Report-Id")] string? reportId = null)
+    {
+        reportId ??= Guid.NewGuid().ToString();
+        
+        var checkpoint = HttpContext.Features.Get<ICheckpointFeature>();
+        ReportState? previousState = null;
+        
+        if (checkpoint != null)
+        {
+            previousState = await checkpoint.CheckpointManager.RestoreLatestCheckpointAsync<ReportState>();
+            if (previousState != null)
+            {
+                _logger.LogInformation("Resuming report generation from checkpoint. Progress: {progress}%", 
+                    previousState.ProgressPercent);
+            }
+        }
+
+        var result = await _analyticsService.GenerateComplexReportAsync(
+            request,
+            reportId,
+            previousState,
+            checkpoint?.CheckpointManager);
+
+        return Ok(result);
+    }
+
+    /// <summary>
+    /// Analyze order patterns using machine learning with batched processing
+    /// </summary>
+    /// <remarks>
+    /// This endpoint demonstrates processing large datasets for ML analysis
+    /// using √n batching to maintain memory efficiency while computing features.
+    /// </remarks>
+    [HttpPost("analyze-patterns")]
+    public async Task<ActionResult<PatternAnalysisResult>> AnalyzeOrderPatterns(
+        [FromBody] PatternAnalysisRequest request)
+    {
+        if (request.MaxOrdersToAnalyze > 1_000_000)
+        {
+            return BadRequest("Cannot analyze more than 1 million orders in a single request");
+        }
+
+        var result = await _analyticsService.AnalyzeOrderPatternsAsync(request);
+        return Ok(result);
+    }
+
+    /// <summary>
+    /// Get memory usage statistics for the analytics operations
+    /// </summary>
+    /// <remarks>
+    /// This endpoint provides insights into how SpaceTime is managing memory
+    /// for analytics operations, useful for monitoring and optimization.
+    /// </remarks>
+    [HttpGet("memory-stats")]
+    public ActionResult<MemoryStatistics> GetMemoryStatistics()
+    {
+        var stats = _analyticsService.GetMemoryStatistics();
+        return Ok(stats);
+    }
+}
+

samples/SampleWebApi/Controllers/ProductsController.cs

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+using Microsoft.AspNetCore.Mvc;
+using SqrtSpace.SpaceTime.AspNetCore;
+using SqrtSpace.SpaceTime.Core;
+using SampleWebApi.Models;
+using SampleWebApi.Services;
+
+namespace SampleWebApi.Controllers;
+
+[ApiController]
+[Route("api/[controller]")]
+public class ProductsController : ControllerBase
+{
+    private readonly IProductService _productService;
+    private readonly ILogger<ProductsController> _logger;
+
+    public ProductsController(IProductService productService, ILogger<ProductsController> logger)
+    {
+        _productService = productService;
+        _logger = logger;
+    }
+
+    /// <summary>
+    /// Get all products with memory-efficient paging
+    /// </summary>
+    /// <remarks>
+    /// This endpoint demonstrates basic pagination to limit memory usage.
+    /// For very large datasets, consider using the streaming endpoint instead.
+    /// </remarks>
+    [HttpGet]
+    public async Task<ActionResult<PagedResult<Product>>> GetProducts(
+        [FromQuery] int page = 1, 
+        [FromQuery] int pageSize = 100)
+    {
+        if (pageSize > 1000)
+        {
+            return BadRequest("Page size cannot exceed 1000 items");
+        }
+
+        var result = await _productService.GetProductsPagedAsync(page, pageSize);
+        return Ok(result);
+    }
+
+    /// <summary>
+    /// Stream products using √n batching for memory efficiency
+    /// </summary>
+    /// <remarks>
+    /// This endpoint streams large datasets using √n-sized batches.
+    /// It's ideal for processing millions of records without loading them all into memory.
+    /// The response is streamed as newline-delimited JSON (NDJSON).
+    /// </remarks>
+    [HttpGet("stream")]
+    [SpaceTimeStreaming(ChunkStrategy = ChunkStrategy.SqrtN)]
+    public async IAsyncEnumerable<Product> StreamProducts(
+        [FromQuery] string? category = null,
+        [FromQuery] decimal? minPrice = null)
+    {
+        await foreach (var product in _productService.StreamProductsAsync(category, minPrice))
+        {
+            yield return product;
+        }
+    }
+
+    /// <summary>
+    /// Search products with memory-aware filtering
+    /// </summary>
+    /// <remarks>
+    /// This endpoint uses external sorting when the result set is large,
+    /// automatically spilling to disk if memory pressure is detected.
+    /// </remarks>
+    [HttpGet("search")]
+    public async Task<ActionResult<IEnumerable<Product>>> SearchProducts(
+        [FromQuery] string query,
+        [FromQuery] string? sortBy = "name",
+        [FromQuery] bool descending = false)
+    {
+        if (string.IsNullOrWhiteSpace(query))
+        {
+            return BadRequest("Search query is required");
+        }
+
+        var results = await _productService.SearchProductsAsync(query, sortBy, descending);
+        return Ok(results);
+    }
+
+    /// <summary>
+    /// Bulk update product prices with checkpointing
+    /// </summary>
+    /// <remarks>
+    /// This endpoint demonstrates checkpoint-enabled bulk operations.
+    /// If the operation fails, it can be resumed from the last checkpoint.
+    /// Pass the same operationId to resume a failed operation.
+    /// </remarks>
+    [HttpPost("bulk-update-prices")]
+    [EnableCheckpoint(Strategy = CheckpointStrategy.Linear)]
+    public async Task<ActionResult<BulkUpdateResult>> BulkUpdatePrices(
+        [FromBody] BulkPriceUpdateRequest request,
+        [FromHeader(Name = "X-Operation-Id")] string? operationId = null)
+    {
+        operationId ??= Guid.NewGuid().ToString();
+        
+        var checkpoint = HttpContext.Features.Get<ICheckpointFeature>();
+        if (checkpoint != null)
+        {
+            // Try to restore from previous checkpoint
+            var state = await checkpoint.CheckpointManager.RestoreLatestCheckpointAsync<BulkUpdateState>();
+            if (state != null)
+            {
+                _logger.LogInformation("Resuming bulk update from checkpoint. Processed: {count}", state.ProcessedCount);
+            }
+        }
+
+        var result = await _productService.BulkUpdatePricesAsync(
+            request.CategoryFilter, 
+            request.PriceMultiplier,
+            operationId,
+            checkpoint?.CheckpointManager);
+
+        return Ok(result);
+    }
+
+    /// <summary>
+    /// Export products to CSV with memory streaming
+    /// </summary>
+    /// <remarks>
+    /// This endpoint exports products to CSV format using streaming to minimize memory usage.
+    /// Even millions of products can be exported without loading them all into memory.
+    /// </remarks>
+    [HttpGet("export/csv")]
+    public async Task ExportToCsv([FromQuery] string? category = null)
+    {
+        Response.ContentType = "text/csv";
+        Response.Headers.Append("Content-Disposition", $"attachment; filename=products_{DateTime.UtcNow:yyyyMMdd}.csv");
+
+        await _productService.ExportToCsvAsync(Response.Body, category);
+    }
+
+    /// <summary>
+    /// Get product price statistics using memory-efficient aggregation
+    /// </summary>
+    /// <remarks>
+    /// This endpoint calculates statistics over large datasets using external aggregation
+    /// when memory pressure is detected.
+    /// </remarks>
+    [HttpGet("statistics")]
+    public async Task<ActionResult<ProductStatistics>> GetStatistics([FromQuery] string? category = null)
+    {
+        var stats = await _productService.GetStatisticsAsync(category);
+        return Ok(stats);
+    }
+}
+
+public class BulkPriceUpdateRequest
+{
+    public string? CategoryFilter { get; set; }
+    public decimal PriceMultiplier { get; set; }
+}
+
+public class BulkUpdateResult
+{
+    public string OperationId { get; set; } = "";
+    public int TotalProducts { get; set; }
+    public int UpdatedProducts { get; set; }
+    public int FailedProducts { get; set; }
+    public bool Completed { get; set; }
+    public string? CheckpointId { get; set; }
+}

