Changes between Initial Version and Version 1 of Normalization

Timestamp:

08/28/26 23:46:10 (13 days ago)

Author:

236021

Comment:

--

Normalization

@@ +1 @@
+= Normalization =
+
+
+== De-normalized database form ==
+
+=== Global set of attributes ===
+
+{{{
+R = {
+  doctor_id, d_first_name, d_last_name, d_email,
+  level_id, level_name,
+  specialization_id, specialization_name,
+  department_id, department_name,
+
+  patient_id, p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg,
+
+  admin_id, admin_username, admin_name, admin_lastname, admin_email,
+  technician_id, tech_username, tech_name, tech_lastname, tech_email,
+  user_id, users_username, users_password, users_role,
+  users_first_name, users_last_name, is_active,
+
+  appointment_id, appointment_date, appointment_time, appointment_status,
+  appt_patient_id, appt_doctor_id,
+
+  diagnosis_id, diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id,
+
+  procedure_id, procedure_type, procedure_sched_date, procedure_description,
+  procedure_cost, proc_doctor_id, proc_diagnosis_id,
+  proc_result_id, proc_result_description, proc_result_date,
+  performed_id, perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes,
+
+  test_id, test_name, test_description, test_cost,
+  lab_result_id, lab_result_value, lab_result_date,
+  performed_test_id, pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes,
+
+  prescription_id, medication_name,
+  restriction_id, restriction_description,
+  dosage, frequency, duration, prescription_notes,
+
+  allergy_id, allergy_name, allergy_severity,
+  record_allergy_reaction, record_allergy_severity,
+
+  symptom_id, symptom_name, symptom_description, record_symptom_severity,
+
+  record_id,
+
+  referral_id, referral_reason, referral_date, ref_from_doctor_id, ref_to_doctor_id,
+  report_id, report_description, report_date, report_doctor_id,
+  bill_id, total_cost, payment_status, payment_date, billing_admin_id
+}
+}}}
+
+=== Functional dependencies ===
+
+`Doctor`
+
+{{{
+F1  level_id          -> level_name
+F2  specialization_id -> specialization_name
+F3  department_id     -> department_name
+F4  doctor_id         -> d_first_name, d_last_name, d_email, level_id, specialization_id, department_id
+}}}
+
+`Patient`
+
+{{{
+F5  patient_id -> p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg
+}}}
+
+`Admin`
+
+{{{
+F6  admin_id -> admin_username, admin_name, admin_lastname, admin_email
+}}}
+
+`Lab Technician`
+
+{{{
+F7  technician_id -> tech_username, tech_name, tech_lastname, tech_email
+}}}
+
+`User`
+
+{{{
+F8  user_id -> users_username, users_password, users_role,
+               users_first_name, users_last_name, is_active
+}}}
+
+**user_id** also has four nullable foreign keys: patient_id, doctor_id, admin_id,
+and technician_id. Only one of these is ever filled in for a given user, depending
+on their role, and the rest stay null. Because of that, `user_id` is not treated as
+determining any of the four below, since a login row only optionally points to one
+profile row rather than always pointing to the same one. This is the same subtype
+idea used for `Admin`, `Clients`, and `Owners` elsewhere, except in our database it keeps all
+four subtypes together in one `users` table instead of giving each one its own table.
