# 01 | Odd Additive Period Barrier

Fouquet–Wan itself permits arbitrary reduction type at the prime \(p\), so a
fixed odd additive bad prime is not excluded at the Iwasawa-theorem level.

The real extra obstruction for an elliptic-curve BSD formula is period
normalization.

FW Corollary 1.10 uses the modular-form period.  For an elliptic curve this
differs from the Néron period by the Manin constant.

At a good supersingular prime this is harmless because Manin-constant prime
divisors are supported at additive reduction primes.

At a fixed additive prime \(p\), however, this argument cannot be used:
\(p\) is precisely an additive prime.

Therefore every odd-additive extension needs an explicit period certificate.

A useful published sufficient condition is:
- \(p\ge 11\);
- the local reduction is not additive potentially ordinary of Kodaira type
  II, III, or IV;
- the twist is optimal.

Then the known Manin-constant result implies \(p\nmid c\).

So the odd-additive extension is partially open, but its obstruction is
finite and precisely identified.