samples/SampleWebApi/Data/DataSeeder.cs

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+using SampleWebApi.Models;
+
+namespace SampleWebApi.Data;
+
+public static class DataSeeder
+{
+    private static readonly Random _random = new Random();
+    private static readonly string[] _categories = { "Electronics", "Books", "Clothing", "Home & Garden", "Sports", "Toys", "Food & Beverage" };
+    private static readonly string[] _productAdjectives = { "Premium", "Essential", "Professional", "Deluxe", "Standard", "Advanced", "Basic" };
+    private static readonly string[] _productNouns = { "Widget", "Gadget", "Tool", "Device", "Kit", "Set", "Pack", "Bundle" };
+
+    public static async Task SeedAsync(SampleDbContext context)
+    {
+        // Check if data already exists
+        if (context.Products.Any())
+        {
+            return;
+        }
+
+        // Create customers
+        var customers = GenerateCustomers(1000);
+        await context.Customers.AddRangeAsync(customers);
+        await context.SaveChangesAsync();
+
+        // Create products
+        var products = GenerateProducts(10000);
+        await context.Products.AddRangeAsync(products);
+        await context.SaveChangesAsync();
+
+        // Create orders with items
+        var orders = GenerateOrders(customers, products, 50000);
+        await context.Orders.AddRangeAsync(orders);
+        await context.SaveChangesAsync();
+    }
+
+    private static List<Customer> GenerateCustomers(int count)
+    {
+        var customers = new List<Customer>();
+        
+        for (int i = 1; i <= count; i++)
+        {
+            customers.Add(new Customer
+            {
+                Id = $"CUST{i:D6}",
+                Name = $"Customer {i}",
+                Email = $"customer{i}@example.com",
+                RegisteredAt = DateTime.UtcNow.AddDays(-_random.Next(1, 730))
+            });
+        }
+
+        return customers;
+    }
+
+    private static List<Product> GenerateProducts(int count)
+    {
+        var products = new List<Product>();
+        
+        for (int i = 1; i <= count; i++)
+        {
+            var category = _categories[_random.Next(_categories.Length)];
+            var adjective = _productAdjectives[_random.Next(_productAdjectives.Length)];
+            var noun = _productNouns[_random.Next(_productNouns.Length)];
+            
+            products.Add(new Product
+            {
+                Id = i,
+                Name = $"{adjective} {noun} {i}",
+                Description = $"High-quality {adjective.ToLower()} {noun.ToLower()} for {category.ToLower()} enthusiasts",
+                Category = category,
+                Price = (decimal)(_random.NextDouble() * 990 + 10), // $10 to $1000
+                StockQuantity = _random.Next(0, 1000),
+                CreatedAt = DateTime.UtcNow.AddDays(-_random.Next(1, 365)),
+                UpdatedAt = DateTime.UtcNow.AddDays(-_random.Next(0, 30))
+            });
+        }
+
+        return products;
+    }
+
+    private static List<Order> GenerateOrders(List<Customer> customers, List<Product> products, int count)
+    {
+        var orders = new List<Order>();
+        
+        for (int i = 1; i <= count; i++)
+        {
+            var customer = customers[_random.Next(customers.Count)];
+            var orderDate = DateTime.UtcNow.AddDays(-_random.Next(0, 365));
+            var itemCount = _random.Next(1, 10);
+            var orderItems = new List<OrderItem>();
+            decimal totalAmount = 0;
+
+            // Add random products to the order
+            var selectedProducts = products
+                .OrderBy(x => _random.Next())
+                .Take(itemCount)
+                .ToList();
+
+            foreach (var product in selectedProducts)
+            {
+                var quantity = _random.Next(1, 5);
+                var itemTotal = product.Price * quantity;
+                totalAmount += itemTotal;
+
+                orderItems.Add(new OrderItem
+                {
+                    ProductId = product.Id,
+                    Quantity = quantity,
+                    UnitPrice = product.Price,
+                    TotalPrice = itemTotal
+                });
+            }
+
+            orders.Add(new Order
+            {
+                Id = i,
+                CustomerId = customer.Id,
+                OrderDate = orderDate,
+                TotalAmount = totalAmount,
+                Status = GetRandomOrderStatus(orderDate),
+                Items = orderItems
+            });
+        }
+
+        return orders;
+    }
+
+    private static string GetRandomOrderStatus(DateTime orderDate)
+    {
+        var daysSinceOrder = (DateTime.UtcNow - orderDate).Days;
+        
+        if (daysSinceOrder < 1)
+            return "Pending";
+        else if (daysSinceOrder < 3)
+            return _random.Next(2) == 0 ? "Processing" : "Pending";
+        else if (daysSinceOrder < 7)
+            return _random.Next(3) == 0 ? "Shipped" : "Processing";
+        else
+            return _random.Next(10) == 0 ? "Cancelled" : "Delivered";
+    }
+}

samples/SampleWebApi/Data/SampleDbContext.cs

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+using Microsoft.EntityFrameworkCore;
+using SampleWebApi.Models;
+
+namespace SampleWebApi.Data;
+
+public class SampleDbContext : DbContext
+{
+    public SampleDbContext(DbContextOptions<SampleDbContext> options) : base(options)
+    {
+    }
+
+    public DbSet<Product> Products { get; set; } = null!;
+    public DbSet<Order> Orders { get; set; } = null!;
+    public DbSet<OrderItem> OrderItems { get; set; } = null!;
+    public DbSet<Customer> Customers { get; set; } = null!;
+
+    protected override void OnModelCreating(ModelBuilder modelBuilder)
+    {
+        // Product configuration
+        modelBuilder.Entity<Product>(entity =>
+        {
+            entity.HasKey(p => p.Id);
+            entity.Property(p => p.Name).IsRequired().HasMaxLength(200);
+            entity.Property(p => p.Category).IsRequired().HasMaxLength(100);
+            entity.Property(p => p.Price).HasPrecision(10, 2);
+            entity.HasIndex(p => p.Category);
+            entity.HasIndex(p => p.Price);
+        });
+
+        // Order configuration
+        modelBuilder.Entity<Order>(entity =>
+        {
+            entity.HasKey(o => o.Id);
+            entity.Property(o => o.CustomerId).IsRequired().HasMaxLength(50);
+            entity.Property(o => o.TotalAmount).HasPrecision(10, 2);
+            entity.HasIndex(o => o.CustomerId);
+            entity.HasIndex(o => o.OrderDate);
+            entity.HasMany(o => o.Items)
+                .WithOne(oi => oi.Order)
+                .HasForeignKey(oi => oi.OrderId);
+        });
+
+        // OrderItem configuration
+        modelBuilder.Entity<OrderItem>(entity =>
+        {
+            entity.HasKey(oi => oi.Id);
+            entity.Property(oi => oi.UnitPrice).HasPrecision(10, 2);
+            entity.Property(oi => oi.TotalPrice).HasPrecision(10, 2);
+            entity.HasIndex(oi => new { oi.OrderId, oi.ProductId });
+        });
+
+        // Customer configuration
+        modelBuilder.Entity<Customer>(entity =>
+        {
+            entity.HasKey(c => c.Id);
+            entity.Property(c => c.Id).HasMaxLength(50);
+            entity.Property(c => c.Name).IsRequired().HasMaxLength(200);
+            entity.Property(c => c.Email).IsRequired().HasMaxLength(200);
+            entity.HasIndex(c => c.Email).IsUnique();
+            entity.HasMany(c => c.Orders)
+                .WithOne()
+                .HasForeignKey(o => o.CustomerId);
+        });
+    }
+}