+
+`Appointment`
+
+{{{
+F9  appointment_id -> appointment_date, appointment_time, appointment_status,
+                       appt_patient_id, appt_doctor_id
+}}}
+
+`Diagnosis`
+
+{{{
+F10 diagnosis_id -> diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id
+}}}
+
+`Procedure`
+
+{{{
+F11 procedure_id   -> procedure_type, procedure_sched_date, procedure_description,
+                       procedure_cost, proc_doctor_id, proc_diagnosis_id
+F12 proc_result_id -> proc_result_description, proc_result_date, procedure_id
+F13 performed_id   -> perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id,
+                       perf_date, perf_notes
+}}}
+
+`Prescription`
+
+{{{
+F14 prescription_id -> medication_name
+F15 restriction_id  -> restriction_description, prescription_id
+}}}
+
+`Lab test`
+
+{{{
+F16 test_id           -> test_name, test_description, test_cost
+F17 lab_result_id     -> lab_result_value, lab_result_date, test_id
+F18 performed_test_id -> pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id,
+                          pt_test_date, pt_notes
+}}}
+
+`Medical record`
+
+{{{
+F19 record_id -> patient_id
+}}}
+
+`Allergy`
+
+{{{
+F20 allergy_id -> allergy_name, allergy_severity
+}}}
+
+`Symptom`
+
+{{{
+F21 symptom_id -> symptom_name, symptom_description
+}}}
+
+`Referral`
+
+{{{
+F22 referral_id -> referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id
+}}}
+
+`Medical report`
+
+{{{
+F23 report_id -> report_description, report_date, record_id, report_doctor_id
+}}}
+
+`Billing`
+
+{{{
+F24 bill_id -> total_cost, payment_status, payment_date, record_id, billing_admin_id
+}}}
+
+`Medical record associations (composite key attributes)`
+
+{{{
+F25 {record_id, symptom_id}      -> record_symptom_severity
+F26 {record_id, allergy_id}      -> record_allergy_reaction, record_allergy_severity
+F27 {prescription_id, record_id} -> dosage, frequency, duration, prescription_notes
+}}}
+
+`Many-to-many association tables (no dependent attribute  trivial so FDs only on the full pair)`
+
+{{{
+{diagnosis_id, record_id}          {doctor_id, record_id}            {record_id, procedure_id}
+{record_id, lab_result_id}         {patient_id, allergy_id}          {patient_id, symptom_id}
+{diagnosis_id, symptom_id}         {diagnosis_id, procedure_id}      {specialization_id, procedure_id}
+{department_id, procedure_id}      {bill_id, procedure_id}           {bill_id, test_id}
+{report_id, lab_result_id}         {allergy_id, restriction_id}
+}}}
+
+----
+=== Candidate keys and primary key ===
+
+A candidate key of the de-normalized relation is found by picking a minimal set of
+identifiers whose closure reaches every attribute of R. Several identifiers already
+determine others through chains inside the FD set — for instance:
+
+proc_result_id -> procedure_id
+lab_result_id -> test_id
+restriction_id -> prescription_id
+referral_id -> record_id, and in turn record_id -> patient_id
+doctor_id -> level_id, specialization_id, department_id
+
+These chains matter because whatever gets reached this way (procedure_id, test_id,
+prescription_id, record_id, patient_id, level_id, specialization_id, department_id)
+does not need to be included in the key separately — it is already recoverable once
+its determinant is present.
+
+'''Left-hand side only''' (identifiers that never appear as a dependent on the right
+side of any FD, and therefore cannot be reached this way):
+`doctor_id, admin_id, technician_id, user_id, appointment_id, diagnosis_id, proc_result_id,
+performed_id, restriction_id, lab_result_id, performed_test_id, allergy_id, symptom_id,
+referral_id, report_id, bill_id`
+
+Since none of these 16 identifiers can be derived from anything else in R, every candidate
+key of R is required to contain all of them:
+
+{{{
+K = { doctor_id, admin_id, technician_id, user_id, appointment_id, diagnosis_id,
+      proc_result_id, performed_id, restriction_id, lab_result_id, performed_test_id,
+      allergy_id, symptom_id, referral_id, report_id, bill_id }
+}}}
+=== Closure proof for K ===
+
+{{{
+Start:
+K+ = {doctor_id, admin_id, technician_id, user_id, appointment_id, diagnosis_id,
+      proc_result_id, performed_id, restriction_id, lab_result_id, performed_test_id,
+      allergy_id, symptom_id, referral_id, report_id, bill_id}
+
+From F4:
+doctor_id -> d_first_name, d_last_name, d_email, level_id, specialization_id, department_id
+
+From F1 using level_id:
+level_id -> level_name
+
+From F2 using specialization_id:
+specialization_id -> specialization_name
+
+From F3 using department_id:
+department_id -> department_name
+
+From F6:
+admin_id -> admin_username, admin_name, admin_lastname, admin_email
+
+From F7:
+technician_id -> tech_username, tech_name, tech_lastname, tech_email
