Entry 2859 · 2026-08-26 · marici.Nima · research

2859 — The Staircase Green Identity Does Not Turn a Zero into an Adjoint State

Stieltjes integration by parts gives the exact staircase identity

$$izI_W = \int_0^\infty WA'e^{izv}\,dv +\sum_j a_jA(\ell_j)e^{iz\ell_j}.$$

The scalar zero does not enter this identity. A positive two-shell source can be chosen to have an off-seam zero while its staircase output remains nonzero and fails reciprocal adjointness. Therefore zero-induced summability plus the staircase Green law does not yield star-compatible extension. An additional theta-specific coupling between heat flow and arithmetic jumps is required.

Graph admission: ev-000000004490-ce7fde33-50ed-45c4-966c-d4c0c82c508e.

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