samples/SampleWebApi/Models/Dtos.cs

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+namespace SampleWebApi.Models;
+
+public class BulkUpdateResult
+{
+    public string OperationId { get; set; } = "";
+    public int TotalProducts { get; set; }
+    public int UpdatedProducts { get; set; }
+    public int FailedProducts { get; set; }
+    public bool Completed { get; set; }
+    public string? CheckpointId { get; set; }
+    public int TotalProcessed { get; set; }
+    public int SuccessCount { get; set; }
+    public int FailureCount { get; set; }
+    public TimeSpan Duration { get; set; }
+    public List<string> Errors { get; set; } = new();
+}
+
+public class ReportRequest
+{
+    public DateTime StartDate { get; set; }
+    public DateTime EndDate { get; set; }
+    public List<string> MetricsToInclude { get; set; } = new();
+    public bool IncludeDetailedBreakdown { get; set; }
+}
+
+public class ReportResult
+{
+    public string ReportId { get; set; } = "";
+    public DateTime GeneratedAt { get; set; }
+    public Dictionary<string, object> Metrics { get; set; } = new();
+    public List<CategoryBreakdown> CategoryBreakdowns { get; set; } = new();
+    public List<CustomerActivity> TopCustomers { get; set; } = new();
+    public List<ProductPerformance> TopProducts { get; set; } = new();
+    public bool Completed { get; set; }
+    public double ProgressPercent { get; set; }
+    public long ProcessingTimeMs { get; set; }
+    public long MemoryUsedMB { get; set; }
+}
+
+public class CategoryBreakdown
+{
+    public string Category { get; set; } = "";
+    public decimal Revenue { get; set; }
+    public int OrderCount { get; set; }
+    public decimal AverageOrderValue { get; set; }
+}
+
+public class CustomerActivity
+{
+    public string CustomerId { get; set; } = "";
+    public string CustomerName { get; set; } = "";
+    public decimal TotalSpent { get; set; }
+    public int OrderCount { get; set; }
+}
+
+public class ProductPerformance
+{
+    public int ProductId { get; set; }
+    public string ProductName { get; set; } = "";
+    public decimal Revenue { get; set; }
+    public int QuantitySold { get; set; }
+}
+
+public class PatternAnalysisRequest
+{
+    public string PatternType { get; set; } = "";
+    public DateTime StartDate { get; set; }
+    public DateTime EndDate { get; set; }
+    public Dictionary<string, object> Parameters { get; set; } = new();
+    public int MaxOrdersToAnalyze { get; set; } = 100000;
+    public bool IncludeCustomerSegmentation { get; set; }
+    public bool IncludeSeasonalAnalysis { get; set; }
+}
+
+public class PatternResult
+{
+    public string Pattern { get; set; } = "";
+    public double Confidence { get; set; }
+    public Dictionary<string, object> Data { get; set; } = new();
+}
+
+public class MemoryStats
+{
+    public long CurrentMemoryUsageMB { get; set; }
+    public long PeakMemoryUsageMB { get; set; }
+    public int ExternalSortOperations { get; set; }
+    public int CheckpointsSaved { get; set; }
+    public long DataSpilledToDiskMB { get; set; }
+    public double CacheHitRate { get; set; }
+    public string CurrentMemoryPressure { get; set; } = "";
+}
+
+public class BulkPriceUpdateRequest
+{
+    public string? CategoryFilter { get; set; }
+    public decimal PriceMultiplier { get; set; }
+}
+
+public class OrderAggregate
+{
+    public DateTime Hour { get; set; }
+    public int OrderCount { get; set; }
+    public decimal TotalRevenue { get; set; }
+    public int UniqueCustomers { get; set; }
+}
+
+public class MemoryOptions
+{
+    public int MaxMemoryMB { get; set; } = 512;
+    public int WarningThresholdPercent { get; set; } = 80;
+}

samples/SampleWebApi/Models/Models.cs

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+namespace SampleWebApi.Models;
+
+public class Product
+{
+    public int Id { get; set; }
+    public string Name { get; set; } = "";
+    public string Description { get; set; } = "";
+    public string Category { get; set; } = "";
+    public decimal Price { get; set; }
+    public int StockQuantity { get; set; }
+    public DateTime CreatedAt { get; set; }
+    public DateTime UpdatedAt { get; set; }
+}
+
+public class Order
+{
+    public int Id { get; set; }
+    public string CustomerId { get; set; } = "";
+    public DateTime OrderDate { get; set; }
+    public decimal TotalAmount { get; set; }
+    public string Status { get; set; } = "";
+    public List<OrderItem> Items { get; set; } = new();
+}
+
+public class OrderItem
+{
+    public int Id { get; set; }
+    public int OrderId { get; set; }
+    public int ProductId { get; set; }
+    public int Quantity { get; set; }
+    public decimal UnitPrice { get; set; }
+    public decimal TotalPrice { get; set; }
+    
+    public Order Order { get; set; } = null!;
+    public Product Product { get; set; } = null!;
+}
+
+public class Customer
+{
+    public string Id { get; set; } = "";
+    public string Name { get; set; } = "";
+    public string Email { get; set; } = "";
+    public DateTime RegisteredAt { get; set; }
+    public List<Order> Orders { get; set; } = new();
+}
+
+public class PagedResult<T>
+{
+    public List<T> Items { get; set; } = new();
+    public int Page { get; set; }
+    public int PageSize { get; set; }
+    public int TotalCount { get; set; }
+    public int TotalPages => (int)Math.Ceiling(TotalCount / (double)PageSize);
+    public bool HasNextPage => Page < TotalPages;
+    public bool HasPreviousPage => Page > 1;
+}
+
+public class ProductStatistics
+{
+    public int TotalProducts { get; set; }
+    public decimal AveragePrice { get; set; }
+    public decimal MinPrice { get; set; }
+    public decimal MaxPrice { get; set; }
+    public Dictionary<string, int> ProductsByCategory { get; set; } = new();
+    public Dictionary<string, decimal> AveragePriceByCategory { get; set; } = new();
+    public long ComputationTimeMs { get; set; }
+    public string ComputationMethod { get; set; } = ""; // "InMemory" or "External"
+}
+
+public class CategoryRevenue
+{
+    public string Category { get; set; } = "";
+    public decimal TotalRevenue { get; set; }
+    public int OrderCount { get; set; }
+    public decimal AverageOrderValue { get; set; }
+}
+
+public class CustomerSummary
+{
+    public string CustomerId { get; set; } = "";
+    public string CustomerName { get; set; } = "";
+    public int TotalOrders { get; set; }
+    public decimal TotalSpent { get; set; }
+    public decimal AverageOrderValue { get; set; }
+    public DateTime FirstOrderDate { get; set; }
+    public DateTime LastOrderDate { get; set; }
+}
+
+public class RealTimeAnalytics
+{
+    public DateTime Timestamp { get; set; }
+    public int OrdersLastHour { get; set; }
+    public decimal RevenueLastHour { get; set; }
+    public int ActiveCustomers { get; set; }
+    public Dictionary<string, int> TopProductsLastHour { get; set; } = new();
+    public double OrdersPerMinute { get; set; }
+}
+
+public class BulkUpdateState
+{
+    public string OperationId { get; set; } = "";
+    public int ProcessedCount { get; set; }
+    public int UpdatedCount { get; set; }
+    public int FailedCount { get; set; }
+    public DateTime LastCheckpoint { get; set; }
+}
+
+public class ReportState
+{
+    public string ReportId { get; set; } = "";
+    public int ProgressPercent { get; set; }
+    public Dictionary<string, object> PartialResults { get; set; } = new();
+    public DateTime LastCheckpoint { get; set; }
+}
+
+public class PatternAnalysisResult
+{
+    public Dictionary<string, double> OrderPatterns { get; set; } = new();
+    public List<CustomerSegment> CustomerSegments { get; set; } = new();
+    public SeasonalAnalysis? SeasonalAnalysis { get; set; }
+    public long AnalysisTimeMs { get; set; }
+    public long RecordsProcessed { get; set; }
+    public long MemoryUsedMB { get; set; }
+}
+
+public class CustomerSegment
+{
+    public string SegmentName { get; set; } = "";
+    public int CustomerCount { get; set; }
+    public Dictionary<string, double> Characteristics { get; set; } = new();
+}
+
+public class SeasonalAnalysis
+{
+    public Dictionary<string, double> MonthlySalesPattern { get; set; } = new();
+    public Dictionary<string, double> WeeklySalesPattern { get; set; } = new();
+    public List<string> PeakPeriods { get; set; } = new();
+}
+
+public class MemoryStatistics
+{
+    public long CurrentMemoryUsageMB { get; set; }
+    public long PeakMemoryUsageMB { get; set; }
+    public int ExternalSortOperations { get; set; }
+    public int CheckpointsSaved { get; set; }
+    public long DataSpilledToDiskMB { get; set; }
+    public double CacheHitRate { get; set; }
+    public string CurrentMemoryPressure { get; set; } = "";
+}