+
+From F8:
+user_id -> users_username, users_password, users_role, users_first_name, users_last_name, is_active
+
+From F9:
+appointment_id -> appointment_date, appointment_time, appointment_status, appt_patient_id, appt_doctor_id
+
+From F10:
+diagnosis_id -> diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id
+
+From F12:
+proc_result_id -> proc_result_description, proc_result_date, procedure_id
+
+From F11 using procedure_id:
+procedure_id -> procedure_type, procedure_sched_date, procedure_description,
+                procedure_cost, proc_doctor_id, proc_diagnosis_id
+
+From F13:
+performed_id -> perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes
+
+From F15:
+restriction_id -> restriction_description, prescription_id
+
+From F14 using prescription_id:
+prescription_id -> medication_name
+
+From F17:
+lab_result_id -> lab_result_value, lab_result_date, test_id
+
+From F16 using test_id:
+test_id -> test_name, test_description, test_cost
+
+From F18:
+performed_test_id -> pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes
+
+From F20:
+allergy_id -> allergy_name, allergy_severity
+
+From F21:
+symptom_id -> symptom_name, symptom_description
+
+From F22:
+referral_id -> referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id
+
+From F19 using record_id:
+record_id -> patient_id
+
+From F5 using patient_id:
+patient_id -> p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg
+
+From F23:
+report_id -> report_description, report_date, record_id, report_doctor_id
+
+From F24:
+bill_id -> total_cost, payment_status, payment_date, record_id, billing_admin_id
+
+From F25 using record_id and symptom_id:
+{record_id, symptom_id} -> record_symptom_severity
+
+From F26 using record_id and allergy_id:
+{record_id, allergy_id} -> record_allergy_reaction, record_allergy_severity
+
+From F27 using prescription_id and record_id:
+{prescription_id, record_id} -> dosage, frequency, duration, prescription_notes
+}}}
+
+Therefore, K+ determines all attributes of R, so K is a `superkey`.
+
+=== Minimality / uniqueness ===
+
+To promote K from only "a candidate key" to the chosen primary key, we also need to show
+that no other candidate key exists.
+
+None of the 16 identifiers in K is functionally determined by another determinant in the
+given FD set:
+
+
+
+ **doctor_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **admin_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **technician_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **user_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **appointment_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **diagnosis_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **proc_result_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **performed_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **restriction_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **lab_result_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **performed_test_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **allergy_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **symptom_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **referral_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **report_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+ **bill_id** does not appear on the right-hand side of any FD, so it cannot be derived.
+
+Every superkey of R must contain all attributes in:
+
+{{{
+E = { doctor_id, admin_id, technician_id, user_id, appointment_id, diagnosis_id,
+      proc_result_id, performed_id, restriction_id, lab_result_id, performed_test_id,
+      allergy_id, symptom_id, referral_id, report_id, bill_id }
+}}}
+
+Because K and E are the same set, and we already showed K+ = R, K qualifies as a
+superkey. And because every superkey is required to contain E, so nothing smaller than K
+could ever work as a key. There's also no way to swap out one of these 16 attributes for
+a different one and still get a valid candidate key, since none of the attributes in E
+can be reached from any other determinant in the functional dependency set so there's simply no substitute
+available for any of them.
+
+This means K stands as the sole candidate key of the de-normalized relation, given the
+functional dependencies defined above.
+
+'''Primary key of the de-normalized relation:'''
+
+{{{
+PK = { doctor_id, admin_id, technician_id, user_id, appointment_id, diagnosis_id,
+       proc_result_id, performed_id, restriction_id, lab_result_id, performed_test_id,
+       allergy_id, symptom_id, referral_id, report_id, bill_id }
+}}}
+----
+
+== 1NF decomposition ==
+
+Every attribute in `R` is single valued and atomic, and the composite `PK` above uniquely identifies each row, so '''`R` satisfies 1NF'''.
