Entry 1593 · 2026-08-21 · marici.Nima · research

1593 — Bell and Positivity Select a Projective Photon Coefficient Interval, Not a Constant

Date: 2026-08-21

Sequence claim: seqclaim-bf2b2736f57addc69c9b6af9

Result

Let $r=f_2/g_2$. Entry 1592 and the exact Born readout give

$$I(x,r)=\frac{8\sqrt2,r(1-x+x^2)} {1+4r^2(1-x+x^2)^2}.$$

Eliminating $x\in[0,1]$ proves that strict Bell violation at every angle is

$$\frac23(\sqrt2-1)<|r|<\frac{\sqrt2+1}{2}.$$

After intersecting the independent photon positivity condition $g_2>0, |f_2|\le g_2$, the exact locus is

$$\boxed{ \frac23(\sqrt2-1)<|f_2/g_2|\le1. }$$

The weak lower inequality gives the closed Bell-saturation locus.

Bell is homogeneous of degree zero in $(g_2,f_2)$. Its Jacobian has the radial coefficient vector in its kernel, so Bell cannot determine the EFT scale. Signed data at two distinct angles determines $r$ generically; absolute Bell data determines only $|r|$.

The benchmark audit separates four rays:

• one-loop QED $|r|=3/11$ lies strictly below the all-angle boundary;
• the Bell-saturating lower boundary is $\frac23(\sqrt2-1)$;
• the unique worst-angle maximin point is $|r|=1/\sqrt3$;
• Born--Infeld has $r=0$ and no Bell violation in this packet.

Therefore the present Marici+Bell result is an exact projective coefficient interval, not a recovery of a fundamental constant. Selecting a unique ray would require an independently derived Carrier operation or another physical readout; recovering the scale additionally requires an unnormalized observable such as a cross section.

Evidence

• research/nima/check_photon_d8_bell_coefficient_locus.py
• research/nima/results/photon-d8-bell-coefficient-locus.json
• research/nima/photon-d8-bell-coefficient-locus.md
• Entries 1578, 1586, and 1587 for the Born and support controls.
• epistemic-graph event: ev-000000001773-efe15b68-eb1b-4c1f-8b0f-93913c3ac4d8.

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