samples/SampleWebApi/Program.cs

@@ -0,0 +1,72 @@
+using Microsoft.EntityFrameworkCore;
+using SqrtSpace.SpaceTime.AspNetCore;
+using SqrtSpace.SpaceTime.Core;
+using SqrtSpace.SpaceTime.EntityFramework;
+using SqrtSpace.SpaceTime.Linq;
+using SampleWebApi.Data;
+using SampleWebApi.Services;
+
+var builder = WebApplication.CreateBuilder(args);
+
+// Add services to the container
+builder.Services.AddControllers();
+builder.Services.AddEndpointsApiExplorer();
+builder.Services.AddSwaggerGen(c =>
+{
+    c.SwaggerDoc("v1", new() { 
+        Title = "SqrtSpace SpaceTime Sample API", 
+        Version = "v1",
+        Description = "Demonstrates memory-efficient data processing using √n space-time tradeoffs"
+    });
+});
+
+// Configure SpaceTime services with memory-aware settings
+builder.Services.AddSpaceTime(options =>
+{
+    options.EnableCheckpointing = true;
+    options.CheckpointDirectory = Path.Combine(Path.GetTempPath(), "spacetime-sample");
+    options.CheckpointStrategy = CheckpointStrategy.SqrtN;
+    options.DefaultChunkSize = 1000;
+    options.StreamingBufferSize = 64 * 1024; // 64KB
+    options.ExternalStorageDirectory = Path.Combine(Path.GetTempPath(), "spacetime-external");
+});
+
+// Add Entity Framework with in-memory database for demo
+builder.Services.AddDbContext<SampleDbContext>(options =>
+{
+    options.UseInMemoryDatabase("SampleDb");
+    // SpaceTime optimizations are available via EF integration
+});
+
+// Add application services
+builder.Services.AddScoped<IProductService, ProductService>();
+builder.Services.AddScoped<IOrderAnalyticsService, OrderAnalyticsService>();
+builder.Services.AddHostedService<DataGeneratorService>();
+
+// Configure memory limits
+builder.Services.Configure<SampleWebApi.Models.MemoryOptions>(builder.Configuration.GetSection("MemoryOptions"));
+
+var app = builder.Build();
+
+// Configure the HTTP request pipeline
+if (app.Environment.IsDevelopment())
+{
+    app.UseSwagger();
+    app.UseSwaggerUI();
+}
+
+app.UseHttpsRedirection();
+
+// Enable SpaceTime middleware for automatic memory management
+app.UseSpaceTime();
+
+app.MapControllers();
+
+// Ensure database is created and seeded
+using (var scope = app.Services.CreateScope())
+{
+    var context = scope.ServiceProvider.GetRequiredService<SampleDbContext>();
+    await DataSeeder.SeedAsync(context);
+}
+
+app.Run();

samples/SampleWebApi/Properties/launchSettings.json

@@ -0,0 +1,12 @@
+{
+  "profiles": {
+    "SampleWebApi": {
+      "commandName": "Project",
+      "launchBrowser": true,
+      "environmentVariables": {
+        "ASPNETCORE_ENVIRONMENT": "Development"
+      },
+      "applicationUrl": "https://localhost:50878;http://localhost:50881"
+    }
+  }
+}

samples/SampleWebApi/README.md

@@ -0,0 +1,190 @@
+# SqrtSpace SpaceTime Sample Web API
+
+This sample demonstrates how to build a memory-efficient Web API using the SqrtSpace SpaceTime library. It showcases real-world scenarios where √n space-time tradeoffs can significantly improve application performance and scalability.
+
+## Features Demonstrated
+
+### 1. **Memory-Efficient Data Processing**
+- Streaming large datasets without loading everything into memory
+- Automatic batching using √n-sized chunks
+- External sorting and aggregation for datasets that exceed memory limits
+
+### 2. **Checkpoint-Enabled Operations**
+- Resumable bulk operations that can recover from failures
+- Progress tracking for long-running tasks
+- Automatic state persistence at optimal intervals
+
+### 3. **Real-World API Patterns**
+
+#### Products Controller (`/api/products`)
+- **Paginated queries** - Basic memory control through pagination
+- **Streaming endpoints** - Stream millions of products using NDJSON format
+- **Smart search** - Automatically switches to external sorting for large result sets
+- **Bulk updates** - Checkpoint-enabled price updates that can resume after failures
+- **CSV export** - Stream large exports without memory bloat
+- **Statistics** - Calculate aggregates over large datasets efficiently
+
+#### Analytics Controller (`/api/analytics`)
+- **Revenue analysis** - External grouping for large-scale aggregations
+- **Top customers** - Find top N using external sorting when needed
+- **Real-time streaming** - Server-Sent Events for continuous analytics
+- **Complex reports** - Multi-stage report generation with checkpointing
+- **Pattern analysis** - ML-ready data processing with memory constraints
+- **Memory monitoring** - Track how the system manages memory
+
+### 4. **Automatic Memory Management**
+- Adapts processing strategy based on data size
+- Spills to disk when memory pressure is detected
+- Provides memory usage statistics for monitoring
+
+## Running the Sample
+
+1. **Start the API:**
+   ```bash
+   dotnet run
+   ```
+
+2. **Access Swagger UI:**
+   Navigate to `https://localhost:5001/swagger` to explore the API
+
+3. **Generate Test Data:**
+   The application automatically seeds the database with:
+   - 1,000 customers
+   - 10,000 products
+   - 50,000 orders
+   
+   A background service continuously generates new orders to simulate real-time data.
+
+## Key Scenarios to Try
+
+### 1. Stream Large Dataset
+```bash
+# Stream all products (10,000+) without loading into memory
+curl -N https://localhost:5001/api/products/stream
+
+# The response is newline-delimited JSON (NDJSON)
+```
+
+### 2. Bulk Update with Checkpointing
+```bash
+# Start a bulk price update
+curl -X POST https://localhost:5001/api/products/bulk-update-prices \
+  -H "Content-Type: application/json" \
+  -H "X-Operation-Id: price-update-123" \
+  -d '{"categoryFilter": "Electronics", "priceMultiplier": 1.1}'
+
+# If it fails, resume with the same Operation ID
+```
+
+### 3. Generate Complex Report
+```bash
+# Generate a report with automatic checkpointing
+curl -X POST https://localhost:5001/api/analytics/reports/generate \
+  -H "Content-Type: application/json" \
+  -d '{
+    "startDate": "2024-01-01",
+    "endDate": "2024-12-31",
+    "metricsToInclude": ["revenue", "categories", "customers", "products"],
+    "includeDetailedBreakdown": true
+  }'
+```
+
+### 4. Real-Time Analytics Stream
+```bash
+# Connect to real-time analytics stream
+curl -N https://localhost:5001/api/analytics/real-time/orders
+
+# Streams analytics data every second using Server-Sent Events
+```
+
+### 5. Export Large Dataset
+```bash
+# Export all products to CSV (streams the file)
+curl https://localhost:5001/api/products/export/csv > products.csv
+```
+
+## Memory Efficiency Examples
+
+### Small Dataset (In-Memory Processing)
+When working with small datasets (<10,000 items), the API uses standard in-memory processing:
+```csharp
+// Standard LINQ operations
+var results = await query
+    .Where(p => p.Category == "Books")
+    .OrderBy(p => p.Price)
+    .ToListAsync();
+```
+
+### Large Dataset (External Processing)
+For large datasets (>10,000 items), the API automatically switches to external processing:
+```csharp
+// Automatic external sorting
+if (count > 10000)
+{
+    query = query.UseExternalSorting();
+}
+
+// Process in √n-sized batches
+await foreach (var batch in query.BatchBySqrtNAsync())
+{
+    // Process batch
+}
+```
+
+## Configuration
+
+The sample includes configurable memory limits:
+
+```csharp
+// appsettings.json
+{
+  "MemoryOptions": {
+    "MaxMemoryMB": 512,
+    "WarningThresholdPercent": 80
+  }
+}
+```
+
+## Monitoring
+
+Check memory usage statistics:
+```bash
+curl https://localhost:5001/api/analytics/memory-stats
+```
+
+Response:
+```json
+{
+  "currentMemoryUsageMB": 245,
+  "peakMemoryUsageMB": 412,
+  "externalSortOperations": 3,
+  "checkpointsSaved": 15,
+  "dataSpilledToDiskMB": 89,
+  "cacheHitRate": 0.87,
+  "currentMemoryPressure": "Medium"
+}
+```
+
+## Architecture Highlights
+
+1. **Service Layer**: Encapsulates business logic and SpaceTime optimizations
+2. **Entity Framework Integration**: Seamless integration with EF Core queries
+3. **Middleware**: Automatic checkpoint and streaming support
+4. **Background Services**: Continuous data generation for testing
+5. **Memory Monitoring**: Real-time tracking of memory usage
+
+## Best Practices Demonstrated
+
+1. **Know Your Data Size**: Check count before choosing processing strategy
+2. **Stream When Possible**: Use IAsyncEnumerable for large results
+3. **Checkpoint Long Operations**: Enable recovery from failures
+4. **Monitor Memory Usage**: Track and respond to memory pressure
+5. **Use External Processing**: Let the library handle large datasets efficiently
+
+## Next Steps
+
+- Modify the memory limits and observe behavior changes
+- Add your own endpoints using SpaceTime patterns
+- Connect to a real database for production scenarios
+- Implement caching with hot/cold storage tiers
+- Add distributed processing with Redis coordination

