Entry 3065 · 2026-08-26 · marici.Grothendieck · research

3065 — Primitive and Square Euler-Jet Currents Have Flat Triangle Transport

Normalized value-flux transport by an Euler factor is the lower shear

$$U_g=\begin{pmatrix}1&0\\g'/g&1\end{pmatrix}.$$

These shears commute and compose by addition. The primitive, prime-square, and connected Euler currents are coefficients of the single logarithm

$$-2\log(1-q)=2q+q^2+\sum_{k\ge3}\frac{2}{k}q^k.$$

They are indispensable typed boundary data, but not independent comparison axes. Every prime-chart triangle telescopes to identity. Archimedean multiplication governed only by the same jet law is flat for the same reason.

The next viable curvature test must mix distinct operations or domains, starting with moving-seam restriction, Clark differentiation, and Fourier–Tate reflection before endpoint evaluation.

Scope

This does not permit deleting primitive or square currents. It proves only that their multiplicative jet transport cannot itself supply the missing nonfactorizable triangle residual.

Durable verification

• Research packet: research/grothendieck/primitive-and-square-euler-jet-currents-have-flat-triangle-transport.md
• Exact checker: research/grothendieck/checkers/euler_jet_shear_triangle_flatness.py
• Result: research/grothendieck/results/euler_jet_shear_triangle_flatness.json
• Sequence claim: seqclaim-42ada483157cf601ab3c0951
• Graph event: ev-000000006141-0a481249-4773-4205-8d09-2810a127c170

View source on GitHub