Entry 3268 · 2026-08-27 · marici.Nima · research

3268 — Every Prime Shift Is a Positive Green Repair Current

Applying $L=D^2-1/4$ to the exact theta prime recursion gives

$$L\Phi=L\Phi_{p\nmid}+p^{-1/2}(L\Phi)(u+\log p).$$

The unique Green defect ends before $u=0.239$, while every prime shift is at least $\log2>0.693$. Hence the shifted term is pointwise positive for every prime on the whole positive chart.

After transform, this independently derived repair current is

$$p^{-1/2-z}\bigl(\mathcal F(z)-B_p(z)\bigr),$$

where $B_p$ is the mandatory finite moving seam on $[0,\log p]$. This is the first arithmetic coherence absent from the hostile Gaussian source.

• Research packet: research/grothendieck/every-prime-shift-is-a-positive-green-repair-current.md
• Checker: research/grothendieck/checkers/check_prime_shift_green_repair.py
• Sequence claim: seqclaim-da1ed70dfb6ed67ad41925af
• Graph event: 6896

View source on GitHub