+
+----
+
+== 2NF decomposition ==
+
+`R` has a composite primary key of 16 attributes, and none of its non-key attributes depends on the whole 16 attribute keys as each one is reachable from just one or two members of K, either directly (F4, F5, F6, ... etc) or through a short chain (e.g. `proc_result_id -> procedure_id -> procedure_type`, `referral_id -> record_id -> patient_id`). Either way, that is a '''partial dependency''' with respect to K, so '''`R` violates 2NF'''. Examples:
+
+{{{
+doctor_id      -> d_first_name, d_last_name, d_email, level_id, specialization_id, department_id
+
+diagnosis_id   -> diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id
+
+proc_result_id -> proc_result_description, proc_result_date, procedure_id
+
+referral_id    -> referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id
+}}}
+
+=== Grouping by determinants ===
+
+{{{
+doctor_id        -> d_first_name, d_last_name, d_email, level_id, specialization_id, department_id
+
+level_id         -> level_name
+
+specialization_id-> specialization_name
+
+department_id    -> department_name
+
+patient_id        -> p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg
+
+admin_id         -> admin_username, admin_name, admin_lastname, admin_email
+
+technician_id    -> tech_username, tech_name, tech_lastname, tech_email
+
+user_id          -> users_username, users_password, users_role, users_first_name, users_last_name, is_active
+
+appointment_id   -> appt_patient_id, appt_doctor_id, appointment_date, appointment_time, appointment_status
+
+diagnosis_id     -> diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id
+
+procedure_id     -> procedure_type, procedure_sched_date, procedure_description, procedure_cost,
+                     proc_doctor_id, proc_diagnosis_id
+
+proc_result_id   -> proc_result_description, proc_result_date, procedure_id
+
+performed_id     -> perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes
+
+prescription_id  -> medication_name
+
+restriction_id   -> restriction_description, prescription_id
+
+test_id          -> test_name, test_description, test_cost
+
+lab_result_id    -> lab_result_value, lab_result_date, test_id
+
+performed_test_id-> pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes
+
+record_id        -> patient_id
+
+allergy_id       -> allergy_name, allergy_severity
+
+symptom_id       -> symptom_name, symptom_description
+
+referral_id      -> referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id
+
+report_id        -> report_description, report_date, record_id, report_doctor_id
+
+bill_id          -> total_cost, payment_status, payment_date, record_id, billing_admin_id
+
+{record_id, symptom_id}      -> record_symptom_severity
+
+{record_id, allergy_id}      -> record_allergy_reaction, record_allergy_severity
+
+{prescription_id, record_id} -> dosage, frequency, duration, prescription_notes
+}}}
+
+`MedicalRecordSymptoms`, `MedicalRecordAllergies` and `PrescriptionRecords` already depend on their whole composite key so these three are already 2NF compliant  and are not split further.
+
+=== 2NF relations ===
+
+* {{{Doctors(doctor_id, d_first_name, d_last_name, d_email, level_id, specialization_id, department_id)}}}
+* {{{DoctorLevels(level_id, level_name)}}}
+* {{{Specializations(specialization_id, specialization_name)}}}
+* {{{Departments(department_id, department_name)}}}
+* {{{Patients(patient_id, p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg)}}}
+* {{{Admin(admin_id, admin_username, admin_name, admin_lastname, admin_email)}}}
+* {{{LabTechnician(technician_id, tech_username, tech_name, tech_lastname, tech_email)}}}
+* {{{Users(user_id, users_username, users_password, users_role, users_first_name, users_last_name, is_active)}}}
+* {{{Appointments(appointment_id, appt_patient_id, appt_doctor_id, appointment_date, appointment_time, appointment_status)}}}
+* {{{Diagnoses(diagnosis_id, diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id)}}}
+* {{{Procedures(procedure_id, procedure_type, procedure_sched_date, procedure_description, procedure_cost, proc_doctor_id, proc_diagnosis_id)}}}
+* {{{ProcedureResults(proc_result_id, proc_result_description, proc_result_date, procedure_id)}}}
+* {{{PerformedProcedures(performed_id, perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes)}}}
+* {{{Prescriptions(prescription_id, medication_name)}}}
+* {{{PrescriptionRestrictions(restriction_id, restriction_description, prescription_id)}}}
+* {{{LabTests(test_id, test_name, test_description, test_cost)}}}
+* {{{LabResults(lab_result_id, lab_result_value, lab_result_date, test_id)}}}
+* {{{PerformedLabTests(performed_test_id, pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes)}}}
+* {{{MedicalRecords(record_id, patient_id)}}}
+* {{{Allergies(allergy_id, allergy_name, allergy_severity)}}}
+* {{{Symptoms(symptom_id, symptom_name, symptom_description)}}}
+* {{{Referrals(referral_id, referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id)}}}
+* {{{MedicalReports(report_id, report_description, report_date, record_id, report_doctor_id)}}}
+* {{{Billing(bill_id, total_cost, payment_status, payment_date, record_id, billing_admin_id)}}}
+* {{{MedicalRecordSymptoms(record_id, symptom_id, record_symptom_severity)}}}
+* {{{MedicalRecordAllergies(record_id, allergy_id, record_allergy_reaction, record_allergy_severity)}}}
+* {{{PrescriptionRecords(prescription_id, record_id, dosage, frequency, duration, prescription_notes)}}}
+
+=== Lossless join ===
+
+A split of relation R into R1 and R2 keeps every row reconstructable  as long as the columns R1 and R2 have in common are by themselves
+sufficient to pin down one of the two sides completely:
+
+{{{
+(R1 ∩ R2) -> R1     or     (R1 ∩ R2) -> R2
+}}}
+
+Each relation below comes from one FD: its determinant becomes the new table's key, and
+that same determinant stays behind as a foreign key connecting it to the rest. Because
+the FD already guarantees the determinant decides everything in the new table, every
+split passes the lossless-join test automatically.