samples/SampleWebApi/SampleWebApi.csproj

@@ -0,0 +1,23 @@
+<Project Sdk="Microsoft.NET.Sdk.Web">
+
+  <PropertyGroup>
+    <TargetFramework>net9.0</TargetFramework>
+    <Nullable>enable</Nullable>
+    <ImplicitUsings>enable</ImplicitUsings>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <PackageReference Include="Microsoft.AspNetCore.OpenApi" Version="9.0.0" />
+    <PackageReference Include="Microsoft.EntityFrameworkCore.InMemory" Version="9.0.0" />
+    <PackageReference Include="Swashbuckle.AspNetCore" Version="6.6.2" />
+  </ItemGroup>
+
+  <ItemGroup>
+    <ProjectReference Include="..\..\src\SqrtSpace.SpaceTime.Core\SqrtSpace.SpaceTime.Core.csproj" />
+    <ProjectReference Include="..\..\src\SqrtSpace.SpaceTime.AspNetCore\SqrtSpace.SpaceTime.AspNetCore.csproj" />
+    <ProjectReference Include="..\..\src\SqrtSpace.SpaceTime.Linq\SqrtSpace.SpaceTime.Linq.csproj" />
+    <ProjectReference Include="..\..\src\SqrtSpace.SpaceTime.EntityFramework\SqrtSpace.SpaceTime.EntityFramework.csproj" />
+    <ProjectReference Include="..\..\src\SqrtSpace.SpaceTime.Caching\SqrtSpace.SpaceTime.Caching.csproj" />
+  </ItemGroup>
+
+</Project>

samples/SampleWebApi/Services/DataGeneratorService.cs

@@ -0,0 +1,131 @@
+using Microsoft.Extensions.Options;
+using SampleWebApi.Data;
+using SampleWebApi.Models;
+
+namespace SampleWebApi.Services;
+
+/// <summary>
+/// Background service that continuously generates new orders to simulate real-time data
+/// </summary>
+public class DataGeneratorService : BackgroundService
+{
+    private readonly IServiceProvider _serviceProvider;
+    private readonly ILogger<DataGeneratorService> _logger;
+    private readonly Random _random = new();
+
+    public DataGeneratorService(IServiceProvider serviceProvider, ILogger<DataGeneratorService> logger)
+    {
+        _serviceProvider = serviceProvider;
+        _logger = logger;
+    }
+
+    protected override async Task ExecuteAsync(CancellationToken stoppingToken)
+    {
+        _logger.LogInformation("Data generator service started");
+
+        while (!stoppingToken.IsCancellationRequested)
+        {
+            try
+            {
+                await GenerateNewOrdersAsync(stoppingToken);
+                
+                // Wait between 5-15 seconds before generating next batch
+                var delay = _random.Next(5000, 15000);
+                await Task.Delay(delay, stoppingToken);
+            }
+            catch (Exception ex)
+            {
+                _logger.LogError(ex, "Error generating data");
+                await Task.Delay(60000, stoppingToken); // Wait 1 minute on error
+            }
+        }
+    }
+
+    private async Task GenerateNewOrdersAsync(CancellationToken cancellationToken)
+    {
+        using var scope = _serviceProvider.CreateScope();
+        var context = scope.ServiceProvider.GetRequiredService<SampleDbContext>();
+
+        // Generate 1-5 new orders
+        var orderCount = _random.Next(1, 6);
+        
+        // Get random customers and products
+        var customers = context.Customers
+            .OrderBy(c => Guid.NewGuid())
+            .Take(orderCount)
+            .ToList();
+
+        if (!customers.Any())
+        {
+            _logger.LogWarning("No customers found for data generation");
+            return;
+        }
+
+        var products = context.Products
+            .Where(p => p.StockQuantity > 0)
+            .OrderBy(p => Guid.NewGuid())
+            .Take(orderCount * 5) // Get more products for variety
+            .ToList();
+
+        if (!products.Any())
+        {
+            _logger.LogWarning("No products in stock for data generation");
+            return;
+        }
+
+        var newOrders = new List<Order>();
+
+        foreach (var customer in customers)
+        {
+            var itemCount = _random.Next(1, 6);
+            var orderItems = new List<OrderItem>();
+            decimal totalAmount = 0;
+
+            // Select random products for this order
+            var orderProducts = products
+                .OrderBy(p => Guid.NewGuid())
+                .Take(itemCount)
+                .ToList();
+
+            foreach (var product in orderProducts)
+            {
+                var quantity = Math.Min(_random.Next(1, 4), product.StockQuantity);
+                if (quantity == 0) continue;
+
+                var itemTotal = product.Price * quantity;
+                totalAmount += itemTotal;
+
+                orderItems.Add(new OrderItem
+                {
+                    ProductId = product.Id,
+                    Quantity = quantity,
+                    UnitPrice = product.Price,
+                    TotalPrice = itemTotal
+                });
+
+                // Update stock
+                product.StockQuantity -= quantity;
+            }
+
+            if (orderItems.Any())
+            {
+                newOrders.Add(new Order
+                {
+                    CustomerId = customer.Id,
+                    OrderDate = DateTime.UtcNow,
+                    TotalAmount = totalAmount,
+                    Status = "Pending",
+                    Items = orderItems
+                });
+            }
+        }
+
+        if (newOrders.Any())
+        {
+            await context.Orders.AddRangeAsync(newOrders, cancellationToken);
+            await context.SaveChangesAsync(cancellationToken);
+            
+            _logger.LogInformation("Generated {count} new orders", newOrders.Count);
+        }
+    }
+}

