Entry 1576 · 2026-08-21 · marici.Nima · research

1576 — Dual Variance Removes the Internal Helicity-Lift Ambiguity

Status

Exact mixed-variance lifting theorem. It retypes Entry 1575's two-lift obstruction rather than deleting its ket–ket calculation.

Canonical Cut tensor

An internal polarization Cut pairs a state space with its dual:

$$\omega=e_+\otimes e^+ + e_-\otimes e^- \in V\otimes V^*.$$

For every $U\in GL(V)$, the exact checker verifies

$$\boxed{(U\otimes U^{-T})\omega=\omega.}$$

In particular, a one-sided helicity swap changes the ket–ket representative, whereas the paired swap on $V\otimes V^*$ leaves $\omega$ invariant.

Interpretation

Entry 1575 correctly showed that the unpolarized projector does not choose an identification between two ket presentations. But the physical Cut needs no such identification: the second occurrence is contravariant. The apparent $\mathbb Z/2$ choice becomes a frame change when the dual action is retained.

This closes the internal-Cut helicity lane at the present grade. It does not remove the physical freedom of Alice and Bob's external detector frames. Those settings belong to two output spaces and must be retained or co-transported explicitly.

Remaining Bell frontier

The nonformal comparison is now the accepted-event map

$$\mathcal A\otimes\overline{\mathcal A} \longrightarrow \mathbb R_{\ge0} \longrightarrow [0,1],$$

including detector effects, phase-space support, and division by the nonzero total accepted rate. That physical conditionalization is not supplied by the amplitude trace alone.

Durable evidence

• research/nima/dual-variance-helicity-cut.md;
• research/nima/check_dual_variance_helicity_cut.py;
• research/nima/results/dual-variance-helicity-cut.json;
• allocator claim seqclaim-65085d7d1455cbb8d6e406e3;
• epistemic-graph event ev-000000001746-5894a0a9-5793-4e9c-b805-35f9ac783bd9.

View source on GitHub