feat(domain): add core domain layer

Entities:
- Student: core entity with email validation
- Subject: course with credits (3 each)
- Professor: instructor managing 2 subjects
- Enrollment: student-subject relationship

Value Objects:
- Email: validated email with domain rules

Domain Services:
- EnrollmentDomainService: validates business rules
  - Max 3 subjects per student (9 credits)
  - No duplicate professor constraint

Ports:
- Repository interfaces for dependency inversion

src/backend/Domain/Domain.csproj

@@ -0,0 +1,9 @@
+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <TargetFramework>net10.0</TargetFramework>
+    <Nullable>enable</Nullable>
+    <ImplicitUsings>enable</ImplicitUsings>
+  </PropertyGroup>
+
+</Project>

src/backend/Domain/Entities/Enrollment.cs

@@ -0,0 +1,20 @@
+namespace Domain.Entities;
+
+public class Enrollment
+{
+    public int Id { get; private set; }
+    public int StudentId { get; private set; }
+    public Student Student { get; private set; } = null!;
+    public int SubjectId { get; private set; }
+    public Subject Subject { get; private set; } = null!;
+    public DateTime EnrolledAt { get; private set; }
+
+    private Enrollment() { }
+
+    public Enrollment(int studentId, int subjectId)
+    {
+        StudentId = studentId;
+        SubjectId = subjectId;
+        EnrolledAt = DateTime.UtcNow;
+    }
+}

src/backend/Domain/Entities/Professor.cs

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+namespace Domain.Entities;
+
+public class Professor
+{
+    public int Id { get; private set; }
+    public string Name { get; private set; } = string.Empty;
+
+    private readonly List<Subject> _subjects = [];
+    public IReadOnlyCollection<Subject> Subjects => _subjects.AsReadOnly();
+
+    private Professor() { }
+
+    public Professor(string name)
+    {
+        if (string.IsNullOrWhiteSpace(name))
+            throw new ArgumentException("Professor name is required", nameof(name));
+
+        Name = name;
+    }
+
+    public void AddSubject(Subject subject)
+    {
+        if (_subjects.Count >= 2)
+            throw new InvalidOperationException("A professor can only teach 2 subjects");
+
+        _subjects.Add(subject);
+    }
+}

src/backend/Domain/Entities/Student.cs

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+namespace Domain.Entities;
+
+using Domain.ValueObjects;
+
+public class Student
+{
+    public const int MaxEnrollments = 3;
+
+    public int Id { get; private set; }
+    public string Name { get; private set; } = string.Empty;
+    public Email Email { get; private set; } = null!;
+
+    private readonly List<Enrollment> _enrollments = [];
+    public IReadOnlyCollection<Enrollment> Enrollments => _enrollments.AsReadOnly();
+
+    public int TotalCredits => _enrollments.Sum(e => e.Subject?.Credits ?? Subject.CreditsPerSubject);
+
+    private Student() { }
+
+    public Student(string name, Email email)
+    {
+        if (string.IsNullOrWhiteSpace(name))
+            throw new ArgumentException("Student name is required", nameof(name));
+
+        Name = name;
+        Email = email ?? throw new ArgumentNullException(nameof(email));
+    }
+
+    public void UpdateName(string name)
+    {
+        if (string.IsNullOrWhiteSpace(name))
+            throw new ArgumentException("Student name is required", nameof(name));
+
+        Name = name;
+    }
+
+    public void UpdateEmail(Email email)
+    {
+        Email = email ?? throw new ArgumentNullException(nameof(email));
+    }
+
+    public bool HasProfessor(int professorId) =>
+        _enrollments.Any(e => e.Subject?.ProfessorId == professorId);
+
+    public bool CanEnroll() => _enrollments.Count < MaxEnrollments;
+
+    public void AddEnrollment(Enrollment enrollment)
+    {
+        _enrollments.Add(enrollment);
+    }
+
+    public void RemoveEnrollment(Enrollment enrollment)
+    {
+        _enrollments.Remove(enrollment);
+    }
+}

src/backend/Domain/Entities/Subject.cs

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+namespace Domain.Entities;
+
+public class Subject
+{
+    public const int CreditsPerSubject = 3;
+
+    public int Id { get; private set; }
+    public string Name { get; private set; } = string.Empty;
+    public int Credits { get; private set; } = CreditsPerSubject;
+    public int ProfessorId { get; private set; }
+    public Professor Professor { get; private set; } = null!;
+
+    private readonly List<Enrollment> _enrollments = [];
+    public IReadOnlyCollection<Enrollment> Enrollments => _enrollments.AsReadOnly();
+
+    private Subject() { }
+
+    public Subject(string name, int professorId)
+    {
+        if (string.IsNullOrWhiteSpace(name))
+            throw new ArgumentException("Subject name is required", nameof(name));
+
+        Name = name;
+        Credits = CreditsPerSubject;
+        ProfessorId = professorId;
+    }
+}

