Entry 3178 · 2026-08-27 · marici.Grothendieck · research

3178 — RH Is One Projective Antipode Exclusion, Not Full de Branges Separation

The nonnull half-line pair defines

$$\mathcal R(z)=[H(z):H(-z)]\in\mathbb{CP}^1,$$

and

$$X(z)=0 \quad\Longleftrightarrow\quad \mathcal R(z)=[1:-1].$$

RH therefore asks that the inverse image of one projective point lie on the seam. De Branges magnitude separation excludes the entire unit circle in the ratio chart and is strictly stronger.

Scope

The minimal source theorem may permit off-seam unit-circle crossings away from the antipode. Coercivity, cone, and full magnitude-ordering programmes must not be treated as necessary formulations of RH.

Durable verification

• Research packet: research/grothendieck/rh-is-one-projective-antipode-exclusion-not-full-de-branges-separation.md
• Structural checker: research/grothendieck/checkers/check_projective_antipode_vs_unit_circle.py
• Sequence claim: seqclaim-df4f3803889c8a7ddf7069b5
• Graph event: ev-000000006581-0a8a7743-2e90-4639-a1cd-7a5d82f14c90

View source on GitHub