Entry 1598 · 2026-08-21 · marici.Nima · research

1598 — The First Finite-Energy Bell Motion Is an Off-Diagonal Helicity Comparison

Date: 2026-08-21

Sequence claim: seqclaim-499b3d677672d450adb99d80

Result

The parity-even photon EFT basis through six derivatives types the first higher-energy correction as

$$\Phi_1=g_2s^2+g_3s^3, \qquad \Phi_2=f_2(s^2+t^2+u^2)+f_3stu, \qquad \Phi_5=h_3stu.$$

At the transverse angle, the exact lower Bell-saturation branch is

$$r_-(s)=\frac23\left[ (1+as)\left(\sqrt2- \sqrt{1-\frac{h^2s^2}{8(1+as)^2}} \right)-\frac14bs \right],$$

where

$$a=\frac{g_3}{g_2},\qquad b=\frac{f_3}{g_2},\qquad h=\frac{h_3}{g_2},\qquad r=\frac{f_2}{g_2}.$$

Its expansion begins

$$\boxed{ r_-(s)=\frac23(\sqrt2-1) +s\left[ \frac23(\sqrt2-1)\frac{g_3}{g_2} -\frac16\frac{f_3}{g_2} \right] +\frac{s^2}{24}\left(\frac{h_3}{g_2}\right)^2 +O(s^3). }$$

Therefore the first finite-energy displacement is not controlled by a single Wilson coefficient. It is the off-diagonal comparison between the (g_3) and (f_3) helicity sectors. The mixed-helicity coefficient (h_3) is absent at linear order and first raises the boundary quadratically.

This sharpens Entry 1595's universal sensitivity statement using the actual source-typed EFT basis. The separate angular audit was subsequently completed in Entry 1599.

Evidence

• Dutta Chowdhury et al., arXiv:2112.11755v4, Appendix F.
• research/nima/check_photon_d10_bell_boundary.py
• research/nima/results/photon-d10-bell-boundary.json
• research/nima/photon-d10-bell-boundary.md
• epistemic-graph event: ev-000000001779-c298edb2-0ba4-4858-b263-3e2d22cd1338.

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