+
+||= # =||= Relation produced =||= Shared column =||= FD used =||
+|| 1  || `Doctors` || `doctor_id` || F4 ||
+|| 2  || `DoctorLevels` || `level_id` || F1 ||
+|| 3  || `Specializations` || `specialization_id` || F2 ||
+|| 4  || `Departments` || `department_id` || F3 ||
+|| 5  || `Patients` || `patient_id` || F5 ||
+|| 6  || `Admin` || `admin_id` || F6 ||
+|| 7  || `LabTechnician` || `technician_id` || F7 ||
+|| 8  || `Users` || `user_id` || F8 ||
+|| 9  || `Appointments` || `appointment_id` || F9 ||
+|| 10 || `Diagnoses` || `diagnosis_id` || F10 ||
+|| 11 || `Procedures` || `procedure_id` || F11 ||
+|| 12 || `ProcedureResults` || `proc_result_id` || F12 ||
+|| 13 || `PerformedProcedures` || `performed_id` || F13 ||
+|| 14 || `Prescriptions` || `prescription_id` || F14 ||
+|| 15 || `PrescriptionRestrictions` || `restriction_id` || F15 ||
+|| 16 || `LabTests` || `test_id` || F16 ||
+|| 17 || `LabResults` || `lab_result_id` || F17 ||
+|| 18 || `PerformedLabTests` || `performed_test_id` || F18 ||
+|| 19 || `MedicalRecords` || `record_id` || F19 ||
+|| 20 || `Allergies` || `allergy_id` || F20 ||
+|| 21 || `Symptoms` || `symptom_id` || F21 ||
+|| 22 || `Referrals` || `referral_id` || F22 ||
+|| 23 || `MedicalReports` || `report_id` || F23 ||
+|| 24 || `Billing` || `bill_id` || F24 ||
+|| 25 || `MedicalRecordSymptoms` || `{record_id, symptom_id}` || F25 ||
+|| 26 || `MedicalRecordAllergies` || `{record_id, allergy_id}` || F26 ||
+|| 27 || `PrescriptionRecords` || `{prescription_id, record_id}` || F27 ||
+
+Rows 25–27 work the same way, just with two columns acting as the determinant instead of
+one. F25, F26, and F27 each show that the pair alone determines the whole relation and
+that pair is the new table's primary key, so the same test still applies.
+
+Since each of the 27 splits is lossless on its own, the whole chain is too, therefore joining the
+pieces back together, one at a time in reverse order, which rebuilds R exactly.
+
+=== Dependency preservation ===
+
+Every FD from F1 through F27 landed fully inside one relation, its determinant and all
+of its dependents together, never split across two tables and never left out entirely.
+So the FDs that hold across `Doctors`, `DoctorLevels`, and every relation through
+`PrescriptionRecords` are the same as the FDs we started with, which is what makes the
+decomposition dependency preserving.
+
+----
+== 3NF check ==
+
+2NF removed **partial** dependencies. We now check whether any **transitive**
+dependency remains so a non-key attribute reachable only through another non-key
+attribute. Because the 2NF grouping step split on every determinant found in F1–F27,
+no relation ended up keeping a borrowed descriptive attribute alongside the foreign
+key that points to where it actually lives — so no transitive dependency survived
+into the 2NF output. A few examples confirm this:
+
+`Doctors` keeps level_id, specialization_id, department_id as foreign keys, but
+level_name, specialization_name, department_name stay in `DoctorLevels`,
+`Specializations`, `Departments` are never duplicated back into `Doctors`.
