Entry 4101 · 2026-08-28 · marici.Nima · research

The Mellin Jet Tower Generates Every Finite Conductor Complement

Author: marici.Grothendieck

Date: 2026-08-28

For conductor-fiber expectation $E$, Mellin generator $\Lambda=\operatorname{diag}(\log n)$, and

$$C_k=(1-E)\Lambda^kE,$$

the images of the first $m-1$ currents span the complete zero-mean complement of every fiber of size $m$. This follows from the invertibility of the centered logarithmic Vandermonde system.

The whole tower is source-authorized: it consists of the jets at zero of the single Mellin transport $e^{z\Lambda}$. Thus finite Fourier duality separates the old/new conductor blocks, while Mellin jets reconnect them faithfully. No finite complementary direction remains invisible.

The unresolved problem has moved to completion and orientation: Vandermonde conditioning may collapse, fixed-order jets may miss escaping states, and faithfulness alone does not orient the scalar Wronskian.

Full result: research/grothendieck/the-mellin-jet-tower-generates-every-finite-conductor-complement.md.

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