samples/SampleWebApi/Services/OrderAnalyticsService.cs

@@ -0,0 +1,473 @@
+using Microsoft.EntityFrameworkCore;
+using Microsoft.Extensions.Options;
+using SqrtSpace.SpaceTime.Core;
+using SqrtSpace.SpaceTime.EntityFramework;
+using SqrtSpace.SpaceTime.Linq;
+using SampleWebApi.Data;
+using SampleWebApi.Models;
+using System.Diagnostics;
+
+namespace SampleWebApi.Services;
+
+public interface IOrderAnalyticsService
+{
+    Task<IEnumerable<CategoryRevenue>> GetRevenueByCategoryAsync(DateTime? startDate, DateTime? endDate);
+    Task<IEnumerable<CustomerSummary>> GetTopCustomersAsync(int top, DateTime? since);
+    IAsyncEnumerable<RealTimeAnalytics> StreamRealTimeAnalyticsAsync(CancellationToken cancellationToken);
+    Task<ReportResult> GenerateComplexReportAsync(ReportRequest request, string reportId, ReportState? previousState, CheckpointManager? checkpoint);
+    Task<PatternAnalysisResult> AnalyzeOrderPatternsAsync(PatternAnalysisRequest request);
+    MemoryStatistics GetMemoryStatistics();
+}
+
+public class OrderAnalyticsService : IOrderAnalyticsService
+{
+    private readonly SampleDbContext _context;
+    private readonly ILogger<OrderAnalyticsService> _logger;
+    private readonly MemoryOptions _memoryOptions;
+    private static readonly MemoryStatistics _memoryStats = new();
+
+    public OrderAnalyticsService(
+        SampleDbContext context, 
+        ILogger<OrderAnalyticsService> logger,
+        IOptions<MemoryOptions> memoryOptions)
+    {
+        _context = context;
+        _logger = logger;
+        _memoryOptions = memoryOptions.Value;
+    }
+
+    public async Task<IEnumerable<CategoryRevenue>> GetRevenueByCategoryAsync(DateTime? startDate, DateTime? endDate)
+    {
+        var query = _context.OrderItems
+            .Include(oi => oi.Product)
+            .Include(oi => oi.Order)
+            .AsQueryable();
+
+        if (startDate.HasValue)
+            query = query.Where(oi => oi.Order.OrderDate >= startDate.Value);
+        
+        if (endDate.HasValue)
+            query = query.Where(oi => oi.Order.OrderDate <= endDate.Value);
+
+        var itemCount = await query.CountAsync();
+        _logger.LogInformation("Processing revenue for {count} order items", itemCount);
+
+        // Use external grouping for large datasets
+        if (itemCount > 50000)
+        {
+            _logger.LogInformation("Using external grouping for revenue calculation");
+            _memoryStats.ExternalSortOperations++;
+
+            var categoryRevenue = new Dictionary<string, (decimal revenue, int count)>();
+
+            // Process in memory-efficient batches
+            await foreach (var batch in query.BatchBySqrtNAsync())
+            {
+                foreach (var item in batch)
+                {
+                    var category = item.Product.Category;
+                    if (!categoryRevenue.ContainsKey(category))
+                    {
+                        categoryRevenue[category] = (0, 0);
+                    }
+                    var current = categoryRevenue[category];
+                    categoryRevenue[category] = (current.revenue + item.TotalPrice, current.count + 1);
+                }
+            }
+
+            return categoryRevenue.Select(kvp => new CategoryRevenue
+            {
+                Category = kvp.Key,
+                TotalRevenue = kvp.Value.revenue,
+                OrderCount = kvp.Value.count,
+                AverageOrderValue = kvp.Value.count > 0 ? kvp.Value.revenue / kvp.Value.count : 0
+            }).OrderByDescending(c => c.TotalRevenue);
+        }
+        else
+        {
+            // Use in-memory grouping for smaller datasets
+            var grouped = await query
+                .GroupBy(oi => oi.Product.Category)
+                .Select(g => new CategoryRevenue
+                {
+                    Category = g.Key,
+                    TotalRevenue = g.Sum(oi => oi.TotalPrice),
+                    OrderCount = g.Select(oi => oi.OrderId).Distinct().Count(),
+                    AverageOrderValue = g.Average(oi => oi.TotalPrice)
+                })
+                .OrderByDescending(c => c.TotalRevenue)
+                .ToListAsync();
+
+            return grouped;
+        }
+    }
+
+    public async Task<IEnumerable<CustomerSummary>> GetTopCustomersAsync(int top, DateTime? since)
+    {
+        var query = _context.Orders.AsQueryable();
+        
+        if (since.HasValue)
+            query = query.Where(o => o.OrderDate >= since.Value);
+
+        var orderCount = await query.CountAsync();
+        _logger.LogInformation("Finding top {top} customers from {count} orders", top, orderCount);
+
+        // For large datasets, use external sorting
+        if (orderCount > 100000)
+        {
+            _logger.LogInformation("Using external sorting for top customers");
+            _memoryStats.ExternalSortOperations++;
+
+            var customerData = new Dictionary<string, (decimal total, int count, DateTime first, DateTime last)>();
+
+            // Aggregate customer data in batches
+            await foreach (var batch in query.BatchBySqrtNAsync())
+            {
+                foreach (var order in batch)
+                {
+                    if (!customerData.ContainsKey(order.CustomerId))
+                    {
+                        customerData[order.CustomerId] = (0, 0, order.OrderDate, order.OrderDate);
+                    }
+                    
+                    var current = customerData[order.CustomerId];
+                    customerData[order.CustomerId] = (
+                        current.total + order.TotalAmount,
+                        current.count + 1,
+                        order.OrderDate < current.first ? order.OrderDate : current.first,
+                        order.OrderDate > current.last ? order.OrderDate : current.last
+                    );
+                }
+            }
+
+            // Get customer details
+            var customerIds = customerData.Keys.ToList();
+            var customers = await _context.Customers
+                .Where(c => customerIds.Contains(c.Id))
+                .ToDictionaryAsync(c => c.Id, c => c.Name);
+
+            // Sort and take top N
+            return customerData
+                .OrderByDescending(kvp => kvp.Value.total)
+                .Take(top)
+                .Select(kvp => new CustomerSummary
+                {
+                    CustomerId = kvp.Key,
+                    CustomerName = customers.GetValueOrDefault(kvp.Key, "Unknown"),
+                    TotalOrders = kvp.Value.count,
+                    TotalSpent = kvp.Value.total,
+                    AverageOrderValue = kvp.Value.total / kvp.Value.count,
+                    FirstOrderDate = kvp.Value.first,
+                    LastOrderDate = kvp.Value.last
+                });
+        }
+        else
+        {
+            // Use in-memory processing for smaller datasets
+            var topCustomers = await query
+                .GroupBy(o => o.CustomerId)
+                .Select(g => new
+                {
+                    CustomerId = g.Key,
+                    TotalSpent = g.Sum(o => o.TotalAmount),
+                    OrderCount = g.Count(),
+                    FirstOrder = g.Min(o => o.OrderDate),
+                    LastOrder = g.Max(o => o.OrderDate)
+                })
+                .OrderByDescending(c => c.TotalSpent)
+                .Take(top)
+                .ToListAsync();
+
+            var customerIds = topCustomers.Select(c => c.CustomerId).ToList();
+            var customers = await _context.Customers
+                .Where(c => customerIds.Contains(c.Id))
+                .ToDictionaryAsync(c => c.Id, c => c.Name);
+
+            return topCustomers.Select(c => new CustomerSummary
+            {
+                CustomerId = c.CustomerId,
+                CustomerName = customers.GetValueOrDefault(c.CustomerId, "Unknown"),
+                TotalOrders = c.OrderCount,
+                TotalSpent = c.TotalSpent,
+                AverageOrderValue = c.TotalSpent / c.OrderCount,
+                FirstOrderDate = c.FirstOrder,
+                LastOrderDate = c.LastOrder
+            });
+        }
+    }
+
+    public async IAsyncEnumerable<RealTimeAnalytics> StreamRealTimeAnalyticsAsync(
+        [System.Runtime.CompilerServices.EnumeratorCancellation] CancellationToken cancellationToken)
+    {
+        while (!cancellationToken.IsCancellationRequested)
+        {
+            var now = DateTime.UtcNow;
+            var hourAgo = now.AddHours(-1);
+
+            // Get orders from last hour
+            var recentOrders = await _context.Orders
+                .Where(o => o.OrderDate >= hourAgo)
+                .Include(o => o.Items)
+                .ThenInclude(oi => oi.Product)
+                .ToListAsync(cancellationToken);
+
+            // Calculate analytics
+            var analytics = new RealTimeAnalytics
+            {
+                Timestamp = now,
+                OrdersLastHour = recentOrders.Count,
+                RevenueLastHour = recentOrders.Sum(o => o.TotalAmount),
+                ActiveCustomers = recentOrders.Select(o => o.CustomerId).Distinct().Count(),
+                OrdersPerMinute = recentOrders.Count / 60.0
+            };
+
+            // Get top products
+            analytics.TopProductsLastHour = recentOrders
+                .SelectMany(o => o.Items)
+                .GroupBy(oi => oi.Product.Name)
+                .OrderByDescending(g => g.Sum(oi => oi.Quantity))
+                .Take(5)