+
+`ProcedureResults` keeps only the foreign key procedure_id, the procedure's own
+procedure_type, procedure_cost, etc. stay in `Procedures`. `Procedures`
+keeps only proc_diagnosis_id, the diagnosis's diagnosis_name and diagnosis_description
+stay in `Diagnoses`.
+
+`LabResults` keeps only the foreign key test_id. test_name, test_description and
+test_cost stay in `LabTests`.
+
+`Referrals`, `MedicalReports`, `Billing`, `Appointments`, `PerformedProcedures`,
+`PerformedLabTests`, `PrescriptionRestrictions` each carry only foreign keys back to
+record_id / doctor_id / patient_id / admin_id / technician_id / procedure_id
+/ test_id / prescription_id and never the descriptive attributes belonging to the
+entity on the other end of that key. 
+`MedicalRecordSymptoms`, `MedicalRecordAllergies`,
+`PrescriptionRecords` have composite keys with no non-key attribute that could point
+through another non-key attribute, so they aren't affected either way.
+
+In conclusion, every non-key attribute in every relation depends only and
+fully on that relation's own key. The schema is in '''3NF''', and since this is a
+by-product of how the 2NF split was done rather than a separate fix meaning that no further
+decomposition is needed at this stage.
+
+== BCNF check ==
+
+BCNF requires every non-trivial determinant to be a superkey. This is stronger than
+3NF, which still allows a non-superkey determinant as long as the dependent attribute
+is itself part of some candidate key. Below is a check of each 3NF relation. The primary key is bolded.
+
+||= Relation =||= Key =||= BCNF? =||
+|| `DoctorLevels` || '''level_id''', alt. key `level_name` || Yes ||
+|| `Specializations` || '''specialization_id''', alt. key `specialization_name` || Yes ||
+|| `Departments` || '''department_id''', alt. key `department_name` || Yes ||
+|| `Doctors` || '''doctor_id''', alt. key `d_email` || Yes ||
+|| `Patients` || '''patient_id''', alt. key `embg` || Yes ||
+|| `Admin` || '''admin_id''', alt. keys `admin_username`, `admin_email` || Yes ||
+|| `LabTechnician` || '''technician_id''', alt. keys `tech_username`, `tech_email` || Yes ||
+|| `Users` || '''user_id''', alt. key `users_username` || Yes ||
+|| `Appointments` || '''appointment_id''' || Yes ||
+|| `Diagnoses` || '''diagnosis_id''' || Yes ||
+|| `Procedures` || '''procedure_id''' || Yes ||
+|| `ProcedureResults` || '''proc_result_id''' || Yes ||
+|| `PerformedProcedures` || '''performed_id''' || Yes ||
+|| `Prescriptions` || '''prescription_id''' || Yes ||
+|| `PrescriptionRestrictions` || '''restriction_id''' || Yes ||
+|| `LabTests` || '''test_id''' || Yes ||
+|| `LabResults` || '''lab_result_id''' || Yes ||
+|| `PerformedLabTests` || '''performed_test_id''' || Yes ||
+|| `MedicalRecords` || '''record_id''' || Yes ||
+|| `Allergies` || '''allergy_id''', alt. key `allergy_name` || Yes ||
+|| `Symptoms` || '''symptom_id''', alt. key `symptom_name` || Yes ||
+|| `Referrals` || '''referral_id''' || Yes ||
+|| `MedicalReports` || '''report_id''' || Yes ||
+|| `Billing` || '''bill_id''' || Yes ||
+|| `MedicalRecordSymptoms` || '''{record_id, symptom_id}''' || Yes ||
+|| `MedicalRecordAllergies` || '''{record_id, allergy_id}''' || Yes ||
+|| `PrescriptionRecords` || '''{prescription_id, record_id}''' || Yes ||
+
+`p_email` (`patients.email_address`) is left off as an alternate key as it carries a `UNIQUE`
+constraint but is nullable, so it doesn't function as a true candidate key under the
+relational model.
+
+No relation has a non-key attribute determining part of a candidate key without itself being a superkey so the schema **satisfies BCNF**.