src/backend/Domain/Exceptions/DomainException.cs

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+namespace Domain.Exceptions;
+
+public abstract class DomainException : Exception
+{
+    public string Code { get; }
+
+    protected DomainException(string code, string message) : base(message)
+    {
+        Code = code;
+    }
+}
+
+public class MaxEnrollmentsExceededException : DomainException
+{
+    public MaxEnrollmentsExceededException(int studentId)
+        : base("MAX_ENROLLMENTS", $"Student {studentId} cannot enroll in more than 3 subjects") { }
+}
+
+public class SameProfessorConstraintException : DomainException
+{
+    public SameProfessorConstraintException(int studentId, int professorId)
+        : base("SAME_PROFESSOR", $"Student {studentId} already has a subject with professor {professorId}") { }
+}
+
+public class StudentNotFoundException : DomainException
+{
+    public StudentNotFoundException(int studentId)
+        : base("STUDENT_NOT_FOUND", $"Student {studentId} was not found") { }
+}
+
+public class SubjectNotFoundException : DomainException
+{
+    public SubjectNotFoundException(int subjectId)
+        : base("SUBJECT_NOT_FOUND", $"Subject {subjectId} was not found") { }
+}
+
+public class EnrollmentNotFoundException : DomainException
+{
+    public EnrollmentNotFoundException(int enrollmentId)
+        : base("ENROLLMENT_NOT_FOUND", $"Enrollment {enrollmentId} was not found") { }
+}
+
+public class DuplicateEnrollmentException : DomainException
+{
+    public DuplicateEnrollmentException(int studentId, int subjectId)
+        : base("DUPLICATE_ENROLLMENT", $"Student {studentId} is already enrolled in subject {subjectId}") { }
+}

src/backend/Domain/Ports/Repositories/IEnrollmentRepository.cs

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+namespace Domain.Ports.Repositories;
+
+using Domain.Entities;
+
+public interface IEnrollmentRepository
+{
+    Task<Enrollment?> GetByIdAsync(int id, CancellationToken ct = default);
+    Task<Enrollment?> GetByStudentAndSubjectAsync(int studentId, int subjectId, CancellationToken ct = default);
+    Task<IReadOnlyList<Enrollment>> GetByStudentIdAsync(int studentId, CancellationToken ct = default);
+    Task<IReadOnlyList<Enrollment>> GetBySubjectIdAsync(int subjectId, CancellationToken ct = default);
+    Task<IReadOnlyList<Student>> GetClassmatesAsync(int studentId, int subjectId, CancellationToken ct = default);
+    Task<IReadOnlyDictionary<int, IReadOnlyList<Student>>> GetClassmatesBatchAsync(
+        int studentId, IEnumerable<int> subjectIds, CancellationToken ct = default);
+    void Add(Enrollment enrollment);
+    void Delete(Enrollment enrollment);
+}

src/backend/Domain/Ports/Repositories/IProfessorRepository.cs

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+namespace Domain.Ports.Repositories;
+
+using Domain.Entities;
+using System.Linq.Expressions;
+
+public interface IProfessorRepository
+{
+    Task<Professor?> GetByIdAsync(int id, CancellationToken ct = default);
+    Task<IReadOnlyList<Professor>> GetAllAsync(CancellationToken ct = default);
+    Task<IReadOnlyList<Professor>> GetAllWithSubjectsAsync(CancellationToken ct = default);
+
+    // Projection support
+    Task<IReadOnlyList<TResult>> GetAllProjectedAsync<TResult>(
+        Expression<Func<Professor, TResult>> selector,
+        CancellationToken ct = default);
+}

