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A Self-Validating 12-Digit Identifier System

Complete Specification: Structure, Classification Tables, Parity Logic & Checksum

1. Identifier Structure

Every identifier in this system is exactly 12 digits: D₁D₂D₃D₄D₅D₆D₇D₈D₉D₁₀D₁₁D₁₂

┌──────────┬───────────────┬────────────┬─────────────┐
│ D₁–D₆    │ D₇–D₈        │ D₉–D₁₁    │ D₁₂         │
│ Date      │ Region Code   │ Sequence   │ Check Digit │
│ YYMMDD    │ 2-digit index │ 000–999    │ Computed    │
└──────────┴───────────────┴────────────┴─────────────┘

2. Field Breakdown — Example: 900523075049

9 0 | 0 5 | 2 3 | 0 7 | 5 0 4 | 9
 YY   MM    DD    RC    SEQ    CHK
Field Digits Value Meaning
Year (YY) D₁D₂ 90 Year component (last 2 digits)
Month (MM) D₃D₄ 05 5th month
Day (DD) D₅D₆ 23 23rd day
Region Code (RC) D₇D₈ 07 Region index 07 (see lookup table)
Sequence (SEQ) D₉D₁₀D₁₁ 504 504th assignment for this date+region
Check Digit (CHK) D₁₂ 9 Computed checksum + parity classifier

3. Century Disambiguation

The year field YY only provides two digits. The century is determined by the first digit of the sequence field (D₉):

D₉ Value Century Full Year Formula Example
0, 1, 2, 3, 4 2000s 2000 + YY YY=05, D₉=0 → 2005
5, 6, 7, 8, 9 1900s 1900 + YY YY=90, D₉=5 → 1990

For our example: D₉ = 5 ≥ 5 → 1900s → Full year = 1900 + 90 = 1990

Complete date: 1990-05-23

4. Region Code Lookup Table (D₇–D₈)

4.1 Primary Codes (01–16)

Code Region
01 Region Alpha
02 Region Bravo
03 Region Charlie
04 Region Delta
05 Region Echo
06 Region Foxtrot
07 Region Golf
08 Region Hotel
09 Region India
10 Region Juliet
11 Region Kilo
12 Region Lima
13 Region Mike
14 Region November
15 Region Oscar
16 Region Papa

4.2 Legacy / Alternate Codes (21–59)

Some regions have multiple codes due to historical sub-division:

Code Range Maps To
21–24 Region Alpha
25–27 Region Bravo
28–29 Region Charlie
30 Region Delta
31, 59 Region Echo
32–33 Region Foxtrot
34–35 Region Golf
36–39 Region Hotel
40 Region India
41–44 Region Juliet
45–46 Region Kilo
47–49 Region Lima
50–53 Region Mike
54–57 Region November
58 Region Oscar

4.3 External / Foreign Codes (60–99)

Code Classification
60 External Zone A
61 External Zone B
62 External Zone C
63 External Zone D
64 External Zone E
65 External Zone F
66 External Zone G
67 External Zone H
68 External Zone I
71–72 Legacy external (pre-2001 assignments)
74 External Zone J
75 External Zone K
76 External Zone L
77 External Zone M
78 External Zone N
79 External Zone O
82 Unclassified
83 Asia-Pacific group
84 South American group
85 African group
86 European group
87 British-Irish group
88 Middle Eastern group
89 Far Eastern group
90 Caribbean group
91 North American group
92 Eastern European / Post-Soviet group
93 Miscellaneous / Other
98 Unaffiliated entity
99 Unspecified / Special case

For our example: D₇D₈ = 07 → Region Golf

5. Parity Classification (D₁₂)

The check digit simultaneously serves as a binary classifier:

D₁₂ Parity Classification Digit Values
Odd Class A 1, 3, 5, 7, 9
Even Class B 0, 2, 4, 6, 8

The assigning system does not freely choose D₁₂. It iterates through sequences (D₉D₁₀D₁₁) until the computed check digit's parity matches the desired classification.

