Latvian registracijas numurs

What it covers

Returns a valid Latvian registracijas numurs (legal-entity registration number) satisfying the official weighted-sum validity rule. Use `format` for the LV VAT number. Set `invalid=true` for a number with a deliberately broken validity rule.

How it’s calculated

A Latvian legal-entity registration number is valid when the position-weighted sum of all 11 digits is congruent to 3 modulo 11; the last digit acts as the check digit that forces this residue.

First 10 digits d1..d10 = 4 0 0 0 3 0 0 3 0 3; weights w1..w10 = 9 1 4 8 3 10 2 5 7 6.
Products: 9×4=36, 1×0=0, 4×0=0, 8×0=0, 3×3=9, 10×0=0, 2×0=0, 5×3=15, 7×0=0, 6×3=18.
Partial sum P = 36+0+0+0+9+0+0+15+0+18 = 78. P mod 11 = 1 (78 = 7×11 + 1).
Need (P + w11×d11) mod 11 == 3 with w11 = 1, so (78 + d11) mod 11 == 3, i.e. d11 = ((3 − 1) mod 11) = 2.
Check: total S = 78 + 1×2 = 80; 80 mod 11 = 3 (80 = 7×11 + 3). Rule satisfied.

Edge cases

• A valid number ending in 0 (zero-tail) is explicitly generated as an edge case — d11 = 0 is legitimate whenever the partial sum P already satisfies P mod 11 == 3.
• Legal-entity numbers must begin with 4 or 5 (LEGAL_ENTITY_LEADS); the generator forces d1 into {4,5}, and edge mode can force either lead individually.

Gotchas

• The scheme has no dedicated check-digit derivation step in the source. The generator draws all ten free digits and keeps the candidate only if the whole 11-digit weighted sum ≡ 3 (mod 11); it does not solve for the last digit. Because the last weight is 1, the last digit nonetheless functions as the effective check digit.
• The target residue is 3, not 0 — a common mistake is assuming Σ·w mod 11 == 0. Here validity means S mod 11 == 3.
• When the required last digit would be 10 (no single decimal digit), that payload is simply unusable and the loop redraws — so not every arbitrary 10-digit prefix can be completed to a valid number.