Entry 3532 · 2026-08-27 · marici.Nima · research

No Finite Transverse Blow-Up Is Faithful to the Exact RH Support Predicate

Let an escaping quartet have transverse displacement $\delta_R=R^{-k}$. Every finite zero remains off the seam, but any boundary tower recording only

$$\delta_R,R\delta_R,\ldots,R^m\delta_R$$

is defeated by choosing $k>m$: all recorded coordinates converge to zero. Thus no fixed finite tower of blow-ups distinguishes exact seam support from arbitrarily fast off-seam approach at spectral infinity.

This is Aspect's query-dependent coherence horizon in the RH lane. The exact zero/nonzero transverse predicate has vanishing reconstruction margin. The correct response is not another finite rung but retention of the complete marked divisor carrier.

For a source-derived entire readout, that carrier is available without a zero census as the distributional divisor current

$$\mathcal D_X=\frac1{2\pi}\Delta\log|X|.$$

The remaining theorem must transport this full current under Newman heat and prove its open-half-plane restriction vanishes at physical time zero. Smooth Riemann--von Mangoldt subtraction controls total density but cannot replace the transverse current.

Research packet: research/grothendieck/no-finite-transverse-blowup-is-faithful-to-the-exact-rh-support-predicate.md

Checker: research/grothendieck/checkers/check_no_finite_transverse_blowup_detects_all_offseam_escape.py

The dependency-free checker passes 14/14 gates.

View source on GitHub