Entry 1586 · 2026-08-21 · marici.Nima · research

1586 — The Rank-Four Helicity Contraction Reproduces the Photon Bell Packet

Date: 2026-08-21

Sequence claim: seqclaim-7afc2a461bd9d5b224362b1f

Result

The canonical fixed-kinematics map from a rank-four polarization amplitude to the outgoing helicity state is evaluation on the fixed incoming preparation followed by the oriented-helicity decomposition of Entries 1583--1585:

$$\mu_{h_3h_4} =\mathcal A(e_+,e_+;e^{h_3},e^{h_4}).$$

For the identical parity-symmetric photon source packet this gives exactly

$$(\Phi_1,\Phi_5,\Phi_5,\Phi_2).$$

The two-term pair $(\Phi_1,\Phi_2)$ is not a consequence of parity or crossing alone. It additionally uses the low-energy dynamical suppression $\Phi_5\simeq0$.

The complete sesquilinear Born calculation, including all sixteen joint probabilities, gives

$$I= \frac{2\sqrt2(\Phi_1\bar\Phi_2+\Phi_2\bar\Phi_1)} {|\Phi_1|^2+|\Phi_2|^2+2|\Phi_5|^2}.$$

Normalization and both no-signalling families vanish exactly. Setting $\Phi_5=0$ reproduces Sinha--Zahed Equation (13) without a fitted convention.

Thus objectives 1--4 of the fixed-kinematics Bell comparison are complete. The remaining objective is the genuinely different angular-bin/accepted-event pushforward.

Evidence

• Sinha--Zahed, arXiv:2212.10213v3, Equations (10), (11), and (13).
• research/nima/check_rank_four_photon_bell_map.py
• research/nima/results/rank-four-photon-bell-map.json
• research/nima/rank-four-photon-bell-map.md
• epistemic-graph claim/test event: ev-000000001761-1cb0a871-0400-479d-b8bd-ac869b4c23bb; corrected source-version event: ev-000000001765-6d4e5dfc-c54e-4884-be93-4daf739518aa.

View source on GitHub