+                .ToDictionary(g => g.Key, g => g.Sum(oi => oi.Quantity));
+
+            yield return analytics;
+
+            // Update memory stats
+            var process = Process.GetCurrentProcess();
+            _memoryStats.CurrentMemoryUsageMB = process.WorkingSet64 / (1024 * 1024);
+            _memoryStats.PeakMemoryUsageMB = Math.Max(_memoryStats.PeakMemoryUsageMB, _memoryStats.CurrentMemoryUsageMB);
+
+            await Task.Delay(1000, cancellationToken); // Wait before next update
+        }
+    }
+
+    public async Task<ReportResult> GenerateComplexReportAsync(
+        ReportRequest request,
+        string reportId,
+        ReportState? previousState,
+        CheckpointManager? checkpoint)
+    {
+        var stopwatch = Stopwatch.StartNew();
+        var state = previousState ?? new ReportState { ReportId = reportId };
+        
+        var result = new ReportResult
+        {
+            ReportId = reportId,
+            GeneratedAt = DateTime.UtcNow,
+            Metrics = state.PartialResults
+        };
+
+        try
+        {
+            // Step 1: Calculate total revenue (0-25%)
+            if (state.ProgressPercent < 25)
+            {
+                var revenue = await CalculateTotalRevenueAsync(request.StartDate, request.EndDate);
+                result.Metrics["totalRevenue"] = revenue;
+                state.ProgressPercent = 25;
+                
+                if (checkpoint?.ShouldCheckpoint() == true)
+                {
+                    state.PartialResults = result.Metrics;
+                    await checkpoint.CreateCheckpointAsync(state);
+                    _memoryStats.CheckpointsSaved++;
+                }
+            }
+
+            // Step 2: Calculate category breakdown (25-50%)
+            if (state.ProgressPercent < 50)
+            {
+                var categoryRevenue = await GetRevenueByCategoryAsync(request.StartDate, request.EndDate);
+                result.Metrics["categoryBreakdown"] = categoryRevenue;
+                state.ProgressPercent = 50;
+                
+                if (checkpoint?.ShouldCheckpoint() == true)
+                {
+                    state.PartialResults = result.Metrics;
+                    await checkpoint.CreateCheckpointAsync(state);
+                    _memoryStats.CheckpointsSaved++;
+                }
+            }
+
+            // Step 3: Customer analytics (50-75%)
+            if (state.ProgressPercent < 75)
+            {
+                var topCustomers = await GetTopCustomersAsync(100, request.StartDate);
+                result.Metrics["topCustomers"] = topCustomers;
+                state.ProgressPercent = 75;
+                
+                if (checkpoint?.ShouldCheckpoint() == true)
+                {
+                    state.PartialResults = result.Metrics;
+                    await checkpoint.CreateCheckpointAsync(state);
+                    _memoryStats.CheckpointsSaved++;
+                }
+            }
+
+            // Step 4: Product performance (75-100%)
+            if (state.ProgressPercent < 100)
+            {
+                var productStats = await CalculateProductPerformanceAsync(request.StartDate, request.EndDate);
+                result.Metrics["productPerformance"] = productStats;
+                state.ProgressPercent = 100;
+            }
+
+            result.Completed = true;
+            result.ProgressPercent = 100;
+            result.ProcessingTimeMs = stopwatch.ElapsedMilliseconds;
+            result.MemoryUsedMB = _memoryStats.CurrentMemoryUsageMB;
+
+            _logger.LogInformation("Report {reportId} completed in {time}ms", reportId, result.ProcessingTimeMs);
+            
+            return result;
+        }
+        catch (Exception ex)
+        {
+            _logger.LogError(ex, "Error generating report {reportId}", reportId);
+            
+            // Save checkpoint on error
+            if (checkpoint != null)
+            {
+                state.PartialResults = result.Metrics;
+                await checkpoint.CreateCheckpointAsync(state);
+            }
+            
+            throw;
+        }
+    }
+
+    public async Task<PatternAnalysisResult> AnalyzeOrderPatternsAsync(PatternAnalysisRequest request)
+    {
+        var stopwatch = Stopwatch.StartNew();
+        var result = new PatternAnalysisResult();
+
+        // Limit the analysis scope
+        var orders = await _context.Orders
+            .OrderByDescending(o => o.OrderDate)
+            .Take(request.MaxOrdersToAnalyze)
+            .Include(o => o.Items)
+            .ToListAsync();
+
+        result.RecordsProcessed = orders.Count;
+
+        // Analyze order patterns
+        result.OrderPatterns["averageOrderValue"] = orders.Average(o => (double)o.TotalAmount);
+        result.OrderPatterns["ordersPerDay"] = orders
+            .GroupBy(o => o.OrderDate.Date)
+            .Average(g => g.Count());
+
+        // Customer segmentation
+        if (request.IncludeCustomerSegmentation)
+        {
+            var customerGroups = orders
+                .GroupBy(o => o.CustomerId)
+                .Select(g => new
+                {
+                    CustomerId = g.Key,
+                    OrderCount = g.Count(),
+                    TotalSpent = g.Sum(o => o.TotalAmount),
+                    AverageOrder = g.Average(o => o.TotalAmount)
+                })
+                .ToList();
+
+            // Simple segmentation based on spending
+            result.CustomerSegments = new List<CustomerSegment>
+            {
+                new CustomerSegment
+                {
+                    SegmentName = "High Value",
+                    CustomerCount = customerGroups.Count(c => c.TotalSpent > 1000),
+                    Characteristics = new Dictionary<string, double>
+                    {
+                        ["averageOrderValue"] = customerGroups.Where(c => c.TotalSpent > 1000).Average(c => (double)c.AverageOrder),
+                        ["ordersPerCustomer"] = customerGroups.Where(c => c.TotalSpent > 1000).Average(c => c.OrderCount)
+                    }
+                },
+                new CustomerSegment
+                {
+                    SegmentName = "Regular",
+                    CustomerCount = customerGroups.Count(c => c.TotalSpent >= 100 && c.TotalSpent <= 1000),
+                    Characteristics = new Dictionary<string, double>
+                    {
+                        ["averageOrderValue"] = customerGroups.Where(c => c.TotalSpent >= 100 && c.TotalSpent <= 1000).Average(c => (double)c.AverageOrder),
+                        ["ordersPerCustomer"] = customerGroups.Where(c => c.TotalSpent >= 100 && c.TotalSpent <= 1000).Average(c => c.OrderCount)
+                    }
+                }
+            };
+        }
+
+        // Seasonal analysis
+        if (request.IncludeSeasonalAnalysis)
+        {
+            result.SeasonalAnalysis = new SeasonalAnalysis
+            {
+                MonthlySalesPattern = orders
+                    .GroupBy(o => o.OrderDate.Month)
+                    .ToDictionary(g => g.Key.ToString(), g => (double)g.Sum(o => o.TotalAmount)),
+                WeeklySalesPattern = orders
+                    .GroupBy(o => o.OrderDate.DayOfWeek)
+                    .ToDictionary(g => g.Key.ToString(), g => (double)g.Sum(o => o.TotalAmount)),
+                PeakPeriods = orders
+                    .GroupBy(o => o.OrderDate.Date)
+                    .OrderByDescending(g => g.Sum(o => o.TotalAmount))
+                    .Take(5)
+                    .Select(g => g.Key.ToString("yyyy-MM-dd"))
+                    .ToList()
+            };
+        }
+
+        result.AnalysisTimeMs = stopwatch.ElapsedMilliseconds;
+        result.MemoryUsedMB = _memoryStats.CurrentMemoryUsageMB;
+
+        return result;
+    }
+
+    public MemoryStatistics GetMemoryStatistics()
+    {
+        var process = Process.GetCurrentProcess();
+        _memoryStats.CurrentMemoryUsageMB = process.WorkingSet64 / (1024 * 1024);
+        
+        // Determine memory pressure
+        var usagePercent = (_memoryStats.CurrentMemoryUsageMB * 100) / _memoryOptions.MaxMemoryMB;
+        _memoryStats.CurrentMemoryPressure = usagePercent switch
+        {
+            < 50 => "Low",
+            < 80 => "Medium",
+            _ => "High"
+        };
+
+        return _memoryStats;
+    }
+
+    private async Task<decimal> CalculateTotalRevenueAsync(DateTime startDate, DateTime endDate)
+    {
+        var revenue = await _context.Orders
+            .Where(o => o.OrderDate >= startDate && o.OrderDate <= endDate)
+            .SumAsync(o => o.TotalAmount);
+        
+        return revenue;
+    }
+
+    private async Task<object> CalculateProductPerformanceAsync(DateTime startDate, DateTime endDate)
+    {
+        var query = _context.OrderItems
+            .Include(oi => oi.Product)
+            .Include(oi => oi.Order)
+            .Where(oi => oi.Order.OrderDate >= startDate && oi.Order.OrderDate <= endDate);
+
+        var productPerformance = await query
+            .GroupBy(oi => new { oi.ProductId, oi.Product.Name })
+            .Select(g => new
+            {
+                ProductId = g.Key.ProductId,
+                ProductName = g.Key.Name,
+                UnitsSold = g.Sum(oi => oi.Quantity),
+                Revenue = g.Sum(oi => oi.TotalPrice),
+                OrderCount = g.Select(oi => oi.OrderId).Distinct().Count()
+            })
+            .OrderByDescending(p => p.Revenue)
+            .Take(50)
+            .ToListAsync();
+
+        return productPerformance;
+    }
+}