src/backend/Domain/Ports/Repositories/IStudentRepository.cs

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+namespace Domain.Ports.Repositories;
+
+using Domain.Entities;
+using System.Linq.Expressions;
+
+public interface IStudentRepository
+{
+    Task<Student?> GetByIdAsync(int id, CancellationToken ct = default);
+    Task<Student?> GetByIdWithEnrollmentsAsync(int id, CancellationToken ct = default);
+    Task<IReadOnlyList<Student>> GetAllAsync(CancellationToken ct = default);
+    Task<IReadOnlyList<Student>> GetAllWithEnrollmentsAsync(CancellationToken ct = default);
+    Task<bool> ExistsAsync(int id, CancellationToken ct = default);
+    Task<bool> EmailExistsAsync(string email, int? excludeId = null, CancellationToken ct = default);
+
+    // Projection support for optimized queries
+    Task<IReadOnlyList<TResult>> GetAllProjectedAsync<TResult>(
+        Expression<Func<Student, TResult>> selector,
+        CancellationToken ct = default);
+    Task<TResult?> GetByIdProjectedAsync<TResult>(
+        int id,
+        Expression<Func<Student, TResult>> selector,
+        CancellationToken ct = default);
+
+    // Keyset pagination (more efficient than OFFSET)
+    Task<(IReadOnlyList<TResult> Items, int? NextCursor, int TotalCount)> GetPagedProjectedAsync<TResult>(
+        Expression<Func<Student, TResult>> selector,
+        int? afterId = null,
+        int pageSize = 10,
+        CancellationToken ct = default);
+
+    void Add(Student student);
+    void Update(Student student);
+    void Delete(Student student);
+}

src/backend/Domain/Ports/Repositories/ISubjectRepository.cs

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+namespace Domain.Ports.Repositories;
+
+using Domain.Entities;
+using System.Linq.Expressions;
+
+public interface ISubjectRepository
+{
+    Task<Subject?> GetByIdAsync(int id, CancellationToken ct = default);
+    Task<Subject?> GetByIdWithProfessorAsync(int id, CancellationToken ct = default);
+    Task<IReadOnlyList<Subject>> GetAllAsync(CancellationToken ct = default);
+    Task<IReadOnlyList<Subject>> GetAllWithProfessorsAsync(CancellationToken ct = default);
+    Task<IReadOnlyList<Subject>> GetAvailableForStudentAsync(int studentId, CancellationToken ct = default);
+
+    // Projection support
+    Task<IReadOnlyList<TResult>> GetAllProjectedAsync<TResult>(
+        Expression<Func<Subject, TResult>> selector,
+        CancellationToken ct = default);
+}

src/backend/Domain/Ports/Repositories/IUnitOfWork.cs

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+namespace Domain.Ports.Repositories;
+
+public interface IUnitOfWork
+{
+    Task<int> SaveChangesAsync(CancellationToken ct = default);
+}

src/backend/Domain/Services/EnrollmentDomainService.cs

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+namespace Domain.Services;
+
+using Domain.Entities;
+using Domain.Exceptions;
+
+public class EnrollmentDomainService
+{
+    public void ValidateEnrollment(Student student, Subject subject)
+    {
+        if (!student.CanEnroll())
+            throw new MaxEnrollmentsExceededException(student.Id);
+
+        if (student.HasProfessor(subject.ProfessorId))
+            throw new SameProfessorConstraintException(student.Id, subject.ProfessorId);
+
+        if (student.Enrollments.Any(e => e.SubjectId == subject.Id))
+            throw new DuplicateEnrollmentException(student.Id, subject.Id);
+    }
+
+    public Enrollment CreateEnrollment(Student student, Subject subject)
+    {
+        ValidateEnrollment(student, subject);
+
+        var enrollment = new Enrollment(student.Id, subject.Id);
+        student.AddEnrollment(enrollment);
+
+        return enrollment;
+    }
+}

src/backend/Domain/ValueObjects/Email.cs

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+namespace Domain.ValueObjects;
+
+using System.Text.RegularExpressions;
+
+public partial class Email
+{
+    public string Value { get; }
+
+    private Email(string value) => Value = value;
+
+    public static Email Create(string email)
+    {
+        if (string.IsNullOrWhiteSpace(email))
+            throw new ArgumentException("Email is required", nameof(email));
+
+        email = email.Trim().ToLowerInvariant();
+
+        if (!EmailRegex().IsMatch(email))
+            throw new ArgumentException("Invalid email format", nameof(email));
+
+        return new Email(email);
+    }
+
+    public override string ToString() => Value;
+    public override bool Equals(object? obj) => obj is Email other && Value == other.Value;
+    public override int GetHashCode() => Value.GetHashCode();
+
+    public static implicit operator string(Email email) => email.Value;
+
+    [GeneratedRegex(@"^[^@\s]+@[^@\s]+\.[^@\s]+$", RegexOptions.Compiled)]
+    private static partial Regex EmailRegex();
+}