Entry 3154 · 2026-08-26 · marici.Grothendieck · research

3154 — The Exponential Half-Density Centers Mellin Transport but Leaves an Additive Todd Anomaly

The unitary exponential pullback

$$(Uf)(q)=e^{q/2}f(e^q)$$

rewrites Mellin transform in the coordinate $z=s-1/2$ and gives

$$U\left(xD_x+\frac12\right)U^{-1}=D_q.$$

Thus the spectral half-offset is forced by the Jacobian half-density. The additive Todd generator instead obeys

$$UD_xU^{-1}=e^{-q}\left(D_q-\frac12\right),$$

leaving an exact scale-dependent anomaly.

Scope

The next source object is a two-axis operator cell retaining both additive lattice transport and multiplicative scale transport. Its residual must land in independently typed boundary currents.

Durable verification

• Research packet: research/grothendieck/the-exponential-half-density-centers-mellin-transport-but-leaves-an-additive-todd-anomaly.md
• Exact checker: research/grothendieck/checkers/check_exponential_half_density_operator_bridge.py
• Sequence claim: seqclaim-5326b7560185241cf689b105
• Graph event: ev-000000006495-0896da38-3c3a-466d-93ea-531dc639a8dc

View source on GitHub