+
+----
+
+== 4NF check ==
+
+BCNF only removes anomalies caused by functional dependencies. This domain still has
+the fourteen pure many-to-many pairs listed at the end of the FD section, and none of
+them was involved in any FD above, so BCNF does not evaluate them at all.
+
+Four entities in this schema each sit at the center of more than one independent
+many-to-many relationship at once. That's exactly the situation that produces a
+genuine multivalued dependency. If you tried to store two of those relationships in
+the same table, you'd be forced to repeat every combination of the two, even though
+the two facts have nothing to do with each other.
+
+- A **medical record** can be linked to several diagnoses, several doctors, several
+procedures, and several lab results, and each of those four lists grows and shrinks
+on its own. Adding another diagnosis to a record says nothing about how many doctors,
+procedures, or lab results are attached to that same record.
+
+- A **diagnosis** can be linked to several typical symptoms and several procedures used to
+investigate or treat it. Neither list has any bearing on the other.
+
+- A **procedure** can be linked to several specializations qualified to perform it, several
+departments that perform it, and several bills it appears on. Its link to a diagnosis
+was already covered above and isn't repeated here.
+
+- A **patient** can be linked to several allergies and several symptoms, tracked completely
+separately from one another.
+
+This gives eleven multivalued dependencies:
+
+{{{
+record_id     ->> diagnosis_id
+record_id     ->> doctor_id
+record_id     ->> procedure_id
+record_id     ->> lab_result_id
+
+diagnosis_id  ->> symptom_id
+diagnosis_id  ->> procedure_id
+
+procedure_id  ->> specialization_id
+procedure_id  ->> department_id
+procedure_id  ->> bill_id
+
+patient_id    ->> allergy_id
+patient_id    ->> symptom_id
+}}}
+
+The remaining three pairs, `{test_id, bill_id}`, `{report_id, lab_result_id}`, and
+`{allergy_id, restriction_id}`, are different. Each one is the only many-to-many link
+at its anchor, so there's no competing relationship to collide with. They still need
+their own table, since a plain many-to-many link can never be expressed as a
+functional dependency, but they aren't 4NF violations the way the four groups above
+are.
+
+None of the MVDs above are trivial. In each case, the right side isn't already part
+of the left side, and the left side isn't a key of any table that currently holds
+both sides together. So '''4NF is violated''' until all fourteen pairs, the eleven
+grouped above plus these three standalone ones, each get their own table.
+
+
+----
+
+== MVD check ==
+
+Nothing is actually being split here. These fourteen pairs were already separate,
+attribute only tables back in the FD section, since none of them ever had an extra
+column that would tie them to something else during 2NF. This section just confirms
+that keeping them separate was correct. If any two had been merged that would create redundant, repeated rows. Keeping each pair on its own avoids that.
+
+* {{{DiagnosisMedicalRecords(diagnosis_id, record_id)}}}
+* {{{DoctorMedicalRecords(doctor_id, record_id)}}}
+* {{{MedicalRecordProcedures(record_id, procedure_id)}}}
+* {{{MedicalRecordLabResults(record_id, lab_result_id)}}}
+* {{{PatientAllergies(patient_id, allergy_id)}}}
+* {{{PatientSymptoms(patient_id, symptom_id)}}}
+* {{{DiagnosisSymptoms(diagnosis_id, symptom_id)}}}
+* {{{DiagnosisProcedures(diagnosis_id, procedure_id)}}}
+* {{{SpecializationProcedures(specialization_id, procedure_id)}}}
+* {{{DepartmentProcedures(department_id, procedure_id)}}}
+* {{{BillingProcedures(bill_id, procedure_id)}}}
+* {{{BillingLabTests(bill_id, test_id)}}}
+* {{{MedicalReportLabResults(report_id, lab_result_id)}}}
+* {{{AllergyPrescriptionRestrictions(allergy_id, restriction_id)}}}
+
+'''Lossless join'''
+The general MVD theorem guarantees that for any relation
+containing `X`, `Y`, and other attributes `Z` where `X ->> Y` holds, splitting into
+`(X, Y)` and `(X, Z)` always reconstructs the original without loss. Since none of
+these fourteen pairs was ever combined with a competing multivalued group in any
+table we produced, that theorem is satisfied trivially rather than needing to be
+invoked as an active repair.