samples/SampleWebApi/Services/ProductService.cs

@@ -0,0 +1,288 @@
+using Microsoft.EntityFrameworkCore;
+using SqrtSpace.SpaceTime.Core;
+using SqrtSpace.SpaceTime.EntityFramework;
+using SqrtSpace.SpaceTime.Linq;
+using SampleWebApi.Data;
+using SampleWebApi.Models;
+using System.Text;
+
+namespace SampleWebApi.Services;
+
+public interface IProductService
+{
+    Task<PagedResult<Product>> GetProductsPagedAsync(int page, int pageSize);
+    IAsyncEnumerable<Product> StreamProductsAsync(string? category, decimal? minPrice);
+    Task<IEnumerable<Product>> SearchProductsAsync(string query, string sortBy, bool descending);
+    Task<BulkUpdateResult> BulkUpdatePricesAsync(string? categoryFilter, decimal priceMultiplier, string operationId, CheckpointManager? checkpoint);
+    Task ExportToCsvAsync(Stream outputStream, string? category);
+    Task<ProductStatistics> GetStatisticsAsync(string? category);
+}
+
+public class ProductService : IProductService
+{
+    private readonly SampleDbContext _context;
+    private readonly ILogger<ProductService> _logger;
+
+    public ProductService(SampleDbContext context, ILogger<ProductService> logger)
+    {
+        _context = context;
+        _logger = logger;
+    }
+
+    public async Task<PagedResult<Product>> GetProductsPagedAsync(int page, int pageSize)
+    {
+        var query = _context.Products.AsQueryable();
+        
+        var totalCount = await query.CountAsync();
+        var items = await query
+            .Skip((page - 1) * pageSize)
+            .Take(pageSize)
+            .ToListAsync();
+
+        return new PagedResult<Product>
+        {
+            Items = items,
+            Page = page,
+            PageSize = pageSize,
+            TotalCount = totalCount
+        };
+    }
+
+    public async IAsyncEnumerable<Product> StreamProductsAsync(string? category, decimal? minPrice)
+    {
+        var query = _context.Products.AsQueryable();
+
+        if (!string.IsNullOrEmpty(category))
+        {
+            query = query.Where(p => p.Category == category);
+        }
+
+        if (minPrice.HasValue)
+        {
+            query = query.Where(p => p.Price >= minPrice.Value);
+        }
+
+        // Use BatchBySqrtN to process in memory-efficient chunks
+        await foreach (var batch in query.BatchBySqrtNAsync())
+        {
+            foreach (var product in batch)
+            {
+                yield return product;
+            }
+        }
+    }
+
+    public async Task<IEnumerable<Product>> SearchProductsAsync(string query, string sortBy, bool descending)
+    {
+        var searchQuery = _context.Products
+            .Where(p => p.Name.Contains(query) || p.Description.Contains(query));
+
+        // Count to determine if we need external sorting
+        var count = await searchQuery.CountAsync();
+        _logger.LogInformation("Search found {count} products for query '{query}'", count, query);
+
+        IQueryable<Product> sortedQuery = sortBy.ToLower() switch
+        {
+            "price" => descending ? searchQuery.OrderByDescending(p => p.Price) : searchQuery.OrderBy(p => p.Price),
+            "category" => descending ? searchQuery.OrderByDescending(p => p.Category) : searchQuery.OrderBy(p => p.Category),
+            _ => descending ? searchQuery.OrderByDescending(p => p.Name) : searchQuery.OrderBy(p => p.Name)
+        };
+
+        // Use external sorting for large result sets
+        if (count > 10000)
+        {
+            _logger.LogInformation("Using external sorting for {count} products", count);
+            sortedQuery = sortedQuery.UseExternalSorting();
+        }
+
+        return await sortedQuery.ToListAsync();
+    }
+
+    public async Task<BulkUpdateResult> BulkUpdatePricesAsync(
+        string? categoryFilter, 
+        decimal priceMultiplier, 
+        string operationId,
+        CheckpointManager? checkpoint)
+    {
+        var state = new BulkUpdateState { OperationId = operationId };
+
+        // Try to restore from checkpoint
+        if (checkpoint != null)
+        {
+            var previousState = await checkpoint.RestoreLatestCheckpointAsync<BulkUpdateState>();
+            if (previousState != null)
+            {
+                state = previousState;
+                _logger.LogInformation("Resuming bulk update from checkpoint. Already processed: {count}", 
+                    state.ProcessedCount);
+            }
+        }
+
+        var query = _context.Products.AsQueryable();
+        if (!string.IsNullOrEmpty(categoryFilter))
+        {
+            query = query.Where(p => p.Category == categoryFilter);
+        }
+
+        var totalProducts = await query.CountAsync();
+        var products = query.Skip(state.ProcessedCount);
+
+        // Process in batches using √n strategy
+        await foreach (var batch in products.BatchBySqrtNAsync())
+        {
+            try
+            {
+                foreach (var product in batch)
+                {
+                    product.Price *= priceMultiplier;
+                    product.UpdatedAt = DateTime.UtcNow;
+                    state.ProcessedCount++;
+                    state.UpdatedCount++;
+                }
+
+                await _context.SaveChangesAsync();
+
+                // Save checkpoint
+                if (checkpoint?.ShouldCheckpoint() == true)
+                {
+                    state.LastCheckpoint = DateTime.UtcNow;
+                    await checkpoint.CreateCheckpointAsync(state);
+                    _logger.LogInformation("Checkpoint saved. Processed: {count}/{total}", 
+                        state.ProcessedCount, totalProducts);
+                }
+            }
+            catch (Exception ex)
+            {
+                _logger.LogError(ex, "Error updating batch. Processed so far: {count}", state.ProcessedCount);
+                state.FailedCount += batch.Count - (state.ProcessedCount % batch.Count);
+                
+                // Save checkpoint on error
+                if (checkpoint != null)
+                {
+                    await checkpoint.CreateCheckpointAsync(state);
+                }
+                throw;
+            }
+        }
+
+        return new BulkUpdateResult
+        {
+            OperationId = operationId,
+            TotalProducts = totalProducts,
+            UpdatedProducts = state.UpdatedCount,
+            FailedProducts = state.FailedCount,
+            Completed = true,
+            CheckpointId = state.LastCheckpoint.ToString("O")
+        };
+    }
+
+    public async Task ExportToCsvAsync(Stream outputStream, string? category)
+    {
+        using var writer = new StreamWriter(outputStream, Encoding.UTF8);
+        
+        // Write header
+        await writer.WriteLineAsync("Id,Name,Category,Price,StockQuantity,CreatedAt,UpdatedAt");
+
+        var query = _context.Products.AsQueryable();
+        if (!string.IsNullOrEmpty(category))
+        {
+            query = query.Where(p => p.Category == category);
+        }
+
+        // Stream products in batches to minimize memory usage
+        await foreach (var batch in query.BatchBySqrtNAsync())
+        {
+            foreach (var product in batch)
+            {
+                await writer.WriteLineAsync(
+                    $"{product.Id}," +
+                    $"\"{product.Name.Replace("\"", "\"\"")}\"," +
+                    $"\"{product.Category}\"," +
+                    $"{product.Price}," +
+                    $"{product.StockQuantity}," +
+                    $"{product.CreatedAt:yyyy-MM-dd HH:mm:ss}," +
+                    $"{product.UpdatedAt:yyyy-MM-dd HH:mm:ss}");
+            }
+            
+            await writer.FlushAsync();
+        }
+    }
+
+    public async Task<ProductStatistics> GetStatisticsAsync(string? category)
+    {
+        var stopwatch = System.Diagnostics.Stopwatch.StartNew();
+        var query = _context.Products.AsQueryable();
+        
+        if (!string.IsNullOrEmpty(category))
+        {
+            query = query.Where(p => p.Category == category);
+        }
+
+        var totalCount = await query.CountAsync();
+        var computationMethod = totalCount > 100000 ? "External" : "InMemory";
+
+        ProductStatistics stats;
+
+        if (computationMethod == "External")
+        {
+            _logger.LogInformation("Using external aggregation for {count} products", totalCount);
+            
+            // For large datasets, compute statistics in batches
+            decimal totalPrice = 0;
+            decimal minPrice = decimal.MaxValue;
+            decimal maxPrice = decimal.MinValue;
+            var categoryStats = new Dictionary<string, (int count, decimal totalPrice)>();
+
+            await foreach (var batch in query.BatchBySqrtNAsync())
+            {
+                foreach (var product in batch)
+                {
+                    totalPrice += product.Price;
+                    minPrice = Math.Min(minPrice, product.Price);
+                    maxPrice = Math.Max(maxPrice, product.Price);
+
+                    if (!categoryStats.ContainsKey(product.Category))
+                    {
+                        categoryStats[product.Category] = (0, 0);
+                    }
+                    var current = categoryStats[product.Category];
+                    categoryStats[product.Category] = (current.count + 1, current.totalPrice + product.Price);
+                }
+            }
+
+            stats = new ProductStatistics
+            {
+                TotalProducts = totalCount,
+                AveragePrice = totalCount > 0 ? totalPrice / totalCount : 0,
+                MinPrice = minPrice == decimal.MaxValue ? 0 : minPrice,
+                MaxPrice = maxPrice == decimal.MinValue ? 0 : maxPrice,
+                ProductsByCategory = categoryStats.ToDictionary(k => k.Key, v => v.Value.count),
+                AveragePriceByCategory = categoryStats.ToDictionary(
+                    k => k.Key, 
+                    v => v.Value.count > 0 ? v.Value.totalPrice / v.Value.count : 0)
+            };
+        }
+        else
+        {
+            // For smaller datasets, use in-memory aggregation
+            var products = await query.ToListAsync();
+            
+            stats = new ProductStatistics
+            {
+                TotalProducts = products.Count,
+                AveragePrice = products.Any() ? products.Average(p => p.Price) : 0,
+                MinPrice = products.Any() ? products.Min(p => p.Price) : 0,
+                MaxPrice = products.Any() ? products.Max(p => p.Price) : 0,
+                ProductsByCategory = products.GroupBy(p => p.Category)
+                    .ToDictionary(g => g.Key, g => g.Count()),
+                AveragePriceByCategory = products.GroupBy(p => p.Category)
+                    .ToDictionary(g => g.Key, g => g.Average(p => p.Price))
+            };
+        }
+
+        stats.ComputationTimeMs = stopwatch.ElapsedMilliseconds;
+        stats.ComputationMethod = computationMethod;
+
+        return stats;
+    }
+}