For our example: D₁₂ = 9 → Odd → Class A

6. Sequence Assignment Logic

The system assigns identifiers using this algorithm:

INPUT:  date (YYMMDD), region (RC), desired class (A or B)

FOR seq = 000 to 999:
    candidate = YYMMDD + RC + seq (11 digits)
    C = compute_checksum(candidate)

    IF C = 10:
        SKIP (no single-digit representation)

    ELSE IF C is odd AND desired class is A:
        ASSIGN → identifier = candidate + C
        STOP

    ELSE IF C is even AND desired class is B:
        ASSIGN → identifier = candidate + C
        STOP

    ELSE:
        SKIP (parity mismatch)

What this means in practice:

  • ~9.1% of sequences are impossible (C = 10)
  • ~45.5% of sequences yield odd check digits (Class A)
  • ~45.5% of sequences yield even check digits (Class B)
  • The system never "picks" the last digit — it is always computed

7. Checksum Algorithm (ISO 7064 Mod 11,2)

7.1 Weight Function

W(i) = 2^(i-1) mod 11    for i = 2, 3, ..., 12

Constant values:

W(2)=2  W(3)=4  W(4)=8  W(5)=5  W(6)=10  W(7)=9
W(8)=7  W(9)=3  W(10)=6  W(11)=1  W(12)=2

7.2 Formula

Given:  S = D₁D₂D₃D₄D₅D₆D₇D₈D₉D₁₀D₁₁
Let:    R = reverse(S)

Σ = Σⱼ₌₀¹⁰  R[j] × W(j+2)

C = (12 - (Σ mod 11)) mod 11

Valid iff:  C = D₁₂  ∧  C ∈ {0,1,...,9}

7.3 Edge Cases

Condition Result
C ∈ {0–9} Valid check digit, assign normally
C = 10 Impossible sequence, skip entirely
(12 - remainder) = 11 Wraps to 0 via mod 11
(12 - remainder) = 12 Wraps to 1 via mod 11

8. Worked Example — Full Computation

Identifier: 900523075049

Step 1 — Extract first 11 digits and reverse:

S = [9, 0, 0, 5, 2, 3, 0, 7, 5, 0, 4]
R = [4, 0, 5, 7, 0, 3, 2, 5, 0, 0, 9]

Step 2 — Multiply each reversed digit by its weight:

R[0]  × W(2)  =  4 × 2  = 8
R[1]  × W(3)  =  0 × 4  = 0
R[2]  × W(4)  =  5 × 8  = 40
R[3]  × W(5)  =  7 × 5  = 35
R[4]  × W(6)  =  0 × 10 = 0
R[5]  × W(7)  =  3 × 9  = 27
R[6]  × W(8)  =  2 × 7  = 14
R[7]  × W(9)  =  5 × 3  = 15
R[8]  × W(10) =  0 × 6  = 0
R[9]  × W(11) =  0 × 1  = 0
R[10] × W(12) =  9 × 2  = 18

Step 3 — Sum all products:

Σ = 8 + 0 + 40 + 35 + 0 + 27 + 14 + 15 + 0 + 0 + 18 = 157

Step 4 — Modular reduction:

Σ mod 11 = 157 mod 11 = 3

(Verification: 14 × 11 = 154,  157 - 154 = 3)

Step 5 — Compute check digit:

C = (12 - 3) mod 11
C = 9 mod 11
C = 9

Step 6 — Validate:

Computed:  C   = 9
Actual:    D₁₂ = 9
Match:     9 = 9  ✓

Parity:    9 is odd → Class A  ✓

9. Complete Decoded Summary

Identifier:      900523075049
                  ┌──┬──┬──┬──┬───┬─┐
                  │90│05│23│07│504│9│
                  └──┴──┴──┴──┴───┴─┘
                   YY MM DD RC SEQ CHK

Date:             1990-05-23  (D₉=5 ≥ 5 → 1900s)
Region:           07 → Region Golf
Sequence:         504
Check Digit:      9 (computed, verified ✓)
Classification:   Class A (odd)
Checksum Valid:   YES

10. System Properties

Property Description
Error detection Any single-digit error in D₁–D₁₁ causes checksum mismatch
Dual-purpose D₁₂ Simultaneously encodes binary classification and integrity check
Impossible sequences ~9.1% of sequences yield C=10, are permanently excluded
Parity-balanced ~50/50 split between Class A and Class B assignments
Base Modular arithmetic over Z₁₁
Standard ISO 7064 Mod 11,2
Self-validating Any recipient can verify integrity with just the 12 digits — no external lookup required

This is a complete, self-contained specification for a structured numeric identifier system with embedded date encoding, regional classification, binary parity assignment, and weighted modular checksum validation.