+
+'''Dependency preservation''' 
+None of these fourteen relations carries a non-trivial
+FD of its own. Both attributes are needed together just to identify a membership row,
+so there's nothing beyond the membership fact itself that needs preserving.
+
+The schema satisfies '''4NF'''.
+
+* {{{DoctorLevels(level_id, level_name)}}}
+* {{{Specializations(specialization_id, specialization_name)}}}
+* {{{Departments(department_id, department_name)}}}
+* {{{Doctors(doctor_id, d_first_name, d_last_name, d_email, level_id, specialization_id, department_id)}}}
+* {{{Patients(patient_id, p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg)}}}
+* {{{Admin(admin_id, admin_username, admin_name, admin_lastname, admin_email)}}}
+* {{{LabTechnician(technician_id, tech_username, tech_name, tech_lastname, tech_email)}}}
+* {{{Users(user_id, users_username, users_password, users_role, users_first_name, users_last_name, is_active)}}}
+* {{{Appointments(appointment_id, appt_patient_id, appt_doctor_id, appointment_date, appointment_time, appointment_status)}}}
+* {{{Diagnoses(diagnosis_id, diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id)}}}
+* {{{Procedures(procedure_id, procedure_type, procedure_sched_date, procedure_description, procedure_cost, proc_doctor_id, proc_diagnosis_id)}}}
+* {{{ProcedureResults(proc_result_id, proc_result_description, proc_result_date, procedure_id)}}}
+* {{{PerformedProcedures(performed_id, perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes)}}}
+* {{{LabTests(test_id, test_name, test_description, test_cost)}}}
+* {{{LabResults(lab_result_id, lab_result_value, lab_result_date, test_id)}}}
+* {{{PerformedLabTests(performed_test_id, pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes)}}}
+* {{{MedicalRecords(record_id, patient_id)}}}
+* {{{Referrals(referral_id, referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id)}}}
+* {{{MedicalReports(report_id, report_description, report_date, record_id, report_doctor_id)}}}
+* {{{Billing(bill_id, total_cost, payment_status, payment_date, record_id, billing_admin_id)}}}
+* {{{Prescriptions(prescription_id, medication_name)}}}
+* {{{PrescriptionRestrictions(restriction_id, restriction_description, prescription_id)}}}
+* {{{Allergies(allergy_id, allergy_name, allergy_severity)}}}
+* {{{Symptoms(symptom_id, symptom_name, symptom_description)}}}
+* {{{MedicalRecordSymptoms(record_id, symptom_id, record_symptom_severity)}}}
+* {{{MedicalRecordAllergies(record_id, allergy_id, record_allergy_reaction, record_allergy_severity)}}}
+* {{{PrescriptionRecords(prescription_id, record_id, dosage, frequency, duration, prescription_notes)}}}
+* {{{DiagnosisMedicalRecords(diagnosis_id, record_id)}}}
+* {{{DoctorMedicalRecords(doctor_id, record_id)}}}
+* {{{MedicalRecordProcedures(record_id, procedure_id)}}}
+* {{{MedicalRecordLabResults(record_id, lab_result_id)}}}
+* {{{PatientAllergies(patient_id, allergy_id)}}}
+* {{{PatientSymptoms(patient_id, symptom_id)}}}
+* {{{DiagnosisSymptoms(diagnosis_id, symptom_id)}}}
+* {{{DiagnosisProcedures(diagnosis_id, procedure_id)}}}
+* {{{SpecializationProcedures(specialization_id, procedure_id)}}}
+* {{{DepartmentProcedures(department_id, procedure_id)}}}
+* {{{BillingProcedures(bill_id, procedure_id)}}}
+* {{{BillingLabTests(bill_id, test_id)}}}
+* {{{MedicalReportLabResults(report_id, lab_result_id)}}}
+* {{{AllergyPrescriptionRestrictions(allergy_id, restriction_id)}}}
+
+----
+
+== Conclusion ==
+
+Decomposing the de-normalized relation from scratch, following only the formal rules through 1NF, 2NF, 3NF, BCNF, and 4NF, produced the same 41 relations already present in the Phase 2 design — same keys, same columns, same many-to-many tables. The normalization process confirms the same structural design obtained from the ER model in Phase 2.