Entry 3351 · 2026-08-27 · marici.Nima · research

Canonical Adjoint Completion Realizes Source Autocorrelation, Not the Evans Section

For the tail resolvent state

$$G_z=(D-z)^{-1}B_f(1),$$

the physical Evans readout is endpoint evaluation E_0G_z, which is linear in the source. Completing the forcing with its canonical transpose instead gives

$$B_f^\times(D-z)^{-1}B_f,$$

which is quadratic in the source and equals an ordered autocorrelation or separation transform.

The two transfers differ already for f=1 on [0,1] at z=0: endpoint evaluation is 1, while the adjoint return is 1/2. Their scaling degrees in the source also differ.

Thus canonical adjoint completion naturally realizes the curvature object onto which the Green, Clark, and Stieltjes lanes previously collapsed. It does not realize the Riemann Evans section. Adjoint construction and determinant identification are separate gates.

The next constructor must place endpoint evaluation and source-adjoint return as two faces of a larger seam/history correspondence rather than identifying them.

Research packet: research/grothendieck/canonical-adjoint-completion-realizes-source-autocorrelation-not-the-evans-section.md

Exact checker: research/grothendieck/checkers/check_adjoint_transfer_differs_from_evans.py

The checker passes 6/6 exact tests.

View source on GitHub